(Front Cover) BULLETIN OF STATE TEACHERS COLLEGE KIRKSVILLE, MISSOURI VOL. XXIV AUGUST-SEPTEMBER, 1924 Nos. 8-9 PUBLISHED MONTHLY Entered as second class mail matter April 29, 1915, at the post office at Kirksville, Missouri, under the Act of Congress of August 24, 1912. Accepted for mailing at special rate of postage provided for in section 1103, Act of October 3, 1917, authorized July 26, 1919. JOURNAL PRINTING COMPANY KIRKSVILLE, MISSOURI (Page 2) INTRODUCTORY NOTE For some years the State Teachers College at Kirksville has encouraged its faculty members to prepare monthly bulletins appertaining to the subject matter of their several specialties. The purpose is to encourage habits of research. We find thereby that the spirit of investigation characterizes more and more the mental movements of the faculty. We find, also, relief from the monotony of personal repetitions and the deadening trend which sometimes leads to well worn grooves in consciousness. Observing ones are well aware of the fact that the alert and promising students among us are selecting their colleges and their teachers inside the colleges on the basis of productive scholarship and the individual initiative of the faculty men and women. Each new bulletin issued by a growing faculty member or group is an evident stimulus to all the wakeful faculty members. This volume on “The Relation of Extra-mural Study to Residence Enrolment and Scholastic Standing" represents many months of research by Dean Wm. H. Zeigel, Chairman of the Department of Mathematics. It comprises his dissertation for the Ph. D. degree. It is especially gratifying to me because it points to high attainment in scholarship by a long time associate. JOHN R. KIRK, President. State Teachers College Kirksville, Missouri August, 1924 (Page 3) THE RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT AND SCHOLASTIC STANDING BY WILLIAM HENRY ZEIGEL, PH. D. GEORGE PEABODY COLLEGE FOR TEACHERS CONTRIBUTION TO EDUCATION NUMBER TWELVE PUBLISHED UNDER THE DIRECTION OF GEORGE PEABODY COLLEGE FOR TEACHERS NASHVILLE, TENN. 1924 (Page 4) ACKNOWLEDGMENTS This study was undertaken at the suggestion of Dr. Shelton Phelps of George Peabody College for Teachers. His constructive criticism has been invaluable. The writer is also under obligation to the presidents of the teachers colleges of Missouri and to the President of the Teachers College at Macomb, Illinois, for access to data and files of information which were absolutely necessary for a worth while study. Members of faculties in these schools were accommodating and in many cases helped personally in the collection of valuable data. Dr. John R. Kirk, President of the Teachers College at Kirksville, has looked with favor upon this study and has lent encouragement and help in many ways. My son, William, gave generous assistance in collecting and tabulating data and in making numerous computations. The writer is also indebted to Miss T. Jennie Green and Mrs. Wilhelmina Burk, colleagues in the State Teachers College, who read manuscript, and to Mrs. Jo Walker Humphrey, Dean of Women, who read galley and page proof. To all these and many others grateful acknowledgment is made. W. H. Z. State Teachers College Kirksville, Missouri August, 1924 (Page 5) CONTENTS PART ONE THE RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT CHAPTER I Methods of Investigation Section Page I. TYPE OF DATA..............................13 II. TYPES OF CORRELATION AND REGRESSION.........13 III. CORRELATION RATIO..........................15 IV. A NEW METHOD OF DETERMINING CORRELATION.....16 1. Explanation of method 2. New method applied to concrete problems V. ANOTHER NEW METHOD OF DETERMINING CORRELATION...24 1. Explanation of method 2. Application of method VI. TETRACHORIC FUNCTIONS.................28 1. Explanation of method 2. Application of method VII. MEAN SQUARE CONTINGENCY...............30 1. Explanation of method 2. Application of method 3. Interpretations VIII. FORMULAE USED FREQUENTLY IN THIS STUDY....35 CHAPTER II CONSENSUS OF OPINION CONCERNING EXTRA-MURAL STUDY I. PURPOSES OF EXTRA-MURAL STUDY.............36 1. As stated in bulletins 2. As given in a master's thesis 3. As shown in Kirksville questionnaire II. RELATIONS AND COMPARISONS EXPRESSED THROUGH QUESTIONNAIRE..................................40 1. Tabulation of replies 2. Interpretation and conclusions III. TIME REQUIRED OF TEACHER FOR A TERM HOUR OF CREDIT.........................................41 IV. EXTRA-MURAL STUDENTS IN TERMS OF RESIDENCE STUDENTS.......................................42 V. THE RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT......................................42 VI. SUMMARY AND CONCLUSIONS.....................44 (Page 6) 6 CONTENTS CHAPTER III RELATION BETWEEN RESIDENCE, CORRESPONDENCE, AND EXTENSION ENROLMENTS I. MATERIAL USED..........................45 II. METHOD OF TREATMENT......................45 1. Notation 2. Consistency 3. Association formulae III. ASSOCIATION BETWEEN TYPES OF ENROLMENT...48 1. Complete association 2. Partial association IV. SUMMARY AND CONCLUSIONS..................51 CHAPTER IV INFLUENCE OF EXTRA-MURAL STUDY ON RESIDENCE ENROLMENT I. WHOLE UNIVERSE OF STUDENTS, (1919-1920)....53 1. Description of universe 2. Relation between type of student and first enrolment 3. Comparisons II. UNIVERSE OF STUDENTS WHO HAD BOTH RESIDENCE AND EXTRA-MURAL STUDY, (1919-1920)...........56 1. Relation between residence enrolments and first enrolments 2. Observations III. UNIVERSE OF PUBLIC SCHOOL TEACHERS OF NORTHEAST MISSOURI, (1921-1922)...................58 1. Description of universe 2. Factors affecting residence enrolment 3. Data and notation 4. Association between type of study and first enrolment 5. Summary and comparisons 6. Intensity of associations IV. COMPARISONS OF RATIOS......................65 V. CORRELATION BETWEEN RESIDENCE STUDY AND FIRST ENROLMENT IN EXTRA-MURAL STUDY—UNIVERSE OF TEACHERS......66 VI. SUMMARY AND CONCLUSIONS....................66 CHAPTER V THE UNIVERSE OF HIGH SCHOOL GRADUATES AS A BASIS OF COMPARISON I. NEED OF A STANDARD..........................67 II. HIGH SCHOOL VISITATION.....................67 (Page 7) CONTENTS 7 III. RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION.............................68 1. Need for knowing the relationship 2. School preference, alternate variate 3. School registration, alternate variate 4. Strength of school preference 5. Conclusion IV. TIME BETWEEN HIGH SCHOOL GRADUATION AND COLLEGE REGISTRATION........................72 1. Preliminary statement 2. Registration by quarters V. SUMMARY AND CONCLUSIONS................77 CHAPTER VI EXTRA-MURAL STUDENTS AS PROSPECTIVE COLLEGE STUDENTS I. THE SCOPE OF STUDY EXTENDED.........78 II. THE MISSOURI STATE TEACHERS COLLEGES.....78 1. Universe of extra-mural students with residence study. 2. Whole universe of extra-mural students 3. Observations and comparisons 4. Other methods for determining relationship 5. Summary III. WESTERN ILLINOIS STATE TEACHERS COLLEGE, MACOMB, ILLINOIS...........................85 1. Introductory statement 2. Universe of extra-mural students with residence study 3. Whole universe of extra-mural students 4. Discussion of results IV. MACOMB COMPARED WITH TEACHERS COLLEGES OF MISSOURI.................................87 1. Observations and comparisons 2. Universe of extra-mural students with extra-mural study first V. COMPARISON WITH A STANDARD.............89 1. Another new universe 2. Standards used VI. SUMMARY AND CONCLUSIONS...............93 CHAPTER VII RELATION BETWEEN TYPES OF STUDY AND ORDER OF ENROLMENT I. PROBLEM AND PLAN OF APPROACH.......95 II. METHOD OF TREATMENT...................95 1. Data treated by mean square contingency 2. Data treated by Pearson’s new method of correlation III. SUMMARY AND CONCLUSIONS.............106 (Page 8) 8 CONTENTS CHAPTER VIII COLLEGE GRADUATES AND EXTRA-MURAL STUDY I. NUMBER AND ORDER OF ENROLMENT OF STUDENTS RECEIVING BACHELOR’S DEGREE...............108 1. Introductory statement 2. Tabulations by schools arid years 3. Summary II. OTHER METHODS OF ANALYSIS..............112 1. Type of study and order of enrolment 2. Strength of association 3. Interpretation's and comparisons III. SUMMARY AND CONCLUSIONS...............114 CHAPTER IX VIEWS OF STUDENTS AS, TO INFLUENCES THAT LED TO RESIDENCE ENROLMENT I. QUESTIONNAIRES AS TO REASONS FOR ENROLLING IN RESIDENCE.................................116 1. First questionnaire 2. Second questionnaire II. A METHOD DEVISED FOR DEALING WITH MATERIAL...121 1. General survey of material 2. Strength of influence defined 3. Orders of influence 4. Determination of weights of orders of influence 5. Total strength of influence determined III. COMPLETE TABULATIONS OF DATA.........124 1. Tables—year, 1923 2. Comments IV. RELIABILITY OF NEW METHOD TESTED......131 1. Position of column of weighted means 2. Coefficients of correlation between columns 3. Reliability of column of weighted means V. FINAL EXPRESSION FOR STRENGTH OF INFLUENCE....133 1. Tabulation of columns of weighted means 2. Interpretations and comparisons VI. SUMMARY AND CONCLUSIONS................135 PART TWO THE RELATION OF EXTRA-MURAL STUDY TO SCHOLASTIC STANDING CHAPTER I GRADES IN DIFFERENT TYPES OF STUDY I. INTRODUCTORY STATEMENT................136 II. THE GRADING SYSTEM.....................136 1. Plan of grading at Kirksville 2. The system justified 3. Grades that were studied (Page 9) CONTENTS 9 III. COMPARISON OF GRADES AT KIRKSVILLE.............140 1. Residence and correspondence grades, residence-correspondence universe 2. Residence and extension grades, residence-extension universe 3. Residence, correspondence, and extension grades—whole universe of each 4. Residence and extra-mural grades—each universe excluding the other 5. Residence grades of extra-mural students and grades of students with residence study only IV. COMPARISON OF GRADES AT MACOMB, ILLINOIS............151 1. General statement 2. Residence and extension grades V. SUMMARY AND CONCLUSIONS..............................153 1. Summary of facts relative to grades at Kirksville 2. Conclusions CHAPTER II RELATION OF GRADES TO AGE AND ADVANCEMENT I. INTRODUCTORY statement............................156 II. ADVANCEMENT AND GRADES..............................156 1. Students with both residence and correspondence study 2. Students with both residence and extension study 3. Students with residence study only 4. Summary III. AGE AND GRADES.....................................159 1. Students with both residence and correspondence study 2. Students with both residence and extension study 3. Students with both residence and extra-mural study 4. Students with residence study only 5. Summary IV. SUMMARY AND CONCLUSIONS FOR THE CHAPTER.............171 CHAPTER III RELATION OF HEALTH TO NUMBER OF STUDIES, GRADES, AND TYPE OF STUDY I. INTRODUCTORY STATEMENT............................173 II. HEALTH AND NUMBER OF RESIDENCE STUDIES..............173 1. Students with residence study only 2. Students with both residence and extra-mural study (Page 10) 10 CONTENTS III. HEALTH AND NUMBER OF EXTRA-MURAL STUDIES.......175 1. Relations involved 2. Interpretations IV. HEALTH AND RESIDENCE GRADES........................176 1. Students with residence study only 2. Students with both residence and extra-mural study V. HEALTH AND EXTRA-MURAL GRADES........................178 1. Relations involved 2. Interpretations VI. HEALTH AND TYPE OF STUDY............................178 1. Relations involved 2. Interpretations VII. SUMMARY AND CONCLUSIONS...........................179 CHAPTER IV RELATION BETWEEN MENTAL ABILITY, AGE, ADVANCEMENT, GRADES, AND TYPE OF STUDY I. INTRODUCTORY STATEMENT............................181 II. MENTAL STABILITY AND AGE.............................181 1. Students with both residence and extra-mural study 2. Students with residence study only 3. Conclusions III. MENTAL ABILITY AND ADVANCEMENT....................185 1. Students with both residence and extra-mural study 2. Students with residence study only 3. Conclusions IV. MENTAL ABILITY AND RESIDENCE GRADES................187 1. Students with both residence and extra-mural study 2. Students with residence study only 3. Conclusions V. MENTAL ABILITY AND TYPE OF STUDY.....................187 1. Relations involved 2. Comparisons VI. SUMMARY AND CONCLUSIONS............................192 CHAPTER V FACTORS THAT ACCOUNT FOR HIGH GRADES I. COMPARISONS OF GRADES IN DIFFERENT TYPES OF STUDY.................................................194 II. COMPARISONS OF RESIDENCE GRADES FOR DIFFERENT TYPES OF STUDENTS.....................................194 III. INFLUENCE OF AGE AND ADVANCEMENT ON RESIDENCE GRADES..........................................195 IV. SUMMARY AND CONCLUSIONS...........................195 (Page 11) CONTENTS 11 CHAPTER VI RELATIONS INVOLVING NUMBER OF STUDIES, ORDER OF ENROLMENT, AND GRADES I. STATEMENT OF QUESTION AT ISSUE.......................197 II. RELATION BETWEEN NUMBER OF RESIDENCE AND NUMBER OF EXTRA-MURAL STUDIES.............................198 1. Kirksville 2. Warrensburg and Springfield 3. Conclusions III. ORDER OF ENROLMENT AND NUMBER OF RESIDENCE STUDIES...................................................198 1. Kirksville 2. Warrensburg 3. Springfield 4. Macomb, Illinois 5. Conclusions IV. ORDER OF ENROLMENT AND NUMBER OF EXTRA-MURAL STUDIES....206 1. Statement of problem 2. Universe of extra-mural students 3. Conclusions V. ORDER OF ENROLMENT AND RESIDENCE GRADES..................209 1. Statement of problem 2. Universe of extra-mural students with residence study 3. Conclusions VI. RELATION BETWEEN EXTRA-MURAL STUDY AND THE NUMBER OF SEMESTER HOURS COMPLETED IN RESIDENCE............210 1. Amount of residence credit completed, when advancement and time at which residence study began are not taken into account 2. Amount of residence credit completed, when advancement and time at which residence study began are taken into account 3. Conclusions VII. SUMMARY AND CONCLUSIONS................................214 PART THREE CHAPTER I SUMMARY AND CONCLUSION I. METHODS OF INVESTIGATION..............................216 1. General statement 2. Statistical procedure II. RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT..................................................216 1. Consensus of opinion concerning extra-mural study (Page 12) 12 CONTENTS 2. Relation between residence, correspondence, and extension enrolments 3. Influence of extra-mural study on residence enrolment 4. Extra-mural students as prospective college students 5. College graduates, and extra-mural study 6. Views of students as to influences that led to residence enrolment 7. Relation between types of study and order of enrolment III. RELATION OF EXTRA-MURAL STUDY TO SCHOLASTIC STANDING............................................................224 1. Consensus of opinion concerning extra-mural study 2. Grades in different types of study 3. Relation of grades to age, and advancement 4. Relation of health to number of studies, grades, and type of study 5. Relation of mental ability to age, advancement, grades, and type of study 6. Factors that account for high grades; 7. Relations involving number of studies, order of enrolment, and grades IV. BRIEF SUMMARY OF FINDINGS......................................229 1. Relation of extra-mural study to residence enrolment 2. Relation of extra-mural study to scholastic standing 3. General observations V. THE PROBLEM FOR THE ADMINISTRATOR..............................233 1. Meeting the public need 2. Decision for or against extra-mural study 3. Growth of extension study 4. Proposed plan of organization for extra-mural study in Missouri VI. FURTHER STUDIES SUGGESTED.......................................237 (Page 13) THE RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT AND SCHOLASTIC STANDING PART ONE THE RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT CHAPTER 1 METHODS OF INVESTIGATION I. TYPE OF DATA This study is based on data collected from original sources. It is therefore almost entirely of a statistical nature, and it deals with certain types of data not usually found in school surveys and ordinary educational investigations; therefore, some methods of procedure are used that call for explanation and illustration. However, no special consideration is given to methods that are in current use in the field of educational literature. The reader who is familiar with the methods dealt with in this chapter, may pass immediately to Chapter II in which begins the study of the problem. The last chapter gives a summary of preceding chapters. II. TYPES OF CORRELATION AND REGRESSION Use is made of certain tupes of correlation other than r = (∑xy)/(Nσxσy).......................(Ia), the correlation coefficient, found by Pearson's product-moment method and its modifications where x and y are the deviations of each measure from the true mean of its respective distribution X and Y, and σx and σy are the respective standard deviations of the distributions. The standard deviation is the square root of the arithmetic mean of the squares of all deviations measured from the arithmetic mean of the observations. Thus σx = √(∑x2)/N is frequently called the root-mean-square deviation from the mean, and it is less than the root-mean-square deviation from any other origin. Now if x-arrays of type y and y-arrays of type x be formed from a twofold distribution, and we take for instance the mean of each y-array, defined in certain intervals of x, and join these points in a graph by a curve, and do likewise for the x-arrays, the two regression curves are obtained. In uncorrelated data the mean of (Page 14) 14 THE RELATION OF EXTRA-MURAL STUDY TO an array does not depend on the type or position of the array. In other words, the means are the same from array to array as for the whole distribution. In this event the means for the x and y-arrays approximate straight lines and will coincide respectively with the y and x-axes if the axes are taken through the center of the distribution. But for correlated data the regression curve diverges from the position of coincidence with the axes. The degree of correlation is determined by the distance of the means of arrays from the axis. The numerical measure of the correlation of the data involved depends on the deviation of the means from the horizontal axis through the center of the distribution. For example, when the means of rows (x-arrays) lie on a straight line, we have what is called straight line regression denoted by the equation x = r(σx/σy)y, where all terms are defined as given above. If means of columns are used, the equation is y = r(σy/σx)x In the equations b1 = r(σx/σy), and b2 = r(σy/σx), b1 and b2 are called regression coefficients, and represent the respective slopes of the two lines with the y and x-axes through the center of the distribution. It is also seen that b1 is the reciprocal of the slope with the x-axis. In case the means of arrays do not lie on a straight line, and this situation generally exists, we still compute r = ∑xy/Nσxσy as before and take the two straight lines, x = b1y and y = b2x, where b1 and b2 are defined as noted above. These two lines have the property of being the best fitting straight lines for the means of rows and columns respectively. This result signifies for example, that when b1 = r(σx/σy), the sum of the squares of the distances of the row means (x-arrays) measured horizontally from the line x = b1y, each multiplied by the corresponding frequency, is the least possible. Also the standard error or deviation of estimating x from b1y, represented by Sx2 = ∑(x-b1y)2/N = σx2(1-r2) (Page 15) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 15 is a minimum. The straight lines, x = b1y and y = b2x, are again called the lines of regression and have their evident mathematical interpretations. Moreover, since x = X — x̄ and y = Y — ȳ, if Y and x̄ and ȳ are given, the most probable value of X can be determined. Here X and Y are particular observations and x̄ and ȳ, the means of the X and Y distributions. But, since there are two such lines, a change in y produces a change in x from the first equation and this change in x cannot be calculated at all from the second equation. Similar statements hold concerning the use of the second equation. These lines of regression and the value of r can be computed for any set of data involving two measured attributes. But it is evident, if the means of arrays do not lie close to the line of regression, that the coefficients of correlation and regression do not give a true measure of the actual relationship between the two attributes. However, under such conditions, r always understates the actual relationship that exists.1 To get at the true relationship, when the regression is not linear, the correlation ratio is used. III. CORRELATION RATIO Suppose we consider the y-arrays and take the means of each array ȳx, while the mean of the whole distribution along the y-axis is ȳ. If, then, we get the mean square deviation of the means of arrays from the mean of the whole distribution and divide this by the standard deviation of the whole distribution, the quotient is a measure of relationship called the correlation ratio, η. It is given by the formula ηyx2 = ∑[ηx(ȳx — ȳ)2]/Nσy2....................(Ib) Thus the correlation ratio is seen to be the standard deviation of means of y-arrays divided by the standard deviation of the whole distribution along the y-axis. Since η is a quotient of two standard deviations, it is always positive. There are two correlation ratios ηyx, read correlation of y on x, and ηxy, read correlation of x on y. The first is obtained from using y-arrays, the second, from using x-arrays, and the two may differ considerably. For data of zero correlation the means lie exactly on the two axes. Hence each separate difference in the numerator of the correlation ratio would equal zero. Therefore η = 0 for zero correlation. Also ηxy2 = 1 — (yσx/σx)2, where yσx is an average of the standard deviations of x-arrays of type y, and σx is the standard deviation of the x’s.2 But ηxy2 > 0. Therefore yσx2 < σx2, and ηxy2 < 1, and, as previously observed, η is always positive. Moreover, 1West’s Introduction to Mathematical Statistics, p. 85. 2Yule, An Introduction to the Theory of Statistics (1), p. 205. (Page 16) 16 THE RELATION OF EXTRA-MURAL STUDY TO (ηxy2 — r2) = σd2/σx2 where σd is the standard deviation of means of x-arrays from the line of regression measured parallel to the x-axis.3 Therefore 0 < ηxy < 1, and also 0 < ηyx < 1, and ηxy > |r|, and ηyx > |r|. Hence r never overstates the correlation between two attributes but may considerably understate it when the regression is far from linear. The reason for using the correlation ratio in certain cases now becomes evident. Applications of this method to particular problems may be found in Rugg’s STATISTICAL METHOD, p. 281, West’s MATHEMATICAL STATISTICS, p. 77, and Yule’s, INTRODUCTION TO STATISTICS, p. 207; consequently, illustrations of the process as applied to particular problems may be omitted; in fact, the formula makes the process clear. IV. A NEW METHOD OF DETERMINING CORRELATION Pearson develops a “new method of determining correlation when one variable is given by alternative and the other by multiple categories.”4 1. Explanation of method Let y be the categoric variate divided into multiple classes and x be the alternative variate—the A and non-A classes. The alternate variate is supposed to be continuous, but y is not necessarily continuous. As has already been seen, the correlation ratio η has a very definite meaning for such a system. It is the ratio of the standard deviation of the weighted means of the y- arrays of type x to the standard deviation of the y’s for the whole distribution. A similar statement holds for x-arrays of type y. The equation, ηxy2 = ∑ηy(x̄y — x̄)2/Nσx2..............(Ic), was found where ηy is the number of individuals in any y-category; x̄y is the mean of x of the category of type y, and x̄ is the mean and σx is the standard deviation of the whole number of observations N. It was also seen that 0 < η < 1, and η becomes r when the regression is linear, for, then σd2 = 0 in the equation ηxy2 — r2 = σd2/σx2. The quantity yσx, in the equation (yσx)2 = σx2(1 — ηxy2)..............(1), is the arithmetic mean of standard deviations of weighted arrays of type y, and it becomes very small, as η approaches unity.5 Then (Ic) gives 3Yule, An Introduction to the Theory of Statistics (7), p. 206. 4Biometrika, VoL VII, p. 248. 5Yule, An Introduction to the Theory of Statistics, p. 205. (Page 17) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 17 ηxy2 = 1/N∑[ny(x̄y2 — 2x̄yx̄ + x̄2)/σx2], or ηxy2 = 1/N∑[ny(x̄y2/yσx2) ∙ (yσx2/σx2)] — 2∑(nyx̄yx̄)/Nσx2 + ∑(nyx̄2)/Nσx2 = 1/N∑(ny(x̄y2/yσx2 ∙ yσx2/σx2 — 2Nx̄2/Nσx2 + x̄2/σx2) since ∑nyx̄y = Nx̄. Therefore ηxy2 = 1/N∑(nyx̄y2/yσx2 ∙ yσx2/σx2) — (x̄/σx)2................(II) Now, if we assume that the distributions are homoscedastic, that is, all x-arrays have the same or approximately the same standard deviations, it follows from (1) that for yσx2/ σx2 in (II), we may put its value 1 — ηxy2. Hence ηxy2 = (1 — ηxy2)∑[ny/N ∙ x̄y2/yσx2] - (x̄/σx)2. By solving, we have ηxy2 = 1/N∑[ny(x̄y/yσx)2] — (x̄/σx)2 / 1 + 1/N∑[ny(x̄y/yσx)2].........(III) These are the two values of the correlation ratio which are useful in case one or both of the attributes are not measured. These formulae were deduced by making the following assumptions: (1) The alternate variate is sufficiently Gaussian to permit finding the means from tables of the probability integral. The means of x show whether this variate is Gaussian. The x-arrays do not continuously increase or decrease as they do in a symmetrical distribution where two variates are correlated. When used in a non-Gaussian distribution, η may even turn out imaginary. (2) For formula (III) the arrays are approximately homoscedastic, but for formula (II) when the alternate variate with two classes is replaced by one grouped in three classes the arrays need not be homoscedastic. 2. New method applied to concrete problems This method of calculating correlation ratios is now applied to certain problems that have arisen in this study. After these explanations when the body of the study is reached, only the correlation ratio and certain facts necessary for its interpretation shall be given. A correlation ratio always demands an interpretation since it is always positive, and since there are two such ratios. a. First method—formula (II) (1) Application Determining the influence of college preference of high school (Page 18) 18 THE RELATION OF EXTRA-MURAL STUDY TO graduates on later registration at a particular college, affords a good illustration of the need and use of this method. This problem occurs in Chapter V in connection with Table XII. TABLE XII COLLEGE PREFERENCE AND LATER REGISTRATION Preference for Registration at Kirksville* Registered Did not register Total Kirksville 151 286 437 No school 52 271 323 Other schools 39 354 393 Total 242 911 1153 School preference is taken as the x or alternate variate divided into three classes. The y or categoric variate is registration at Kirksville. As far as the plan of work is concerned the categoric variate could be divided into any number of classes and the procedure would be the same. But, if the number of divisions exceeds 5 or 6, the labor of computation is great. For this work is used formula (II) which is formula (II) of Biometrika, Vol. VII, p. 250. It is η2 = 1/N∑(nyx̄y2/yσx2 ∙ yσx2/σx2) - (x̄/σx)2. For obtaining the mean values of x-arrays divided by their respective standard deviations we use Sheppard’s Tables, p. 182, Vol. II, Biometrika. The area under the probability curve is 1. If an area a/2 is taken on either side of the vertical mean and an ordinate erected, the lesser area cut off is 1/2(1 — a) and the greater area is 1/2(1 + a). The former expression is less than one-half the whole area; the latter, greater. If it is agreed to measure area from the extreme left through the mean to the right, then the abscissa of the limiting ordinate of 1/2(1 — a) is negative while that of 1/2(1 + a) is positive. This procedure is followed for each vertical array including the total array in the distribution in the tables above. Suppose we take the upper horizontal or y-array, and begin with 437. But 437/1153 < 1/2, and it represents the proportion of the total area under the curve for the Kirksville preference group; therefore, 1/2(1 — a) = 437/1153 = .3790. But by agreement the area 1/2(1 — a) is to the left of the mean of the *Registration in all tables means residence enrolment. (Page 19) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 19 array of totals, then the abscissa of its limiting ordinate is negative, though evidently the area 1/2(1 + a) just to its right has the same limiting ordinate. Thus the sign of the abscissa is negative when the portion of the area under the curve is less than 1/2. Next we take from the upper horizontal array the 151 in the first column, and find the proportion of this array that is under the curve. It is 151/242 = .6239 which is greater than 1/2, and by agreement the abscissa of its ordinate is positive. Finally, we take from the same horizontal array the 286 in the second column. The proportion of this array that is under the curve is 286/911 = .3139 = 1/2(1 — a), and its abscissa is negative. These abscissae are expressed in terms of their respective standard deviations, and in formulae (II) and (III) they are the mean values of x-arrays of type y. When the alternate variate is divided into three classes, as in the proposed problem, two sets of abscissae are needed. The second set is obtained by adding the elements of the horizontal array first used to the corresponding elements of the intermediate horizontal row, and then by proceeding and choosing signs of mean values of abscissae just as done for set (1). We have explained the whole process involved in formula (II) except the determination of the width, h, of the intermediate horizontal row. That problem will be taken up a little later when the need arises. It is evident that 1/2(1 + a) is obtained by subtracting 1/2(1 — a) from 1. Sheppard’s Tables are used in the work which follows.6 From the upper row of our tabulation we obtain set (1) of values below, and from the two upper rows combined , we obtain set (2) below. SET (1) 1/2(1 — a) = 437/1153 = .3790; 1/2(1 + a) = .6210; therefore x̄/σx = —.308. 1/2(1 + a) = 151/242 = .6239; " x̄1/σ1 = .313. 1/2(1 — a) = 286/911 = .3139; 1/2(1 + a) = .6861;” x̄2/σ2 = —.485. SET (2) 1/2(1 + a) = 760/1153 = .6591; therefore x̄'/σx = .410. 1/2(1 + a) = 203/242 = .8399;" x̄'1/σ1 = .994. 1/2(1 + a) = 557/911 = .6134;" x̄'2/σ2 = .288 6Biometrika, Vol. II, p. 188. (Page 20) 20 THE RELATION OF EXTRA-MURAL STUDY TO Now if the corresponding parts of set (1) are subtracted from set (2), set (3) is obtained, the meaning of which is explained later. It gives a constant, h, divided by the respective standard deviations. Set (4) is obtained by dividing the first ratio in set (3) by the second and third ratios of the same set. SET (3) SET (4) h/σx = .718 Therefore h/σ1 = .681 σ1/σx = 1.054 h/σ2 = .773 σ2/σx = .929 Set (4) shows that the x-arrays are nearly homoscedastic, for they change but little in passing from array to array. A test of the Gaussian character of the distribution is for the means of x-arrays continuously to increase or decrease. This same test is applicable when the y-category has 3 or more divisions. If it is desirable, we can multiply the means of arrays in sets (1) and (2) by the quotients of standard deviations in set (4) and thus obtain the means of x-arrays in terms of a common unit σx. By using values in set (1), substituting in formula (II), and employing logarithms, we find η2 = 1/1153 [242(.313)2(1.054)2 + 911(.485)2(.929)2] — (.308)2 = .0884. Therefore η = .299. By using values in set (2), we find η2 = 1/1153 [242(.944)2(1.054)2 + 911(.288)2(.929)2] — (.41)2 = .1075. Therefore η = .328. The agreement between the results obtained by using values in sets (1) and (2) is remarkably close, and it affords an almost perfect check on the validity of the application of this method to data in hand. This agreement shows that the x-variate, school preference, is also approximately Gaussian. Doubtless this method would prove valuable in treating great quantities of data relative to influence on school attendance, and material relating to similar influences in business and trade. (2) Interpretations Even if η should not be found by this method because of the wide departure of the x-variate from a Gaussian distribution, which may even show η imaginary, still sets of values (1) and (2) may in any event tell a great deal about the distribution and the relation of the attributes. (Page 21) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 21 In this particular problem Kirksville preference is the x-variate, and registration the y-variate. The type of the horizontal array used in the calculation, that is, school preference, should denote the positive end of the x-axis in the graph. With this understanding using values in set (1) and placing the x-axis vertical as in the tabulation we have: FIG. 1 This graph shows clearly that, as we pass from registered to non-registered students, the preference for Kirksville declines, or, as we pass from non-registered to registered, the preference for Kirksville increases rapidly. In other words, η = .299 and η = .328 show strong positive correlation between preference for Kirksville and later enrolment. We still have left the necessity of explaining the meaning of h in set (3) of our calculated values. In Fig. 1 above, let h/σx = BQ + QA be the range of the non-preference group. It happens that Q, the mean of the whole distribution, falls inside this range in our representation above, but the result is the same and follows by the same argument whether Q falls into either of the other two horizontal arrays. Now x̄/σx is measured from the boundary of the Kirksville preference, and no preference groups, while x̄'/σx is measured as seen in the calculations of values in set (2) from the boundary of other school preference and no preference groups. Then AQ = x̄/σx = —.308, and BQ = x̄'/σx = .410. But h/σx = BQ — AQ = x̄'/σx - x̄/σx = .410 — (—.308) = .718. (Page 22) 22 THE RELATION OF EXTRA-MURAL STUDY TO This calculation is made for the sum of x-arrays or array of totals. It is the same for each individual x-array. Thus the following rule is deduced: to obtain the values in set (3) subtract values in set (1) from corresponding values in set (2). Moreover, it is seen that h/σx, h/σ1, and h/σ2 represent the depth of the middle horizontal range as it is found in the whole distribution, and as it passes from x-array to x-array. b. Second method—formula (III) (1) Application The application of formula (III) now becomes easy. We may combine the two lower rows of the preceding table into one row so as to have strictly alternate classes in the x-variate, or we may change our variates and let school preference become the categoric or y-variate of three classes and registration become the alternate variate where registration represents a relationship passing from remoteness of affiliation to actual affiliation with the school. The latter course is adopted and, when the direction of axes are interchanged, the table appears as follows: TABLE XIIa COLLEGE PREFERENCE AND LATER REGISTRATION Preference for Registration Kirksville No school Other schools Total Registered 151 52 39 242 Did not register 286 271 354 911 Total 437 323 393 1153 The lower horizontal row is used and signs are interpreted as in the work with formula (II). Using Sheppard’s Tables, we have: 1/2(1 + a) = 911/1153 = .7901; therefore x̄/σx = .8068. 1/2(1 + a) = 286/437 = .6545; therefore x̄1/σ1 = .3976. 1/2(1 + a) = 271/323 = .8390; therefore x̄2/σ2 = .9900. 1/2(1 + a) = 354/393 = 0.9008; therefore x̄3/σ3 = 1.2865. Formula (III) is η2 = A - b2/1 + A, where A = 1/N∑[ny(x̄y/yσx)2] and b = x̄/σx. (Page 23) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 23 Then A = 1/1153[437(.3976)2 + 323(.99)2 + 393(1.2865)2] = .7779, b2 = (.8068)2 = .6509; therefore η2 = .7779 — .6509/1 + .7779 = .0714; therefore η1 = .268. Had we used the upper row, we should have obtained 1/2(1 — a) instead of 1/2(1 + a), and the means of arrays would have been negative and exactly equal in absolute value to the values already found. Hence η will have the same value no matter which row is used. (2) Interpretations We may again use the graph of the means of arrays for interpreting the nature of the correlation and other properties of the distribution. Of course the mean of the x-array representing the whole distribution is not included in the main part of the graph which shows variations in x-arrays of certain types. FIG. 2 From the graph of means it is seen that the means of x-arrays increase continuously as we pass from left to right; that is, as we pass from Kirksville preference, through no preference, to preference for other schools, non-registration increases continuously or affiliation with school decreases continuously. Also it is seen that as we pass from right to left along the y-axis the abscissae decrease continuously; that is, as we pass from preference for other schools, (Page 24) 24 THE RELATION OF EXTRA-MURAL STUDY TO through no preference, to preference for Kirksville, registration increases continuously. The fact that P, Q, and R are above the y-axis has no important bearing on our interpretation of relationships. The direction in which these points move is the important thing. c. Comparisons and conclusions Strong positive correlation exists between Kirksville preference and registration; that is, between school affiliation and school preference. The correlation is the same between preference for other schools and non-registration. In both cases η = .268. Hence we need to examine the means of arrays to interpret the correlation. The continuous increase of means of arrays tells us that we are dealing with a variate that is reasonably Gaussian in character. Moreover, when comparison is made of the three values of η secured from different sets of data the agreement is remarkably close. We have η = .268; η = .299; η = .328. Karl Pearson interprets η = .07 as being significant when obtained by these methods. With this statement in mind the strength of the correlations noted above will be appreciated.7 The same plan of procedure used in interpreting correlation under formula (II) holds also for formula (III) when the categoric or y-variate has more than two classes. V. ANOTHER NEW METHOD OF DETERMINING CORRELATION We make use also of a method of correlation between a measured character A, and a character B, of which only the percentage of cases wherein B exceeds or falls short of a given intensity is recorded for each grade of A. We shall not go into so much detail in explaining this formula derived by Pearson since it has been in use for some time. Dr. Jasper N. Mallory made extensive use of this method of correlation in his doctor’s dissertation on THE RELATION OF SOME PHYSICAL DEFECTS TO ACHIEVEMENT IN THE ELEMENTARY SCHOOL. 1. Explanation of method Pearson’s illustration is used to make clear the problem. The example is as follows: we are given the ages A of all candidates who took an examination for a government position; the papers were merely marked passed or failed—capacity, B. We desire to correlate capacity and age. Then the Pearson formula is r = p̄/σ1 ÷ q̄/σ2.......................(IV), where p̄ is the mean value of the age group, which passed, measured from the means of the two variates parallel to the age or x-axis. σ1 is the standard deviation of age; σ2, the standard deviation of capacity, and q̄/σ2 = z/1/2(1 - a) of Sheppard’s Tables.8 7Biometrika, Vol. VII, p. 253. 8Biometrika, Vol. II, p. 182. (Page 25) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 25 Pearson supposes a normal frequency surface in that the regression is linear. Now all sections of such a surface parallel to the x-y plane are contour lines that are similar ellipses. All vertical sections of this surface give normal curves.9 If a volume of the frequency surface is cut off by a vertical plane at a given value of the variate B (capacity) then the vertical through the centroid of this volume will in general cut both regression lines which may be considered as lying in the x-y plane. Let us take the point of section T with the regression line RR' that contains the means of the B variate, (Fig. 3). Then if (p̄, q̄) be the coordinates of this point of section with the regression line, we have p̄ = rσ1/σ2q̄, where r = p̄/σ1/q̄/σ2. FIG. 3 Now measuring from the lower horizontal and left vertical lines we have p̄ = GS — GM. But GS = LT is the mean of the A-variate of type B (in this case, passed) and GM is the mean of the whole age distribution; therefore, p̄ is, in this particular case, the mean age of candidates who passed less the mean age of all candidates. σ1 is the standard deviation of the whole age distribution. Thus p̄ and σ1 are readily found. But the B-variate is not given quantitatively. However, we know the percentage of B beyond the arbitrary point of division; 9Yule, An Introduction to the Theory of Statistics, p. 321. (Page 26) 26 THE RELATION OF EXTRA-MURAL STUDY TO that is, the number of candidates who passed. If now we assume the B-variate to follow reasonably closely a Gaussian distribution, the percentage of the B-variate gives, by means of the probability integral tables, the ratio of y/σ2 for the distance from the mean at which the B-variate is divided, and then10 q̄/σ2 = N/√2πσ22 ∫∞yye-1/2 y2/σ22dy / N/√2πσ2 ∫∞ye-1/2 y2/σ22dy = 1/√2π e-1/2 y2/σ22 / 1/√2π ∫∞y/σ2e-1/2 y2dy.......................(1) Here both numerator and denominator are known as soon as y/σ2 has been found. They are, for example, the z and 1/2(1 — a) of Sheppard’s Tables. The probability integral z = 1/√2π e-1/2 x2.11 The abscissa x is measured from the central ordinate about which the curve is symmetrical, and its unit of measurement is the standard deviation. The whole area of the curve is unity. If this whole area be divided by the ordinate z, at distances x from the central ordinate, into portions 1/2(1 + a) and 1/2(1 — a), then 1/2(1 + a) = ∫x—∞zdx; 1/2(1 - a) = ∫∞xzdx; a = 2∫x0zdx, where a has the value given above. Our x = y/σ2 in formula (1). So the final numerator in (1) = z. By the same changes in the limits, the denominator in (1) becomes 1/√2π ∫∞xe-1/2 y2dy = 1/2(1 — a). In this integral there is no need to change the y and dy to x and dx in as much as the particular letter used makes no difference in a definite integral since the limits are really the variables. So we have shown that q̄/σ2 = z / 1/2(1 - a) given in Sheppard’s Tables. We are now in a position to use this second method devised by Pearson for finding the correlation between a measured character A, and a character B, of which only the percentage of cases wherein B exceeds (or falls short of) a given intensity is recorded for each grade of A. 10Biometrika, Vol. VII, p. 97. 11Biometrika, Vol. II, p. 174. (Page 27) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 27 2. Application of method A problem that occurred in Chapter I, Part Two, of this study is used to illustrate this method. We desired to know whether among bachelor degree graduates at Kirksville there is a correlation between being a student with both residence and extra¬mural study, and residence grades. TABLE V (PART TWO) RESIDENCE GRADES BACHELOR DEGREE STUDENTS Grades No. with residence study only No. with both residence and extra-mural study (b) Total fn d fd fd2 Total with both fb 8-9 2 0 2 -5 -10 50 0 9-10 4 4 8 -4 -32 128 -16 10-11 16 11 27 -3 -81 243 -33 11-12 40 19 59 -2 -118 236 -38 12-13 39 20 59 -1 -59 59 -20 13-14 32 34 66 0 0 0 0 14-15 36 26 62 1 62 62 26 15-16 22 18 40 2 80 160 36 16-17 16 9 25 3 75 225 27 17-18 7 10 17 4 68 272 40 18-19 9 6 15 5 75 375 30 Total 223 157 380 60 1810 52 Mean of residence grades for whole distribution, 13.655; mean of grades for those with both types of study, 13.831; standard deviation for whole distribution, 2.177. Then p̄/σn = 13.831 — 13.655 / 2.177 = .0809. 1/2(1 — a) = 157/380 = .4132; 1/2(1 + a) = .5868. Then from Sheppard’s Tables z = .3895. Hence q̄/σb = z / 1/2(1 — a) = .9426. Therefore rbg = .0809/.9426 = .086. (Page 28) 28 THE RELATION OF EXTRA-MURAL STUDY TO Thus there is a slight but sensible correlation between being a student with both residence and extra-mural study and high residence grades. The foregoing problem illustrates the method in all cases; consequently, in succeeding chapters, only the essentials of the procedure will be given. VI. TETRACHORIC FUNCTIONS 1. Explanation of method Pearson works out a method of correlation for fourfold tables.12 A normal frequency surface has x and y-axes through the center. This surface is divided into four parts by planes at right angles to the axes at distances h and k measured in terms of standard deviations. FIG. 4 The volumes or frequencies in the four divisions NGM', M'GN', N'GM, and MGN are represented respectively by a, c, d, and b. If the frequency surface is normal, it is evident that b + d and c + d, owing to the position given the point of intersection of the traces of the dividing planes, cannot exceed 1/2N. Pearson shows in an extensive article that r, the coefficient of correlation between the variates, is given by the equation d/N = b + d / N ∙ c + d / N + ∑∞1(rn/n! H. K.V̅n - 1W̅n - 1).................(2) where H and K are the ordinates of the normal curve of area N corresponding to the abscissae h and k and, consequently, dividing 12Phil. Trans. A. Vol. 195, pp. 1-47. (Page 29) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 29 the curve into areas of which the proportions to the whole are (b + d)/N, and (c + d)/N respectively, while V̅n = hV̅n - 1 - (n - 1)V̅n - 2, W̅n = kW̅n - 1 - (n - 1)W̅n - 2. Therefore V̅0 = 1, V̅1 = h; W̅0 = 1, W̅1 = k.13 Everitt sets Tn = HV̅n - 1 / √n!, Tn' = KW̅n - 1 / √n!, and equation (2) becomes d/N = b + d / N ∙ c + d / N + ∑∞1(TnTn'rn).............(V) It is clear that Tn' is the same function of (c + d)/N that Tn is of (b + d)/N. Everitt then works out extensive tables for the values of these functions, and it is seen that one table will do for both Tn and Tn'. It is also evident that (b + d)/N and (c + d)/N are the 1/2(1 — a) and 1/2(1 + a) of Sheppard’s Tables. This method is probably the most accurate known for dealing with fourfold tables. But it is long, and usually involves the use of Homer’s method in the solution of equations of high degree. However, the method is becoming well known and is made use of in a few cases in this study as a check on less exact methods of procedure. 2. Application of method As an illustration of the use of tetrachoric functions for fourfold tables, let us take one of the problems arising in connection with our study in Chapter IV, Table X. This table deals with teachers of northeast Missouri and the order in which, enrolments in residence and extra-mural study took place at Kirksville. If we use the same notation and rearrange the table, it assumes the following form: TABLE X TYPE OF STUDY AND ORDER OF ENROLMENT (TEACHERS 1921-1922) Classification as to first enrolment Type of study (e) (E) Total (r) 1751 32 1783 (R) 867 14 881 Total 2618 46 2664 Type of study as explained in Chapter IV, Part One, means residence, correspondence, or extension study. Sometimes the last two are combined under the head of extra-mural or non-residence study. Order of enrolment indicates the numerical sequence of types of study. In the notation used under tetrachoric functions, a = 1751; b = 867; c = 32; d = 14. Therefore b + d = 891; c + d = 46; N = 2664. 13P. F. Everitt, Biometrika, Vol. VII, p. 56. (Page 30) 30 THE RELATION OF EXTRA-MURAL STUDY TO Then d/N = .00525; (b + d)/N = 1/2(1 — a) = .01725; (c + d)/N = 1/2 (1 — a') = .33070. From Everitt’s Tables we have the following for the unprimed and primed rows.14 1/2 (1 — a) T1 T2 T3 T4 T5 T6 (aT)-row: .01725, .04269, .06381, .06170, .02682, —.01496, —.03268. (a'T')-row: .33070, .36245, .11223, —.11985, —.09100, .06238, .07761. Now formula (4) indicates that we are to take d/N equal to the algebraic sum of column products pair by pair from the rows (aT) and (a'T') above, and with each product insert the factor r with an exponent equal to the subscript of T which heads the column. This procedure gives .00525 = .0057 + .01548r + .00716r2 — .00738r3 — .00244r4 — .00093r5 — .00255r6, or r6 + .365r5 + .957r4 + 2.89r3 — 2.808r2 — 6.07r — .137 = 0. We are interested only in values of r between plus and minus 1 since plus 1 is the maximum of the absolute value of the coefficient of correlation. By Descartes’ rule of signs there are not more than five negative roots or more than one positive root. There is a positive root greater than 1 which must be excluded. Then any real root that will serve as a value of r must be negative and lie between —1 and 0. By Horner’s method r = —.023, and Sturm’s theorem shows there is no other negative root within these limits. We therefore reach the remarkable conclusion that in the universe of teachers, residence study is negatively correlated with first enrolment in extra-mural study. This result will be referred to again at the proper time and place. VII. MEAN SQUARE CONTINGENCY 1. Explanation of method G. Udny Yule shows in his theory of statistics that C = √S - N/S, called “Pearson’s mean square contingency coefficient,” is a measure of relationship between two attributes A and B. N denotes the number of observations. The meaning of S is made clear later. If A and B be divided into any number of classes (Am) and (Bn) and A be taken horizontally and B vertically, then (Am) and (Bn) denote the sum of frequencies in the mth column and nth row respectively. Now it is well known that dmn = (AmBn) — (AmBn)0 is the measure of dependence of the two pairs of values of A and B where (AmBn)0 = (Am)(Bn)/N. 15 14Biometrika, Vol. VII, p. 442. 15Yule, An Introduction to the Theory of Statistics, pp. 36 and 64. (Page 31) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 31 If d = 0, the pair is completely independent. But, if A and B are not completely independent, this difference will not be zero for all values of m and n. Thus (AmBn)0 is appropriately called the independence values of Am and Bn, and is used in calculating a table of independence values for the frequencies in a given table. If we square dmn and form the ratio d2mn / (AmBn)0 and place x2 = ∑d2mn / (AmBn)0 and then let C = √x2/N + x2.......(1), we have a measure of the association between A and B. Now We may write x2 = ∑[(AmBn) — (AmBn)0]2 / (AmBn)0 = ∑ [(AmBn)2 — 2(AmBn) (AmBn)0 — (AmBn)02 / (AmBn)0] = ∑ [(AmBn)2/(AmBn)0 — 2(AmBn) + (AmBn)0]. Therefore x2 = ∑(AmBn)2/(AmBn)0 — 2∑(AmBn) + ∑(AmBn)0. But the second term equals 2N, and the last term equals N. Therefore x2 = ∑(AmBn)2/(AmBn)0 — N......(2) If we let S = ∑(AmBn)2/(AmBn)0, we may write (1) in the form C = √S — N / S...........(VI), which is the mean square contingency coefficient. This formula is a conservative statement of association, and is smaller when the attributes have fewer classes. The following considerations show that it is a conservative measure: (1) If dmn = 0, then (AmBn) = (AmBn)0. Hence S = ∑(AmBn)2/(AmBn)0 = ∑(AmBn) = N; therefore, C = 0 for complete independence. (2) The association is greatest when ∑d2mn is greatest or when S is greatest. But when S = ∞, even then C equals only 1. Now conceivably S might become infinite in either of two ways. The first one would be for ∑(AmBn)2 to become infinite, but it cannot because it is the sum of a finite number of finite terms, and must therefore always be far short of an infinite number. The second way would be for the factor (Page 32) 32 THE RELATION OF EXTRA-MURAL STUDY TO (AmBn)0 = (Am)(Bn)/N = 0. Then S = ∞, and C = 1. But this result is manifestly impossible unless either (Am), the sum of a column, or (Bn), the sum of a row, or both of them equal zero in (Am)(Bn)/N. But we can exclude from our table whole rows or columns that are zero. Hence (AmBn)0 cannot be zero, and C cannot equal 1. So it is evident that C must be a conservative measure of relationship since S cannot begin to assume an infinite value. Pearson shows that e = (m — 1)(n — 1)/N is the correction to be subtracted from C2; where m equals the number of rows; n, the number of columns; and N, the total number of observations.16 2. Application of method The following problem taken from Chapter VII, Table XXXVIII illustrates the procedure in calculating this coefficient. In this problem we have the order in which extra-mural students in three teachers colleges of Missouri enrolled in different types of study. We wish to find the association between type of study and order of enrolment among these extra-mural students. TABLE XXXVIII TYPE OF STUDY AND ORDER OF ENROLMENT (3 MISSOURI TEACHERS COLLEGES)* Contact with teacher—type of study Order of Enrolment (f) First (s) Second (t) Third Total Residence (r) 2117 192 5 2314 Extension (e) 640 768 117 1525 Correspondence (c) 215 1432 170 1817 Total 2972 2392 292 5656 16Biometrika, Vol. 9, p. 216. *For definitions see under Table X of this chapter. (Page 33) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 33 TABLE XXXVIIIa INDEPENDENCE VALUES FOR FREQUENCIES IN TABLE XXXVIII Order of Enrolment (f) (s) (t) Type of study First Second Third Residence (r) 1216 978 119 Extension (e) 801 645 79 Correspondence (c) 919 768 94 Table XXXVIIIa of independence values is formed by taking Imn = (Am)(Bn)/N = (AmBn)0 as noted in our explanations. The subscripts f, s, t stand for first, second, and third columns, while subscripts r, e, c stand for first, second, and third rows. Then by referring to Table XXXVIII, we have Ifr = (2972)(2314)/5656 = 1216 Ife = (2972)(1525)5656 = 801 Ifc = (2972)(1817)/5656 = 955 Isr = (2392)(2314)/5656 = 978 Ise = (2392)(1525)/5656 = 645 Isc = (2392)(1817)/5656 = 768 Itr = (292)(2314)/5656 = 119 Ite = (292)(1525)/5656 = 79 Itc = (292)(1817)/5656 = 94 These values set in Table XXXVIIIa above constitute a table of independence values. Each value is a denominator of a term in S = ∑(AmBn)2/(AmBn)0. Then the individual terms in S are obtained as follows: Sfr = (2117)2/1216 = 3685.6 Sfe = (640)2/801 = 511.4 Ssr = (192)2/978 = 37.7 Sse = (768)2/645 = 914.4 Str = (5)2/119 = .2 Ste = (117)2/79 = 173.3 (Page 34) 34 THE RELATION OF EXTRA-MURAL STUDY TO Sfc = (215)2/955 = 48.4 Ssc = (1432)2/768 = 2670.0 Stc = (170)2/94 = 307.5 By adding the separate terms in S we have S = 8348.5: N = 5656; S — N = 2692.5 Therefore C = √S — N / S = √.3225 =.57 The coefficient of contingency shows that order of enrolment among extra-mural students as a universe is highly associated with the type of study, for C is a conservative measure of relationship. However, the nature of the relationship is not yet clear. 3. Interpretations If we now take in the original table rows (1) and (2), and form association ratios as we proceed from column marked “first” enrolment to column marked “third” enrolment, and then take rows (2) and (3), and proceed in the same manner, we get two sets of ratios, designated sets (1) and (2) which pass from tetrad to tetrad each containing two tetrads in this table. In set (1) a > b > c; in set (2) a > b, b < c. When passing from tetrad to tetrad we may say the signs run as follows: In set (1) + + In set (2) + — The distribution fails by only a small amount in the last tetrad of being isotrophic. Set (1) shows, if we take the first two rows of our table, that residence is positively associated with first enrolment when extension and second enrolment are considered, and positively associated with second enrolment when extension and third enrolment are considered. Set (2) shows, if we take rows (2) and (3), that extension is positively associated with first enrolment when correspondence and second enrolment are considered, and slightly negatively associated with second enrolment when correspondence and third enrolment are considered. These results indicate that, as we pass from residence study, through extension to correspondence, the association in order of strength declines from first enrolment, through second enrolment, to third enrolment with only a slight turning back for extension and correspondence when we come to third enrolment. (Page 35) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 35 These results indicate also that “type of study” is a continuous function representing closeness of contact with the teacher, and that it increases in strength from correspondence, through extension to residence; and that order of enrolment is a continuous function of established relations with a school; and that it increases in strength from third enrolment to first enrolment, and that with but the slight exception noted, these two functions increase together. Hence we may say that affiliation with school (order of enrolments) is highly correlated with contact with teacher (type of study). Hereafter we need not go into such detailed explanations when using the mean square contingency coefficients. VIII. FORMULAE USED FREQUENTLY IN THIS STUDY The following important formulae of this chapter will be referred to by number in the remaining chapters of this study: (Ia) r = ∑xy/Nσxσy. (Ib) ηyx2 = ∑[nx(ȳx — ȳ)2] / Nσy2. (II) ηxy2 = 1/N ∑(Nyx̄y2/yσx2 1. yσx2/σx2) — (x̄/σx)2. (III) ηxy2 = A — b2/1 + A, where A = 1/N ∑[ny(x̄y2/yσx2)] and b = x̄/σx. (IV) r = p̄/σ1 ÷ q̄/σ2, where p̄/σ1 = A2 — A1/σ1, and q̄/σ2 = z/1/2(1 — a). A2 is the arithmetic mean of the smaller division considered, and A1, of the whole distribution. (V) d/N = b + d / N ∙ c + d / N + ∑∞1(TnTn'rn). (VI) C = √S — N / S. (VII) Q = (AB)(ab) — (Ab)(aB) / (AB)(ab) + (Ab)(aB). (VIII) r12.3 = r12 — r13r23 / √(1 — r23)(1 — r13). (Page 36) CHAPTER II CONSENSUS OF OPINION CONCERNING EXTRA-MURAL STUDY This chapter gives the consensus of opinion of administrators, teachers, and authors concerning the purpose and value of extra-mural instruction, its influence on residence enrolment, standards used for reporting residence arid extra-mural grades, ability of students in different types of study, and relative amount of time required for instruction. I. PURPOSES OF EXTRA-MURAL STUDY 1. As stated in bulletins Numerous reasons are assigned for offering extra-mural courses. A study of catalogs shows that many different reasons are given by forty-seven leading teachers colleges and normal schools in their published statements. Twenty-four schools state, “It (extra-mural study) extends the opportunity for an education to all;” eighteen, “It extends the means of education to those whose schooling has been interfered with;” fourteen, “It improves the teacher while in service;” ten, “It extends the possibilities of culture and academic training;” seven, “It helps to complete graduation requirements;” five, “It keeps the school in close relationship with the people of the state;” and two, “It leads students to enroll for residence study.” Naturally the last named reason would not be advanced very often in a published statement. 2. As given in a master’s thesis Mr. Clarence B. Collier wrote a master’s thesis at George Peabody College for Teachers on THE ADMINISTRATION OF EXTENSION COURSES IN STATE NORMAL SCHOOLS. In this study when only the first or leading reply from sixty-four schools was used, Mr. Collier found the following reasons advanced for offering extra-mural courses; thirty-four schools state, “It aids teachers in service to improve in efficiency;” eight, “It aids teachers to secure higher certificates;” seven, “It takes normal schools to those who cannot go to school;” four, “It widens service of the normal schools;” three, ‘'It improves the public schools;” three, “It enables students to continue school work;” two, “It directs teachers and others in use of spare time;” one, “It stimulates residence enrolment;” one, “It is good advertising;” and one, “It improves residence instruction.” These reasons for extra-mural study accord well with those given in published statements in bulletins. However, as stated, Mr. Collier listed only the first purpose assigned although individuals answering enumerated several others. There was nothing in the questionnaire used by Mr. Collier that called for a ranking of the relative values of purposes assigned. Mr. Collier was kind enough to allow access to his (Page 37) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 37 files of original data. If purposes are tabulated as of equal weight, the results are: forty-two replies state, “It aids teachers in service;” fifteen, “It stimulates residence enrolment;” eleven, “It aids teachers to secure higher certificates;” seven, “It takes normal schools to those who cannot go to school;” five, “It enables students to continue study and complete residence requirements for certificates and diplomas;” four, “It widens service of normal schools;” and three, “It improves the public schools.” There were four other types of answers ranging in numbers from one to two inclusive. When all answers are considered and placed on a par, the thought that extra-mural study leads to residence enrolment holds an important place. It. is mentioned by 23.4 per cent of all directors and administrators who replied to the questionnaire. As a reason for offering extra-mural courses it stands second only to the purpose of “aiding teachers in service.” It is also to be observed that “aiding teachers in service” does not at all exclude the thought of getting teachers to enroll for residence study. In fact, some persons would say that the best way of improving teachers who are in service is to induce them to attend school for residence study at least for summer sessions, and for the whole school year if possible. 3. As shown in Kirksville questionnaire In order to secure the views of faculty members of teacher producing-institutions on some phases of extra-mural study, the following list of questions was submitted to fifty-eight leading normal schools and teachers colleges that are state supported. a. Form of questionnaire March 10, 1923. Dear Sir: At Kirksville State Teachers College we are making a study of correspondence and extension work. Your judgment and assistance are wanted. Will you help in this study by taking ten or fifteen minutes right now to fill out this blank so that it may reach us if possible by return mail. We shall be greatly obliged to you. JOHN R. KIRK, President. WM. H. ZEIGEL, Dean. A. Reasons for offering correspondence and class extension courses (Extra-mural courses mean correspondence or extension courses taken for credit) Please indicate the three chief reasons why your institution offers extra-mural study by placing the figures 1, 2, 3, in the parentheses after the statements below which in order of importance express your first (1), second (2), and third (3) .reasons respectively for offering such courses. a. Improves teachers while in service ( ) b. Extends the influence of the school ( ) c. Leads to residence enrolment ( ) (Page 38) 38 THE RELATION OF EXTRA-MURAL STUDY TO d. Helps to meet certification and graduation requirements ( ) e. Helps persons to secure an education who are not financially able to enroll in residence ( ) f.____________________________________( ) g.____________________________________() B. Relations and comparisons in connection with extra¬mural and residence study Please indicate the statement that expresses your view by placing a check mark (x) in the appropriate parentheses in each group below. a. The influence of extra-mural study in leading to later residence enrolment is: (1) Pronounced ( ); (2) Moderate ( ); (3) Inconsequential ( ) b. When extra-mural grades are compared with residence grades, the extra-mural grades are: (1) Higher ( );(2) Equal ( ); (3) Lower ( ) c. When the residence grades of students who have done both residence and extra-mural study are compared with the residence grades of students who have not had extra-mural study, the extra-mural students have: (1) Higher grades ( ); (2) Equal grades ( ); (3) Lower grades ( ) d. When extra-mural students are compared with regular residence students who have not had extra-mural study, the extra-mural students are of: (1) Superior ability ( ); (2) Equal ability ( ); (3) Inferior ability ( ) Consider ability as meaning capability or intelligence. e. When extra-mural study and residence study are considered from the standpoint of helpfulness to the student, extra¬mural study is: (1) Superior ( ); (2) Equal ( ); (3) Inferior ( ) C. Time requirement of teacher per student per hour of credit* Use the actual conditions that apply to your classes in residence, in correspondence, and in class extension study; and give *To illustrate: Suppose that the size of the average class in residence is 15 students, that the class meets 5 one-hour periods per week for 12 weeks, and that the teacher spends additional 1.5 hours a day on the class in preparation of lessons and marking papers. Hence during the quarter the teacher spends 150 hours on this class—10 hours per student—and each student earns 5 term hours of credit. Hence the teacher gives 2 hours of time to each student for each term hour of credit earned. Now compute in your own way the time that is required of the teacher for a student to earn one term hour of credit in correspondence study, and one term hour of credit in extension study. If you prefer to use semester hour, do so, and indicate the fact by striking out the word “term” in (a) above and inserting the word “semester”. In computing time required of teacher in correspondence study, include time used for preparing questions, marking papers, selecting reference material, etc. In computing time required of teacher in extension study, include preparation of lessons, teaching of classes, marking of papers; and add to this from 1/3 to 1/2 of the time spent in making trips for the class, proportioning the amount added to the difficulty of the trip—long drives, exposure, loss of sleep, etc. (Page 39) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 39 your answers to the following questions by placing the proper figures in the parentheses in each group below. a. Number of hours required of teacher for a student to earn one term hour of credit: (1) 1 correspondence student = how many ( ) residence students. (2) 1 class extension student = how many ( ) residence students. Signature............... Position or title....................School....... City..................... State................. b. Reasons for offering extra-mural study Section (A) of this questionnaire was answered by 152 persons. The following tabulation shows the consensus of opinion of those replying: TABLE I REASONS FOR OFFERING EXTRA-MURAL STUDY First Second Third Total (a) 81 24 24 129 (b) 21 51 38 110 (c) 6 23 43 72 (d) 31 26 19 76 (e) 12 25 26 63 (f) 1 3 2 6 Total 152 152 152 456 The letters a, b, c, d, e, f refer to the headings listed in (a) of the questionnaire. It is seen that (a), “Improves teachers while in service”, heads the list as the chief reason for offering extra-mural courses, and also in the column of totals it has the largest frequency. We observe that (c), “Leads to residence enrolment”, stands lowest in the first column if (f) is excluded. Six persons, or 4 per cent of those replying, mention this reason as the chief one for offering extra-mural courses; twenty-three persons, or 15.1 per cent of those replying, mention it as the reason of second order in importance; forty-three persons, or 28.3 per cent of those replying, mention it as the reason of third order in importance; whereas 72 persons, or 47.4 per cent of those replying, refer to ultimate residence enrolment as a reason for offering extra-mural study. Table I is not a bad showing for number (c) when it is re-called that none of the other headings excludes (c) and might readily imply it. (Page 40) 40 THE RELATION OF EXTRA-MURAL STUDY TO II. RELATIONS AND COMPARISONS EXPRESSED, THROUGH QUESTIONNAIRE 1. Tabulation of replies Let us now turn to section (B) of the same questionnaire. The following tabulation shows the consensus of opinion regarding the questions raised: TABLE II RELATIONS AND COMPARISONS IN KIRKSVILLE QUESTIONNAIRE Number of Replies (a) Influence of extra-mural study on residence enrolment Pronounced Moderate Inconsequential Total 51 87 11 149 (b) Extra-mural grades compared with residence grades Higher Equal Lower Total 28 101 21 150 (c) Comparison of residence grades of students having both extra¬mural and residence study with grades of those having residence study only Higher Equal Lower Total 25 100 6 131 (d) Extra-mural students compared with students with residence study only Superior Equal Inferior Total 24 109 10 143 (e) Extra-mural study compared with residence study Superior Equal Inferior Total 9 43 99 151 2. Interpretation and conclusions In Table II, (a), (b), (c), (d), and (e) refer to the questions asked under (B) of the questionnaire. From (a) it is observed that 51 persons, or 31.5 per cent of those replying, believe that the influence of extra-mural study in leading to later residence enrolment is pronounced; 87 persons, or 61.1 per cent, believe its influence is moderate; whereas 11 persons, or 7.4 per cent, believe it is inconsequential. So the belief is common, though probably not often expressed, that extra-mural study leads to residence enrolment. (Page 41) Residence Enrolment and Scholastic Standing 41 In (b) the consensus of opinion is that extra-mural and residence grades are about the same, with the weight of opinion slightly inclined to the view that extra-mural grades are higher. In (c) the view is expressed that the residence grades of persons having both residence and extra-mural credit are higher than the grades of those having residence study only. In (d) the view is expressed that, extra-mural students have ability superior to that of students who have had residence study only. In (e) the consensus of opinion is that extra-mural study is decidedly inferior to residence study from the standpoint of helpfulness to the student. When this same question was referred to 148 students who had both residence and extra-mural study, 22 said that extra-mural study is superior; 95, equal; and 31, inferior to residence study. III. TIME REQUIRED OF TEACHER FOR A TERM HOUR OF CREDIT The following tabulation gives the consensus of opinion expressed in section (C) of the questionnaire as to the time required of the teacher in the various types of study: TABLE III NUMBER OF HOURS REQUIRED OF TEACHER FOR STUDENT TO EARN ONE TERM HOUR OF CREDIT Number of hours Type of study 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 Total Residence 9 49 37 6 8 2 3 114 Extension 4 21 12 12 12 6 2 2 2 1 2 1 1 1 79 Correspondence 1 18 20 16 13 4 3 0 5 1 2 0 1 2 3 2 1 92 Let A represent the arithmetic mean, and M, the median; let r, e, and c, used as subscripts, denote residence, extension, and correspondence respectively. We then have Ar = 2.26 Ae = 3.87 Ac = 4.86 Mr = 2.00 Me = 3.20 Mc = 3.44 It thus appears that residence instruction per term hour of credit requires the least time of the teacher; extension, next; and correspondence, the greatest amount of time. One hour of credit earned through extension study requires 1.71 times as much of the teacher’s time, measured in terms of means, as does one hour of credit earned through residence study, and likewise one hour of credit earned through correspondence study requires 2.15 times as much of the teacher’s time as one hour of credit earned through residence study. (Page 42) 42 THE RELATION OF EXTRA-MURAL STUDY TO IV. EXTRA-MURAL STUDENTS IN TERMS OF RESIDENCE STUDENTS When based on time required of teacher, the following tabulation reduces extension and correspondence students to equivalence in terms of residence students: TABLE IV EXTRA-MURAL STUDENTS IN TERMS OF RESIDENCE STUDENTS Type of student 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 Total Extension 13 26 21 7 1 2 2 0 0 0 0 1 73 Correspondence 11 22 21 4 7 7 2 0 2 1 1 1 79 Using the same notation as in Table III, Ae = 2.1 Ac = 2.9 Me = 2.0 Mc = 2.3 The table above represents the views of teachers of extra-mural courses as indicated by replies to part (C) of the questionnaire. It is seen that one extension student is considered as the equivalent of about two residence students, and that one correspondence student is considered the equivalent of from 2 to 3 residence students. These facts deduced from consensus of opinion were based on the time required of the teacher for a student to earn one hour of credit, and are in reasonable accord with the results derived from Table III. V. THE RELATION OF EXTRA-MURAL STUDY TO RESIDENCE ENROLMENT Concerning this question there is wide divergence of views. It is often said by faculty members and by administrators of normal schools and teachers colleges that extra-mural study increases residence enrolment. The same assumption is made in a recent bulletin issued by the Bureau of Education. Mr. Arthur J. Klein says, “Not only do correspondence students who take up residence work hold a high rank in scholarship, but the number of correspondence students who become residence students is forming an increasingly large proportion of residence students who graduate from the higher educational institutions. In the University of Indiana, in the graduating class of 1919, 38 of the candidates for a degree had taken part of their work by correspondence study. In the University of Kansas, in the fall of 1917, 36 out of a total of 580 correspondence students enrolled in the University. Under the war conditions of 1918 only 10 enrolled in the University, but even under these adverse conditions for the second year, 7.9 per cent of the enrolled correspondence students became residence students.”1 1U. S. Bureau of Education, Bulletin No. 10, 1920, p. 28. (Page 43) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 43 Mr. Klein adds further, “Mr. Mallory, Secretary of the correspondence study department of the University of Chicago, has said that—‘For 10 years or more, one out of every five who have entered into student relations with the university have done so through the correspondence study department. Of the total number who have begun with correspondence study courses from 18 to 20 per cent have come into residence. Out of the 230 students who received bachelor degrees, 47 had taken one or more majors by correspondence. All of the 47 averaged higher in their courses than did their classmates’.” Mr. Klein also says, “It is the common testimony of institutions that students in residence who have taken work by correspondence ordinarily rank in the upper fourth of their classes. In other words, the average of preparation, of earnestness, and of intellectual capacity of correspondence students, when compared with [sic] the average college student in residence, is far higher.” According to Mr. Klein’s statement, 36 out of 580 correspondence students enrolled in the University of Kansas; that is, 1 out of 16. Mr. Klein does not say whether or not these 36 students were enrolled first in correspondence, and then, later, became residence students. If any of these had earlier residence enrolments, and surely a great many of the 580 correspondence students had such enrolments, there is no credit accruing in such cases to extra-mural enrolment in producing residence enrolment. But, granting that none of these 36 had ever had an earlier residence enrolment, what standard for prospective students exists that recognizes 1 enrolment out of 16 prospects as a good showing? But in 1919, 7.9 per cent of those enrolled for correspondence study at the University of Kansas became residence students. The same questions apply to this statement as apply to the one preceding. If Mr. Mallory means that, at the University' of Chicago, 1 student out of every 5 in residence had enrolled first in correspondence, and then, later, entered the University for residence study this ratio would seem to be a good showing in favor of correspondence study as an influence leading to residence enrolment. However, all such data given out should say explicitly that the extra-mural study came first if it is to be considered as a causative factor in leading to residence enrolment. Mr. Klein’s statement, as well as Mr. Mallory’s, leaves the impression that extra-mural study is an important factor in building up residence enrolments. Mr. Clarence B. Collier asks, “Is it not probable that the privilege of having pursued one course in extension and receiving credit at the normal school, will induce the teacher (student) to enter for residence work?” Mr. Collier also says, “When an instructor from a normal school directs a group of teachers, many of them will see the need of further training and go to the normal (Page 44) 44 THE RELATION OF EXTRA-MURAL STUDY TO school, or go because of having made the acquaintance of the instructor.”2 VI. SUMMARY AND CONCLUSIONS It follows from the study of bulletins, the consideration of a master’s thesis, and the consensus of opinion in a questionnaire, that the improvement of teachers in service is the outstanding reason for offering extra-mural courses. With the expression of the purpose there appears a well defined belief that extra-mural instruction leads to residence enrolment. This view is strongly maintained in a bulletin by the Bureau of Education. Briefly stated, the consensus of opinion of administrators, teachers, and authors concerning extra-mural study is as follows: (1) The purpose of extra-mural instruction is to improve teachers while in service. (2) Extra-mural instruction is a strong factor in leading to residence enrolment. (3) Practically the same standards are used for residence and for extra-mural grading. (4) Residence grades of students having two types of study are higher than the residence grades of students having residence study only. (5) Extra-mural study is inferior to residence study. (6) Extra-mural students have superior ability when compared with students having residence study only. (7) One extension student is the equivalent of two residence students and one correspondence student is the equivalent of two or three residence students. (Computation is based on time required of teacher) The results noted above express consensus of opinion, and, in general, have no scientific bases of fact back of them. They show the trend of present day thought, and are referred to by way of comparison in subsequent chapters of this study. 2The Administration of Extension Courses in State Normal Schools, pp. 25, 28. (Page 45) CHAPTER III RELATION BETWEEN RESIDENCE, CORRESPONDENCE, AND EXTENSION ENROLMENTS In this chapter the following questions are considered: (1) When students have one type of study, are they likely to have other types also? (Type of study means either residence, correspondence, or extension study) (2) When students have two types of study, are they likely to have the third type also? (3) From what sources are correspondence and extension students drawn? I. MATERIAL USED This study begins with the State Teachers College at Kirksville. Let us consider all students enrolled in any type of study— residence, correspondence, or extension—for the four years June 1919 to June 1923. In this period 76 students had correspondence study only; 172, had extension study only; 3196, had residence study only; 10, had both correspondence and extension study, but not residence study; 201, had both extension and residence study, but not correspondence study; 455, had both correspondence and residence study, but not extension study; and finally, 131, had all three types of study. II. METHOD OF TREATMENT Use is how made of the theory of attributes such as is found in G. Udny Yule’s INTRODUCTION TO THE THEORY OF STATISTICS. The universe is the number of students enrolled at Kirksville during the years 1919-1923. 1. Notation Let (C) = number who had correspondence study. (c) = number who had no correspondence study. (E) = number who had extension study. (e) = number who had no extension study. (R) = number who had residence study. (r) = number who had no residence study. N = total number of students in universe. (CE) = number who had correspondence and extension study. (CR) = number who had correspondence and residence study. (ER) = number who had extension and residence study. (CER) = number who had correspondence, extension, and residence study. Similar interpretations hold for (Ce), (Cr), (Ec), (Er), (Re), (Rc), (CeR), (Cer), (CEr), (cER), (ceR), (cEr), and (cer). In accordance with the notation above we have Table V. (Page 46) 46 THE RELATION OF EXTRA-MURAL STUDY TO TABLE V POSITIVE CLASS FREQUENCIES FOR STUDENTS AT KIRKSVILLE (1919-1923) (C) = 672 (CR) = 586 (E) = 514 (ER) = 332 (R) = 3983 (CER) = 131 (CE) = 141 N = 4241 2. Consistency The first question that arises is whether or not the frequencies in Table V are consistent. The following four conditions must be satisfied for these data to be consistent:1 (a) (CE) = or > (C) + (E) + (R) — N — (RE) — (RC) (b) (CR) + (ER) — (EC) = or < (R) (c) (CR) — (ER) + (CE) = or < (C) (d) (CR) + (ER) + (CE) = or < (E) Substituting values from Table V, (a) gives 141 > 10 (b) gives 777 < 3983 (c) gives 395 < 672 (d) gives — 113 < 514 Therefore conditions (a), (b), (c), and (d) are satisfied, and the frequencies observed in Table V are consistent. The remaining class frequencies can now be computed. The whole number of class frequencies equals 27, and the third order class frequencies, as also the positive class frequencies, are eight in number.2 From Table V by the theory of attributes, we have Table VI. TABLE VI OTHER CLASS FREQUENCIES FOR STUDENTS AT KIRKSVILLE (1919-1923) (c) = N — (C) = 3569; (cE) = (E) — (CE) = 373 (cR) = (R) — (CR) = 3397; (cr) = (c) — (cR) = 172 (e) = N — (E) = 3727; (eR) = (R) — (ER) = 3651 (er) = (e) — (eR) = 76; (cER) = (ER) — (CER) = 201 (CeR) = (CR) — (CER) = 455; (CEr) = (CE) — (CER) = 10 (r) = N — (R) = 258; (Er) = (E) — (ER) = 182 (ceR) = (eR) — (CeR) = 3196; (Ce) = (C) — (CE) = 531 (Cer)— = (Ce) — (CeR) = 76; (cEr) = (cE) — (cER) = 172 (cer) = (er) — (Cer) = 0; (ce) = (c) — (cE) = 3196 (Cr) = (C) — (CR) = 86; Evidently (cer) would have to be zero, since there could not be a student without correspondence, extension, or residence study and this calculated value of (cer) is a further check on the accuracy of our data. 1Yule, An Introduction to the Theory of Statistics, p. 21. 2Yule, An Introduction to the Theory of Statistics, p. 13. (Page 47) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 47 We also have the following fundamental formulae of attributes: (1) (GER) + (cER) + (CeR) + (CEr) + (Cer) + (cEr) + (cer) + (ceR) = N (2) (R) = (ER) + (eR) = (CR) + (cR) (3) (C) = (EC) + (eC) = (RC) + (rC) (4) (E) = (QE) + (cE) = (RE) + (rE) (5) (r) = (Er) + (er) = (Cr) + (cr) (6) (c) = (Ec) + (ee) = (Rc) + (rc) (7) (r) = (Cr) + (cr) = (Er) + (er) These formulae are all satisfied by the frequencies in Tables V and VI. Since every item in the work checks, we are now prepared to use any association formulae that may be useful for showing relations between attributes involved. 3. Association formulae It is necessary to make use of both complete and partial association formulae in the analysis of data in Tables V and VI. By Yule3 if A and B denote any two characteristics, and a and b, their opposites, the following relations indicate positive association between A and B: (1) (AB)/(B) > (A)/N (2) (AB)/(A) > (B)/N (3) (AB)/(B) > (Ab)/(b) (4) (AB)/(A) > (aB)/(a) When these signs are reversed, there is negative association; when equal, independence. The interpretations are as follows: in (1) the proportion of A’s among the B’s is greater than the proportion of A’s in the whole material represented by N. A similar interpretation holds for (2). In (3) the proportion of A’s among the B’s is greater than the proportion of A’s among the not B’s. A similar interpretation holds for (4). It is generally preferable to use formulae (3) and (4) since they draw their material from an attribute and its contrary in the same universe, and in this way exhibit the full strength of the association. In partial association A and B are attributes in a universe C, in which C itself is an attribute. The formulae quoted above now become: (1) (ABC)/(BC) > (AC)/(C) (2) (ABC)/(AC) > (BC)/(C) (3) (ABC)/(BC) > (AbC)/(bC) (4) (ABC)/(AC) > (aBC)/(aC) The interpretations are as follows: in (1) the proportion of A’s 3An Introduction to the Theory of Statistics, p. 31. (Page 48) 48 THE RELATION OF EXTRA-MURAL STUDY TO among the (BC)’s is greater than the proportion of A’s among the C;s. A similar interpretation holds for (2). In (3) the proportion of A’s among the (BC)'s is greater than the proportion of A’s among the (b-minor C)’s. A similar interpretation holds for (4). III. ASSOCIATION BETWEEN TYPES OF ENROLMENT 1. Complete association a. Application to material Let us take as our material, the whole universe of enrolled students, N, as found in Tables V and VI. (a) Find the association between correspondence and extension enrolments. By formula (1) under complete association we have: (1) The ratio of extension students to all students = (E)/N = 514/4241 = 12.1 per cent. (2) The ratio of correspondence-extension students to cor-respondence students = (CE)/(C) = 141/672 = 21 per cent. But 21 > 12.1. Hence correspondence, and extension enrolments are positively associated in the universe of students. The proportion of correspondence students who take extension study is nearly twice as great as the proportion of students at large who take extension study. The association between extension and correspondence enrolments could also be found. But formulae (1) and (2), and (3) and (4) show that if C is positively associated with E, then E is also positively associated with C, but the associations are not always of the same strength. In the data under consideration extension, and correspondence enrolments have almost the same strength of association as do correspondence, and extension enrolments. However, the numerical calculation need not be set down. (b) Find the association between residence, and correspondence enrolments. (1) The ratio of residence students to all students = (R)/N = 3983/4241 = 93.9 per cent. (2) The ratio of residence correspondence students to correspondence students = (CR)/(C) = 586/672 = 87.2 per cent. But 93.9 > 87.2. Hence residence, and correspondence enrolments are negatively associated in the universe of students. Like- (Page 49) Residence Enrolment and Scholastic Standing 49 wise correspondence, and residence enrolments are negatively associated by about the same strength. (c) Find the association between residence and extension enrolments. (1) The ratio of residence students to all students = (R)/N = 3983/4241 = 93.9 per cent. (2) The ratio of residence-extension students to extension students = (RE)/(E) = 332/514 = 65.8 per cent. But 65.8 < 93.9. Hence residence, and extension enrolments are negatively associated in the universe of students. In (b) residence enrolment is negatively associated with correspondence enrolment. This association indicates that the proportion of residence students in the universe at large is greater than the proportion of residence students coining from all correspondence students alone. However, this result might have been anticipated since the universe is limited to all students: residence; correspondence; and extension for the years 1919-1923. Moreover, the residence enrolment is about seven times as great as the larger of the other two types, and R differs so little from N that there is but little chance for an association between residence and correspondence enrolments to show, unless that association were practically perfect. The proportion of students who have had correspondence, and extension study without residence study is relatively so small that the universe of students is exceptionally favorable to a high ratio for residence enrolment. (d) It is also instructive to find the association between correspondence and residence enrolment. By formula (1), (C)/N = 672/4241 = 15.9 per cent, and (CR)/(R) = 586/3983 = 14.9 per cent. But 14.9 < 15.9. Hence the association between correspondence and residence enrolments is, as might have been, expected, negative. This result shows that the proportion of correspondence students from the whole universe is but slightly greater than the proportion among residence students alone. But by using formula (3) as suggested previously the strength of the association is more evident. It gives (CR)/(R) = 586/3983 = 14.9 per cent, and (Cr)/(r) = 86/258 = 33.3 per cent. But 14.9 < 33.3 and the negative association is stronger than it at first appeared from formula (1). This result shows that the (Page 50) 50 THE RELATION OF EXTRA-MURAL STUDY TO proportion of correspondence students among residence students is about one-half as great as the proportion of correspondence students among those who have had no residence study. Nevertheless, large numbers of correspondence enrolments come from among those who have also been enrolled in residence. Similar observations hold in connection with the association between residence and extension enrolments, except that extension enrolments are not so frequently drawn from among residence students as are correspondence enrolments. b. Conclusions From this discussion three outstanding facts appear: (1) there is a very strong positive association between correspondence and extension enrolments; in other words, correspondence students tend to take extension study, and extension students tend to take correspondence study. (2) Correspondence students, and to a lesser degree extension students, consist of those who have had residence study also. (3) The negative association between residence and correspondence enrolments, and between residence and extension enrolments can to a large extent be accounted for by the fact that residence students so largely make up the universe of students that the proportion of residence students in the whole universe naturally would be larger than the proportion of residence students from among either correspondence or extension enrolments. Hence we are not justified in saying that correspondence, and extension enrolments restrain residence enrolments. 2. Partial association a. Application to material ; Let us now apply partial association formulae to the material. (a) Find the association between correspondence and extension enrolments in the universe of residence students. (1) R—universe (1) The ratio of extension, among correspondence students = (CER)/(CR) = 131/586 = 22.4 per cent. (2) The ratio of extension, among the non-correspondence students = (cER)/(cR)= 201/3397 = 6 per cent. But 22.4 > 6. Hence correspondence, and extension enrolments are strongly associated in the universe of residence students. (b) Find the association between residence and correspondence enrolments in the universe of extension students. (Page 51) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 51 (2) E—universe (1) The ratio of residence, among correspondence students = (CER)/(CE) = 131/141 = 92.6 per cent. (2) The ratio of residence, among non-correspondence students = (cER)/(cR) = 201/373 = 54 per cent. But 92.6 > 54. Hence residence, and correspondence are positively associated in the universe of extension students. (e) Find the association between residence and extension enrolments in the universe of correspondence students. (3) C—universe (1) The ratio of residence, among extension students = (CER)/(CE)= 131/141 = 92.6 per cent. (2) The ratio of residence, among non-extension students = (CeR)/(Ce) = 455/531 = 85.7 per cent. But 92.6 > 85.7. Hence the association between residence and extension study is positive in the universe of correspondence students. However, this association is not nearly as strong as that between residence and correspondence students in the universe of extension students. b. Conclusions Correspondence, and extension enrolments are strongly associated in the universe of residence students; residence, and correspondence enrolments are strongly associated in the universe of extension students.; and residence, and extension enrolments are positively associated in the universe of correspondence students. Then, in so far as the actual status of enrolments is concerned, residence serves as a connecting link between correspondence and extension enrolments; extension, as a connecting link between residence and correspondence enrolments; and correspondence, as a connecting link between residence and extension enrolments. In other words, when a student has had two of these types of study, there is a strong probability of his having had the third type also. IV. SUMMARY AND CONCLUSIONS Thus far without any reference to the type which preceded and the causal factors involved, enrolments in different types of study have been considered merely as accomplished facts. Both complete, and partial association formulae show that correspondence, (Page 52) 52 THE RELATION or EXTRA-MURAL STUDY TO and extension enrolments are strongly associated. The results are not conclusive concerning the association between residence and correspondence enrolments, or between residence and extension enrolments. In the whole universe these associations are negative, but they can be accounted for by the constitution of the universe. The association between residence and correspondence enrolments is positive in the universe of extension students; and the association between residence and extension enrolments is positive in the universe of correspondence students. But here also, the universe of prospective students is too limited. Moreover; since extension serves as a connecting link between residence and correspondence enrolments, and correspondence serves as a connecting link between residence and extension, enrolments, both a correspondence and an extension enrolment are needed to predict with any certainty a residence enrolment also. However, correspondence students, and, to some extent extension’ students, consist largely of persons who have had residence study. From the preceding discussion these facts follow: (1) Correspondence and extension enrolments are strongly associated. Hence correspondence students tend to take extension study and vice versa. (2) Students who have had both correspondence and extension study will, in general, have residence study also. (3) Correspondence students and, to a less degree, extension students consist of those who had residence study also. It is significant that extra-mural students consist chiefly of students who have had residence instruction also. But it is clear that only a preliminary survey has been made of the questions at issue. There are factors involved which are more fundamental than is the relation between types of enrolment. When a student has been enrolled in two or three types of study at an institution, the order in which the enrolments took place becomes very important when the type of enrolment which led to the other types is to be determined. In this chapter these factors have been left out of account, and the universe selected is too limited. (Page 53) CHAPTER IV INFLUENCE OF EXTRA-MURAL STUDY ON RESIDENCE ENROLMENT In this chapter the following questions are considered: (1) Through what type of study do residence students have their first connection with a school? (2) Through what type of study do extra-mural students have their first connection with a school? (3) Does extra-mural study increase residence enrolment? (4) Are extra-mural students better prospective residence students than are public school teachers at large? I. WHOLE UNIVERSE OF STUDENTS, (1919-1920) 1. Description of universe The consideration of the relation between extra-mural study and residence enrolment is now based upon another set of data. In this chapter both the residence and extra-mural students at Kirksville are taken for the year June, 1919 to June, 1920. These data differ materially from those in Chapter III. The data used in Chapter III apply to the four years from 1919-1923, and take no account of the order in which residence and extra-mural enrolments took place. The data in the preceding chapter, and accompanying interpretations merely recorded existing facts and status of enrolments with no particular effort to get at primal or causation factors which would show the dependence of one type of study on another type. Type of study means residence, correspondence, or extension study. The last two are sometimes combined under the single head of extra-mural or non-residence study. A similar meaning holds for type of student. Order of enrolment indicates the numerical sequence of type of study as first, second, or third. Sometimes it is used to indicate no enrolment at all. 2. Relation between type of student and first enrolment ; a. Expressed by coefficient of association We shall now find in the universe of students for the year 1919-1920 the association between being a residence student and first enrolment in residence, and also between being an extra-mural student and first enrolment in residence. Universe of students, (1919-1920) Let (R) = number of residence students. (r) = number of non-residence students. (A) = number of students with first work done in residence. (a) = number of students with first work not done in residence. Then (RA) = number of residence students with first study done in residence. (Ra) = number of residence students with first study not done in residence. (Page 54) 54 THE RELATION OF EXTRA-MURAL STUDY TO (rA) = number of non-residence students with first study done in residence. (ra) = number of non-residence students with first study not done in residence. Where only two attributes are involved, a coefficient of association can be used instead of association formulae. Yule gives this coefficient as Q = (AB)(ab) — (Ab)(aB) / (AB)(ab) + (Ab)(aB) where A is a first attribute and a, its opposite; B, a second attribute and b, its opposite.1 Data to which this formula applies can be conveniently arranged in a table. The following tabulation gives the data for Kirksville State Teachers College in terms of the notation employed for the universe of students for 1919-1920: TABLE VII RELATION BETWEEN TYPE OF STUDENT AND ORDER OF ENROLMENT* (R) (r) N (A) 1421 282 1703 (a) 16 79 95 N 1437 361 1798 Q = (1421)(79) — (282)(16) / (1421)(79) + (282)(16) = .923 This coefficient shows that residence students are very strongly associated with first work in residence. It indicates that nearly all residence students have their first connection with the school through residence study. Were Q = 1, the association between A and R would be complete, and all students of the institution would have had residence enrolment first. The association of R with a, that is, the association of residence students with first enrolment in extra-mural study, is Q = —.923. This coefficient shows that among students in general the probability is very great that a given residence student did not have extra-mural study first. Now the significant fact is not that there is positive association between residence students and first enrolment in residence, for we should expect this, but that the association is so nearly perfect. If the association coefficient had been .077 larger, then no residence student would have had extra-mural study 1Yule, An Introduction to the Theory of Statistics, p. 38. *196 students are counted twice, once in residence and once in extra-mural study since they were enrolled once in each type of study during the year. (Page 55) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 55 first. If (Ra), the number of residence students with extra-mural study first, were equal to zero instead of 16, then Q would equal one, and the association would be complete. b. Expressed by association formulae and by percentages Association formulae (3) and (4) of Chapter III may be used for getting a more detailed understanding of the relations involved. We have by referring to Table VII (1) (RA)/(A) = 1421/1703 = 83.4 per cent (Ra)/(a) = 16/95 = 16.8 per cent (2) (RA)/(R) = 1421/1437 = 98.8 per cent (rA)/(r) = 282/361 = 78.1 per cent From (1) it follows: first, that residence students and first enrolment in residence are positively associated; second, that 83 persons out of each 100 who had in our universe first work in residence were enrolled as residence students in 1919-1920; third, that the ratio of residence students (1919-1920) having had first work in residence to all students having first work in residence is five tim.es as great as the ratio of residence students having first work in extra-mural study to all students having first work in extra-mural study. From (2) it follows: first, that residence students and first enrolments are positively associated; second, that 99 persons out of each 100 in residence had residence work first; third, that 78 persons out of each 100 enrolled in extra-mural work (1919-1920) began with residence study. These figures show that only 22 persons out of each 100 who were enrolled in extra-mural courses in 1919-1920 had their first connection with the school through extra-mural study. Let us write down from Table VII the two ratios: (3) (RA)/(R) = 1421/1437 = 98.8 per cent (4) (Ra)/(r) = 16/361 = 4.4 per cent From (3) the ratio of residence students, with first enrolment in residence, to all residence students is .988. From (4) the ratio of residence students, with first enrolment not in residence, to all non-residence students is .044. Then for the year 1919-1920 the ratio of residence students, with first enrolment in residence, to all residence students is 22.5 times as great as the ratio of residence (Page 56) 56 THE RELATION OF EXTRA-MURAL STUDY TO students, with first enrolment in extra-mural study, to all extra-mural students. 3. Comparisons It is thus seen that, if extra-mural instruction is furnished to approximately 23 students, one of them will come into residence study after having had extra-mural study first. Moreover, ratio (4) shows that 361 different extra-mural students were enrolled, but among the residence students only 16 were enrolled who had had extra-mural study first. Accordingly ordinary common sense would indicate that residence enrolment is not being advanced perceptibly through extra-mural study. These conditions are found in an institution that has been offering large numbers of extra-mural courses for the past ten years. But some one will say here, just as it was suggested for the universe in Chapter III, that the residence enrolment is so large that the ratio (RA)/(R) is bound to be very large, and that of course the association between R and A is positive. However, it was pointed out that the significant fact is not that the association is positive, but that it is so nearly perfect, nevertheless, there is some merit in the contention, and to meet the objection the universe is now limited to the students of 1919-1920 who have had at any time both residence and extra-mural study. These students are acquainted with both types of study; hence, the order of then enrolments in college should be significant. II. UNIVERSE OF STUDENTS WHO HAD BOTH RESIDENCE AND EXTRA-MURAL STUDY, (1919-1920) 1. Relation between residence enrolments and first enrolments a. Expressed by coefficient of association Each student is now counted once in each kind of enrolment. Kind of enrolment means residence or non-residence enrolment; In the universe chosen Let (R) = number of residence enrolments. (r) = number of non-residence enrolments. (F) = number of enrolments coming first. (f) = number of enrolments not coming first. Then (RF) = number of residence enrolments coming first. (rF) = number of non-residence enrolments coming first. (Rf) = number of residence enrolments not coming first. (rf) = number of non-residence enrolments not coming first. The following tabulation in terms of the notation just adopted gives the data as observed at Kirksville: (Page 57) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 57 TABLE VIII RELATION BETWEEN KIND OF ENROLMENT AND ORDER OF ENROLMENT (F) (f) N (R) 481 20 501 (r) 20 481 501 N 501 501 1002 Q = (481)(481) — (20)(20) / (481)(481) + (20)(20) = .996 In this universe also, there is almost perfect association between residence enrolments and first enrolments. It is not surprising that the association is positive and large, but, if extra-mural study were functioning appreciably in bringing students into residence, Q would fall considerably below unity in this universe which contains only students who have had both residence and extra-mural study. b. Expressed by association formulae and by percentages Another picture of the relations involved is obtained by using the association ratios. We have: (1) (RF)/(R) = 481/501 = 96 per cent (2) (rF)/(r) = 20/501 = 4 per cent But 96 > 4. Hence there is a very strong positive association as previously observed between R and F. Out of every hundred students who have had both types of study, 96 had residence study first and 4 had extra-mural study first. Furthermore, it is called to mind that we are not dealing with students en masse but with just those who have had both residence and extra-mural study. 2. Observations But again some may think that our universe is still too narrow to permit extra-mural study to make a fair showing in its influence on residence enrolments; whereas others may hold that to bring into residence one student out of every 23 to 25 who take extra-mural study is a better showing than is made by most agencies when dealing with fair samples of eligible, prospective school populations. Were it possible to select two or three thousand persons who are likely to attend college, and approximately an equal number, who have extra-mural study without residence study, then these samples of prospective college students could be observed through a period of years, and the direct influence of extra-mural study on residence enrolment could be determined very definitely by asso- (Page 58) 58 The RELATION OF EXTRA-MURAL STUDY TO ciation formulae. However, for immediate purposes this direct plan is manifestly impossible. But this condition can be approximated by a plan which meets the objection offered to a universe that may have seemed to some too restricted. The writer has, therefore, extended the study to include a wider universe that represents, he believes, a typical teachers college prospective student constituency. III. UNIVERSE OF PUBLIC SCHOOL TEACHERS OF NORTHEAST MISSOURI, (1921-1922) 1. Description of universe The Kirksville State Teachers College has been offering both correspondence and extension courses since 1913, and has enrolled in credit courses 1072 different extra-mural students from 1914 to 1922, giving persons who have desired it, the opportunity to take extra-mural study; therefore, the influence of extra-mural study on residence enrolment is considered from the standpoint of teachers in service in northeast Missouri in the year 1921-1922. There were 3457 public school teachers in the 25 counties comprising the First District in which the Kirksville State Teachers College is situated.2 By a questionnaire to county and city superintendents the names and addresses of 2664 teachers were secured. This number constitutes 74.1 per cent of the whole teaching population, and, doubtless, is a fair sample. Moreover, the Teachers College at Kirksville is a state institution for preparing teachers, and nearly all the persons who attend it become teachers. Hence it appears that the teachers of northeast Missouri constitute a fair sample of eligible, prospective students for the Teachers College. Also metes and bounds are set that make this sample of teachers conform as nearly as possible to the direct and almost ideal plan of procedure that was proposed, but which for obvious reasons had to be abandoned. Now in as much as the influence of extra-mural study has been operating since 1913, and in as much as only 97 of the 2664 teachers were enrolled in residence before 1914, it is evident that the sample selected contains a representative part of the teachers of each year between 1914 and 1921 that entered and were eligible to enter the State Teachers College at Kirksville. 2. Factors affecting residence enrolment In this problem as set, a point of beginning is needed before which everything is barred save the one item of residence enrolments before that date. Those who enrolled before 1914, especially if they have not been in school since, reduce slightly the influence of extra-mural study on residence enrolment, in as much as they increase first enrolments in residence without offering appreciable opportunity for extra-mural study in the period before 1914. But these early residence enrolments total only 97, 2Report of State Superintendent of Public Schools, 1921. (Page 59) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 59 and are probably more than offset by a counter influence represented by the large number of untrained teachers that enter the profession each year and have as yet had little or no opportunity to attend college at Kirksville. The same reasoning applies to those teachers under 21 years of age who do not have sufficient high school credits to enter, college. Doubtless, these factors are pronounced among new teachers of the year 1920-1921 who have had no chance or incentive as yet to attend college. In these ways the number in the universe of teachers is increased and, since enrolment in residence has not yet begun to take place among the young, untrained teachers, the association between residence and first enrolments will be materially reduced. However, a second tabulation is made in which the 97 teachers enrolled in residence before 1914 are excluded entirely, but the factors unfavorable to the association of residence with first enrolment in residence are retained. 3. Data and notation From the enrolment files of the State Teachers College the type, and order of enrolment, time of enrolment, and number of hours of credit for these 2664 teachers were looked up and tabulated. All these items were considered from the standpoint of the Kirksville State Teachers College alone. For obvious reasons earlier and later connections with other colleges were wholly disregarded. The tabulation is as follows: TABLE IX TEACHERS OF NORTHEAST MISSOURI, (1921-1922) (1) Total number in sample............................2664 (2) Number who had residence study only...................694 (3) Number who had extra-mural study only..................32 (4) Number who had both residence and extra-mural study....187 (a) Number in (4) who had residence study first............173 (b) Number in (4) who had extra-mural study first..........14 (5) Total number who had residence study first ........... 867 (6) Total number who had extra-mural study first............46 (7) Total number who had attended school at Kirksville......913 (8) Total number who had not attended school at Kirksville...1751 This table serves as a basis for further analysis. 4. Association between type of study and first enrolment a. Residence study and first enrolment in extra-mural study (1) Notation for universe of teachers Let (E) = number whose first enrolment was extra-mural. (e) = number whose first enrolment was not extra-mural; that is, all teachers not included in (E). (R) = number who had residence study at Kirksville. (r) = number who had no residence study at Kirksville. (Page 60) 60 THE RELATION OF EXTRA-MURAL STUDY TO Table IX—(Continued) Then (RE) = number with residence study whose first enrolment was extra-mural. (Re) = number with residence study whose first enrolment was not extra-mural. (rE) = number without residence study whose first enrolment was extra-mural. (re) = number without residence study whose first enrolment was not extra-mural. (2) Tabulation for universe of teachers The application of this notation to the material in Table IX gives the following table for the universe of teachers in northeast Missouri for the year 1921-1922: TABLE X RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT (R) (r) N (E) 14 32 46 (e)867 1751 2618 N 881 1783 2664 Q = (ER)(er) — (Er)(eR) / (ER)(er) + (Er)(eR) = (14)(1751) — (32)(867) / (14)(1751) + (32)(867) = —.062 The association between R and E is small and negative. When the whole universe of teachers in northeast Missouri is considered, Q shows that there is a slight negative association between residence study at Kirksville and first enrolment in extra-mural study. In other words, when teachers at large are considered some new, and some old, some students and some graduates of other colleges, some just graduated from high school and some who have been students at Kirksville, it is found that a teacher who begins study as an extra-mural student at Kirksville is less likely to enroll there for residence study than is a teacher selected at random from the universe of teachers exclusive of those who have had residence study at Kirksville. The test just applied is surely a fair one. Teachers and high school graduates who expect to become teachers represent the universe of prospective students. The association between R and E in the universe of teachers should have been positive if there had been any appreciable influence exerted by extra-mural study on residence enrolment. b. Extra-mural study and earlier residence enrolment The influence of first enrolment in residence on later extra-mural study is now considered. (Page 61) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 61 (1) Notation for universe of teachers Let (R) = number whose first enrolment was in residence. (r) = number where first enrolment was not in residence; that is, all teachers not included in (R). (E) = number who had extra-mural study. (e) = number who had no extra-mural study; that is, all teachers not included in (E). Then (RE) = number with extra-mural study whose first enrolment was in residence. (Re) = number with no extra-mural study whose first enrolment was in residence. (rE) = number with extra-mural study whose first enrolment was not in residence. (re) = number with no extra-mural study whose first enrolment was not in residence. (2) Tabulations for universe of teachers By using this notation and applying it to the material in Table IX we have the following table: TABLE XI RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT (R) (r) N (E) 173 46 219 (e)694 1751 2445 N 867 1797 2664 Q = (RE)(re) — (Re)(rE) / (RE)(re) + (Re)(rE) = (173)(1751) — (46)(694) / (173)(1751) + (46)(694) = .809 Extra-mural study is strongly associated with earlier residence enrolment; therefore, extra-mural enrolments consist chiefly of persons who have had earlier residence study. This result fits in perfectly with that obtained in connection with Table X. Accordingly in the universe of teachers there is (1), a slight negative association between residence study and first enrolment in extra-mural study; (2), a strong positive association between extra-mural study and first enrolment in residence. Now let us exclude the 97 teachers referred to in Table IX who had enrolled at Kirksville before 1914. This proposal is more than fair to extra-mural study considered as a factor in advancing residence enrolment, since many of the 97 teachers who had taken residence study before 1914, had residence study again after 1914 before they ever had taken any extra-mural study. However, the whole group of 97 is excluded. Table IX now becomes (Page 62) 62 THE RELATION OF EXTRA-MURAL STUDY TO TABLE IXa TEACHERS OF NORTHEAST MISSOURI—RESTRICTED UNIVERSE, (1921-1922) (1) Total number in sample.............................2567 (2) Number who had residence study only...................626 (3) Number who had extra-mural study only.................32 (4) Number who had both residence and extra-mural study...158 (a) Number in (4) who had residence study first..........144 (b) Number in (4) who had extra-mural study first........14 (5) Total number who had residence study first...........770 (6) Total number who had extra-mural study first..........46 (7) Total number who had attended school at Kirksville...816 (8) Total number who had not attended school at Kirksville..1751 By using the same notation applied in Tables X and XI respectively, we have: (a) Association between residence study and first enrolment in extra-mural study TABLE Xa RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT (R) (r) N (E) 14 32 46 (e) 770 1751 2521 N 784 1783 2567 Q = (ER)(er) — (Er)(eR) / (ER)(er) + (Er)(eR) = (14)(1751) — (32)(770) / (14)(1751) + (32)(770) = —.0026 The association is slightly negative still. (b) Association between extra-mural study and first enrolment in residence study TABLE XIa RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT (R) (r) N (E) 144 46 190 (e) 626 1751 2377 N 770 1797 2567 Q = (RE)(re) — (Re)(rE) / (RE)(re) + (Re)(rE) = (144)(1751) — (46)(626) / (144)(1751) + (46)(626) = .795 The association is still strong and positive; therefore, the coefficients of association in Tables Xa and XIa are not altered (Page 63) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 63 in any material way from those found in Tables X and XI; in fact, these latter values strengthen appreciably our interpretation of results found in Tables X and XI. 5. Summary and comparisons Under Tables X and Xa the values of the coefficients of association are respectively Q=—.062 and Q=—.0026. These co-efficients show a slight negative association between residence study and first enrolment in extra-mural study. They indicate that teachers of northeast Missouri, taken at large, are slightly more likely to attend the Teachers College at Kirksville than are students who had extra-mural study first. It is also seen that, if the 97 teachers who had residence study before 1914 are excluded, the association is still slightly negative. To be sure the negative association is very small, and also (RE) and (rE) are smaller numbers than are desirable, since small changes especially in (RE) affect results greatly. On the other hand, use is made of all available data in connection with 2664 public school teachers of northeast Missouri, where their records have been scrutinized for attendance, type of study, and order of enrolment in a teachers college that has been offering extra-mural study on a large scale since 1913. The sample of teachers used is for the year 1921-1922. It includes persons who were attending school at Kirksville, or were eligible to attend in every year from 1914 to 1922. It is a mosaic of the cross sections of each year, and is a good substitute for the ideal condition mentioned earlier which would have required a large sample of high school graduates interested in teaching, and about an equal number of extra-mural students who had never had residence study. However, if such data were available for a number of years, there is all reason to believe extra-mural students would make a poorer showing in promoting residence enrolment than is made in our sample. Substantiation of this statement appears from the following considerations: (re) = 1751 in Table X, and Q increases directly as (re) increases. But Q = (RE)(re) — (Re)(rE) / (RE)(re) + (Re)(rE) = —.062 in Table X. Now (re) included hundreds of new, inexperienced teachers who have not had a chance to attend college, some of them are not even high school graduates and are not prepared to attend college, whereas others included in (re) are graduated from other colleges, and are for this reason eliminated as prospective college students at Kirksville. These types of individuals are congregated especially in that cross section of our sample that represents the new teachers of the year 1921-1922. They increase Q. To illustrate: if (re), which represents teachers who have had no study of any type at Kirksville, were doubled, Q would be positive instead of negative, and would equal .28 which would represent a strong positive association. (Page 64) 64 THE RELATION OF EXTRA-MURAL STUDY TO From the foregoing considerations it appears that the universe of prospective students has been extended even beyond its legitimate sphere, and that this extension increases mainly (re) which increases Q, the coefficient of association between residence study and first enrolment in extra-mural study, and that, if extra-mural study had any perceptible influence on residence enrolment, Q should be strongly positive instead of slightly negative. Moreover, from Tables XI and XIa it is seen that extra-mural study is strongly associated with first study in residence. It follows that nearly all extra-mural students have residence study first. 6. Intensity of associations Let us examine the intensity of association between attributes in the universe of teachers by comparing ratios. By Yule if |(RE)/(E)| >=< (RE)/(e), then R and E have respectively positive association, no association, or negative association.3 By referring to Table X, we have: (1) (RE)/(E) = 14/46 = .304; (Re)/(e) = 867/2618 = .331 (2) (RE)/(R) = 14/881 = .0159; (rE)/(r) = 32/1783 = .0179 Therefore in both cases residence study has a small negative association with first enrolment in extra-mural study. The ratios in (1) show that the proportion of residence students among all those who had taken extra-mural study first is less than the proportion of residence students among all those who did not take extra-mural study first. The ratios in (2) show that the proportion of those who had taken extra-mural study first among all those who had taken residence study is less than the proportion of those who had taken extra-mural study first among all those who had no residence study. Likewise from Table XI with a notation differing from that in Table X, we have: (3) (RE)/(E) = 173/219 = .790; (Re)/(e) = 694/2445 = .284 Therefore the association between extra-mural study and first enrolment in residence is strongly positive. The ratios in (3) show that the proportion of first enrolments in residence among extramural students is much greater than the proportion of first enrolments in residence among all those teachers who did not have extra-mural study. 3Yule, An Introduction to the Theory of Statistics, p. 31. (Page 65) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 65 The ratios in (1), (2), and (3) lead to the same conclusions, and furnish the same interpretations of facts as resulted from the use of coefficients of association. IV. Comparisons of ratios There are some interesting comparisons between ratios drawn from the universe of teachers for 1921-1922, and the whole universe of residence and extra-mural college students for the year 1919-1920. (a) Among the teachers of 1921-1922 who had both residence and extra-mural study, (the number with extra-mural study first)/(the number with residence study first) = 14/173 = .081. (b) Among the students of 1919-1920 who had both residence and extra-mural study, (the number with extra-mural study first)/ (the number with residence study first) = 20/481 = .042. Therefore, for those with both types of study, the ratio of teachers with extra-mural study first, to teachers with residence study first, is twice as great as the ratio of students with extra-mural study first, to students with residence study first. This result further strengthens the conclusions drawn from the sample of teachers in as much as persons with extra-mural study first when compared with persons with residence study first, are twice as numerous in the universe of teachers as in the universe of students. (a1) Under the conditions imposed in (a) (the number with extra-mural study first) ÷ (the number with extra-mural study only) = 14/32 = .438. (b1) Under the conditions imposed in (b) (the number with extra-mural study first) ÷ (the number with extra-mural study only) = 20/66 = .303. It is also observed that the number of persons with extra-mural study first, when compared with those having extra-mural study only, is greater among teachers of a given year than among students of a given year's enrolment. This result supports also the conclusions, drawn from the sample of teachers. (a2) Among the teachers of 1921-1922, 46 had taken extra-mural study first, and 867 had taken residence study first. Then (the number with extra-mural study first) ÷ (the number with residence study first) = 46/867 = .053. (b2) Among the students of 1919-1920, 85 had taken extra-mural study first, and 1520 had taken residence study first. Then (the number with extra-mural study first) ÷ (the number with residence study first) = 85/1520 = .056. In (a2) and (b2) the ratios were not confined to those who had taken both residence and extra-mural study as it was, in the two preceding comparisons. Here it is found that the ratio of persons, with extra-mural study first, to those, with residence study first, is almost exactly the same among teachers for 1921-1922 as among students in all types of study during 1919-1920. This result furnishes further justification, for the choice of the sample of teachers, and for the (Page 66) 66 THE RELATION OF EXTRA-MURAL STUDY TO conclusions drawn therefrom. In all probability the sample of teachers has shown for extra-mural study a stronger influence on residence enrolment than actually exists. V. CORRELATION BETWEEN RESIDENCE STUDY AND FIRST ENROLMENT IN EXTRA-MURAL STUDY—UNIVERSE OF TEACHERS Finally, if any one should question the validity of association formulae and of coefficients of association, in the problems of this chapter, another method of proof involving tetrachoric functions may be used. This method is probably the most accurate one known for dealing with fourfold tables. The process is long and difficult, hut it applies directly to the tables of this chapter. Since Table X holds a position of prime importance in this chapter tetrachoric functions are used in finding r, the coeficient of correlation between residence study and first enrolment in extra-mural study. This method is explained in Chapter I, and Table X furnishes the illustrative problem, so that we merely give the equation from which r is determined. It is as follows: r6 + .365r5 + .957r4 + 2.89r3 — 2.808r2 — 6.07r — .137 = 0 Whence r = —.023, with probable error of .021. The conclusion reached is identical with that obtained by use of coefficients of association. Restated it is as follows: residence study at Kirksville in the universe of teachers has a slight negative correlation with first enrolment in extra-mural study. VI. SUMMARY AND CONCLUSIONS The following outstanding facts, appear to be established: (1) Nearly all residence students have their first connection with the school through residence study. (2) The great majority of extra-mural students have residence instruction before they take up extra-mural study. (3) Extra-mural study does not increase residence enrolment appreciably. This fact is apparent from the consideration of: first, the universe of students for 1919-1920; second, the universe of students for 1919-1920 who had both residence and extra-mural study; third, the universe of teachers for 1921-1922. (4) Extra-mural students who have had no residence instruction in a school are hardly as good prospective residence students as are public school teachers, chosen at random, who also have had no residence instruction. It is especially significant that nearly all residence students have their first connection with a school through residence study, and that the great majority of extra-mural students have residence instruction before taking up extra-mural instruction. Extra-mural study does not affect residence enrolment appreciably, but residence study affects extra-mural enrolment a great deal. These facts are directly deposed to the consensus of opinion of educators as expressed in Chapter II, Part One. It is even more surprising that public school teachers constitute a better prospective student universe than do extra-mural students. (Page 67) CHAPTER V THE UNIVERSE OF HIGH SCHOOL GRADUATES AS A BASIS OF COMPARISON In this chapter the following questions are considered: (1) Is there a well defined relation between school preference of high school graduates and later college registration? (2) Is there a relation between school preference and time elapsed from high school graduation to college registration? I. NEED OF A STANDARD A standard of measurement is essential for purposes of comparison. If the relation between extra-mural study and residence enrolment is found, however small this relationship proves to be, one could maintain that it is entirely satisfactory unless there is a recognized basis of comparison that may be accepted as a standard of measurement. Therefore we delay the approach to our study, and seek to find a basis of comparison in a recognized universe of prospective students. The universe of high school graduates will be carefully studied. This universe is selected because the prospective student must be a high school graduate, or the equivalent, to meet college entrance requirements. The universe may be too broad, but on no other grounds can exception be taken. II. High school visitation In the winter and spring of 1921, six faculty members and five advanced students, and again in the winter and spring of 1922, three faculty members and four advanced students, at the Teachers College at Kirksville, visited high schools in northeast Missouri. These representatives of the college spent from one to two hours in each school, and devoted about two days each to the work. Forty-eight schools were visited in 1921, and forty, in 1922. These representatives were permitted to use 15 or 20 minutes in each school to explain to the senior class the purpose, function, equipment, curricula, and certificate requirements of the Teachers College. Afterwards, cards calling for the following information were distributed: 1. Name of student; 2. Home address; 3. Name of high school; 4. Name of teachers college, college, or university, student would like to attend after graduation; 5. Intention as to teaching; 6. Names of near relatives that have attended Teachers College at Kirksville. It was urged that students fill out item number (4) with the name of the school that they actually preferred, but, if they had no choice, with the words, “ no preference ”. In 1921 these cards were filled out by 1153 persons nearly all of whom were high school seniors and the rest teachers who had never been to Kirksville. The cards for 1922 were filled out by (Page 68) 68 THE RELATION OF EXTRA-MURAL STUDY TO 957 such persons. Schools in Adair County, where the college is situated, were not included in these high school visitations. The high school graduates of each year were now divided into three groups: (1) Kirksville preference; (2) No preference; (3) Other school preference. If no indication of school preference was given on the card, it was counted in the “no preference” group. After the lapse, of seven quarters, (June 1921-March 1923), the files of student records at the college were examined appertaining to the 1921 group, and after the lapse of five quarters, (June 1922-September 1923), the files were examined appertaining to the 1922 group for the following items: 1. Enrolment; 2. The quarter; 3. Number of months from June following the visitation to enrolment. The facts relative to these tabulations appear in the tables of this chapter. III. RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION 1. Need for knowing the relationship Is there any well defined relation between school preference and later college registration at a given institution? When this question is answered, it will be possible to compare the student universe, or any portion of it, with the high school graduate universe, or any portion of it as represented by “school preference”, “no preference”, or “other school preference”, and to know definitely the relative strength of each of these preference groups in regard to residence enrolment. 2. School preference, alternate variate a. High school data for 1921 Seven quarters elapsed from the time the data were collected until the study was made. TABLE XII RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION Registration at Kirksville Preference for Registration Non-registration Total Kirksville 151 286 437 No school 52 271 323 Other schools 39 354 393 Total 242 911 1153 η1 = .299 η2 = .328 This problem was worked out and explained in detail for Table XII, Chapter I, as an illustration of Pearson’s new method of correlation where one variable is given by alternative, and the other, by multiple categories. (Page 69) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 69 b. High school data for 1922 Five quarters elapsed from the time the data were collected until this study was made. TABLE XIII RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION Registration at Kirksville Preference for Registration Non-registration Total Kirksville 131 201 332 No school 29 246 275 Other schools 20 330 350 Total 180 777 957 Using Sheppard’s Tables, and formula (II) of Chapter I, which is formula (II) of Biometrika, Vol. VII, p. 249, we have, by taking first the upper row, then the sum of the two upper rows, sets of values (1) and (2). Sets (3) and (4) are obtained as explained in Chapter I. Set (1) Set (2) Set (3) Set (4) x̄/σx = -.3938 x̄'/σx = .3432 h/σx = .7370 x̄1 = .6064 x̄1'/σ1 = 1.2205 h/σ1 = .6141 σ1/σx = 1.2001 x̄2/σ2 = -.6475 x̄2'/σ2 = .1900 h/σ2 = .8375 σ2/σx = .8800 From sets (1) and (4), η1 = .456 From sets (2) and (4), η2 = .555 c. Interpretation It will be recalled in Chapter I for Table XII that means of x-arrays in set (1) show that, as we pass from registered to non-registered persons, the preference for Kirksville steadily declines. So also preference for Kirksville increases as we pass from non-registered to registered persons. Thus η1 = .299 and η2 = .328 indicate strong positive correlation, between Kirksville preference and registration. So also from Table XIII the mean of x-arrays in set (1) decreases (beginning always with the means of the first column) as we pass from registered to non-registered persons, and increases sharply as we pass from non-registered to registered persons. The x-variate is somewhat heteroscedastic, but the values of 17 are reasonably near each other. The lowest value indicates a stronger correlation than does the highest in Table XII. This sit- (Page 70) 70 THE RELATION OF EXTRA-MURAL STUDY TO uation is probably due to the fact that students who prefer other schools are slow in registering, and Table XII covers a period longer by two quarters than does Table XIII. 3. School registration, alternate variate As a cheek on our work let us take Tables XII and XIII, and make registration at Kirksville the alternate, or x-variate, and school preference the categoric, or y-variate, and apply formula (III) of Chapter I. a. High school data for 1921 TABLE XIIa RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION Registration at Kirksville Preference for Kirksville No school Other schools Total Registration 151 52 39 242 Non-registration 286 271 354 911 Total 437 323 393 1153 We find: x̄/σx = .8068, x̄1/σ1 = .3976, x̄2/σ2 = .9900, x̄3/σ3 = 1.2865 Therefore, by formula (III), Chapter I, η3 = .268. b. High school data for 1922 TABLE XIIIa RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION Registration at Kirksville Preference for Kirksville No school Other schools Total Registration 131 29 20 180 Non-registration 201 246 330 777 Total 332 275 350 957 We find: x̄/σx = .8848, x̄1/σ1 = .2672, x̄2/σ2 = 1.2056, x̄3 = 1.5800 Therefore, by formula (III), Chapter I, η3 = .473. c. Interpretation Table XIIa was discussed in Chapter I. But Tables XIIa and XIIIa are so much alike that what is said of one applies to the other also. (Page 71) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 71 By examining the means of x-arrays and beginning with under each table we find that they continuously increase as we pass from Kirksville preference, through no preference, to preference for other schools. This relation shows that non-registration continuously increases, that is registration decreases, in each table as we pass continuously from Kirksville preference to preference for other schools. It also shows that registration increases as we pass in the opposite direction from preference for other schools to preference for Kirksville. So here, as also under Tables XII and XIII, there is a strong positive correlation between school preference and later registration. Since the means of arrays increase continuously, registration, or the x-variate, is Gaussian, and since under Tables XII and XIII the school preference variate was found to be reasonably homoscedastic, formula (III) can be, used with confidence. Accordingly in two distinct sets of data, and by two methods of calculation the correlation ratios are found to be as follows: (1) For 1921, η1 = .299, η2 = .328, η3 = .268 (2) For 1922, η1 = .456, η2 = .555, η3= .473 In either case the correlation between school preference and residence registration is very high. 4. Strength of school preference a. Per cent of registration The strength of the three types of school preference, and of the three types combined, as exhibited through school registration where the time since graduation is also taken into account, shows well in a tabulation. These data are drawn from Tables XIIb and XIII. Table XIIb which is Table XII extended recently to 9 quarters is given at the close of this chapter. TABLE XIV RELATION BETWEEN SCHOOL PREFERENCE AND PER CENT OF LATER REGISTRATION Preference for Visitation 1921— 9 quarters elapsed Visitation 1922— 5 quarters elapsed The two visitations combined (1) Registration (2) Non-registration (3)Registration (4)Non-registration (5)Registration (6)Non-registration (1) Kirksville 40.5 59.5 3915 60.5 40.1 59.9 (2) No school 20.1 79.9 10.5 89.5 15.7 84.3 (3) Other schools 10.9 89.1 5.7 94.3 9.0 91 0 (4) All preferences combined 25.1 74.9 18.7 81.3 22.2 77.8 (Page 72) 72 THE RELATION OF EXTRA-MURAL STUDY TO b. Interpretation and comparisons This table reads as follows beginning with the upper row: 40.5 per cent of high school graduates (1921), with Kirksville preference, enroll at Kirksville within 9 quarters after graduation; 59.1 per cent do not enroll. A similar reading holds for the 1922 visitation. For the two visitations combined 40.1 per cent of high school graduates, with Kirksville preference, enroll at Kirksville; 59.9 per cent do not enroll. Similar readings hold for rows (2) and (3). In row (4) for the year 1921, 25.1 per cent of all graduates enroll at Kirksville within nine quarters; 74.9 per cent do not enroll. In 1922, 18.7 per cent enroll within 5 quarters; 81.3 per cent do not enroll. For both visitations combined 22.2 per cent of all graduates enroll at Kirksville; 77.8 per cent do not enroll. Thus four quarters add considerably to the registration. This fact is shown by the per cents in columns (1) and (3). Especially is it true under “no school” and “other school preference”. In four quarters additional, these per cents are doubled. Column five shows the minimum per cent from each preference group that may be expected to enroll for residence study. Thus 40.1 per cent of those who prefer Kirksville will enroll; 15.7 per cent of those who have no school preference will enroll; 9 per cent of those who prefer other schools will enroll; and 22.2 per cent of all high school graduates whose names are secured in the manner indicated will enroll. Of course, it is not maintained that the visitation brings the students to college; it merely furnishes the list of prospective students. 5. Conclusion It is now known definitely that, in the universe of high school graduates, those who prefer a school are the best prospective students by far, those who have no school preference are next, and those who prefer another school are last in the list. It is easy to secure such a list of prospective college students, and to divide them on the basis of interest into three groups which foretell well the probability of registration. A standard has been determined with which residence enrollment of extra-mural students may be compared. IV. TIME BETWEEN HIGH SCHOOL GRADUATION AND COLLEGE REGISTRATION 1. Preliminary statement The time that elapses between high school graduation and college registration as it applies to the “preference, “no preference”, and “other school preference” groups is also another question of interest. The writer has made a detailed study of this question as it applies to the high school graduates of 1921 and of 1922. But since similar data could not be secured on any extensive scale for extra-mural students, only a few striking tabulations with their interpretations are given. If we take from each (Page 73) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 73 list of high school graduates those who have registered for residence study at Kirksville, and form tabulations showing the quarters or seasons of the year during which they enrolled, beginning with the first summer after their graduation, each tabulation will show under each type of preference yearly cycles of change and seasonal fluctuations. It is evident that these two factors cannot well be treated in a single table. It is best to consider them by making one tabulation for the four quarters or seasons of the year, and another, with the summer quarters representing two or more years. 2. Registration by quarters a. Four quarters of the year Let us take the two lists of high school graduates, and form a single tabulation by quarters for a whole year beginning with the summer quarter, which was the first quarter of school after their graduation. S, F, W, and Sp. stand for summer, fall, winter, and spring respectively. TABLE XV RELATION BETWEEN SCHOOL PREFERENCE AND TIME OF LATER REGISTRATION Time elapsed from graduation to enrolment Preference for S F W Sp Total Kirksville 124 54 7 4 189 No school 31 13 2 1 47 Other schools 5 20 1 6 32 Total 160 87 10 11 268 Employing Sheppard’s Tables and using formula (II) of Chapter I, we have from the upper row set (I) and from the two upper rows combined set (2). Sets (3) and (4) are found as explained in Chapter I. The four sets are as follows: Set (1) Set (2) Set (3) Set (4) x̄/σx = .4139 x̄'/σx = 1.1785 h/σx = .7646 x̄1/σ1 = .7553 x̄1'/σ1 = 1.8643 h/σ1 = 1.1090 σ1/σx = .6895 x̄2/σ2 = .3074 x̄2'/σ2 = .7393 h/σ2 = .4319 σ2/σx = 1.7703 x̄3/σ3 = .5243 x̄2'/σ3 = 1.2812 h/σ3 = .7569 σ3/σx = 1.0102 x̄4/σ4 = -.3413 x̄4'/σ4 = -.1140 h/σ4 = .2273 σ4/σx = 3.3594 (Page 74) 74 THE RELATION OF EXTRA-MURAL STUDY TO From sets (1) and (4), η1 = .389 From sets (2) and (4), η2 = .470 These values of η show a high degree of correlation, and are in reasonably close agreement, though the alternate variate is very heteroscedastic. Beginning with x̄1/σ1 and x̄1'/σ1 in sets (1) and (2) of the means of x-arrays we observe that with one exception they continuously decrease. Hence for one year, beginning with the summer quarter, when registration is considered by quarters, the school preference variate is reasonably Gaussian. Moreover, with the one exception noted, Kirksville preference decreases as we pass from summer to spring on the time-axis. Therefore registration having Kirksville preference is negatively correlated with time elapsed between high school graduation and college registration. In other words, registration having preference for “other schools” is positively correlated with time as represented by the four seasons within the period of a year. This relation shows that, the stronger the preference is for a school, the earlier the enrolments take place within a given year. Moreover, this tendency is very strong as indicated by the large correlation ratio. It is interesting to note that if a second summer quarter is added to this table both values of η become imaginary which fact indicates the effect of introducing seasonal fluctuations also. However, the arrays of means indicate that the correlation is actually in harmony with that found in Table XV. b. Two consecutive summer quarters Let us now take two consecutive summer quarters representing a two year period, and use the combined data secured from the two high school visitations. S1 and S2 stand for first and second summers respectively. TABLE XVI RELATION BETWEEN SCHOOL PREFERENCE AND LATER REGISTRATION BY YEARS Time by two successive summers Preference for S1 S2 Total Kirksville 124 82 206 No preference 31 31 62 Other schools 5 17 22 Total 160 130 290 By using first the upper row we obtain set (1); by using the sum of the two upper rows, set (3). Sets (3) and (4) are obtained as explained in Chapter I. (Page 75) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 75 Set (1) Set (2) Set (3) Set (4) x̄/σx = .7104 x̄'/σx = .9241 h/σx = .2137 x̄1/σ1 = .7750 x̄'1/σ1 = .9750 h/σ1 = .2000 σ1/σx = 1.0865 x̄2/σ2 = .6307 x̄2'/σ2 = .8692 h/σ2 = .2385 σ2/σx = .8960 Using formula (II) of Chapter I, we find: From sets (1) and (4), η1 = .173 From sets (2) and (4), η2 = .192 The values of η are in close accord, and the alternate variate is reasonably homoscedastic. From the means in sets (1) and (2) it is seen that as we pass along the time-axis from first summer to second summer, preference for Kirksville decreases, or in other words Kirksville non-preference increases. This result shows that registration having Kirksville preference is negatively correlated with time as expressed by the lapse of two summers; whereas other school preference is positively correlated with the number of summers passed. Hence, it is seen that within the period of two years, as represented by the same seasons, those preferring Kirksville tend to enroll earlier than those not preferring it, and the stronger the preference the sooner the registration. These results are in accord with those observed in connection with the seasons of a single year. C. Three consecutive summer quarters After Tables XII, XV, and XVI were completed, and calculations made, the data involved in the cards for 1921 were brought to date by looking up registrations for two additional quarters. This procedure extends the data for Table XII to nine quarters which include three summer quarters. Thus the tabulation for the high school graduates of 1921 includes three consecutive summer quarters representing a three year period. The frequencies are small, but the tabulation is the best available. The notation is similar to that used in Table XVI. TABLE XVII Relation between school preference and later registration by years Preference for Time by 3 successive summers S1 S2 S3 Total Kirksville 64 49 16 129 No school 22 16 11 49 Other schools 2 11 7 20 Total 88 76 34 198 (Page 76) 76 THE RELATION OF EXTRA-MURAL STUDY TO First using the upper row, and, then, the two upper rows combined we have sets of valued (1) and (2) respectively. Set (1) Set (2) Set (3) Set (4) x̄/σx = .3892 x̄'/σx = 1.2756 h/σx = .8864 x̄1/σ1 = .6048 x̄1'/σ1 = 2.0020 h/σ1 = 1.3972 σ1/σx = .6272 x̄2/σ2 = .3711 x̄2'/σ2 = 1.0576 h/σ2 = .6865 σ2/σx = 1.2912 x̄3/σ3 = -.0738 x̄3'/σ3 = .8207 h/σ3 = .8945 σ3/σx = .9909 By formula (II), Chapter I, η1 = .04. The value for η2 is imaginary. However, when means of arrays are examined in both sets (1) and (2), they are found to decrease continuously as we pass from Kirksville preference, through no preference to preference for other schools. This situation indicates a slight negative correlation between Kirksville preference, and time measured by three consecutive years. The correlation, though small, appears to be significant, and is in harmony with the facts brought out in Tables XV and XVI. d. Comparisons and conclusions Facts deduced from Table XVII, and from other sources not given in this brief survey seem to indicate that after the second year the correlations noted between school preference and time, as represented by the seasons of the year; and between school preference and time, as represented by consecutive years, begin to disappear. However, this result may be due to the paucity of observations in later periods. There is a fruitful field for extensive research in this connection. Moreover, as the time is extended, the numerical value of the correlation, decreases. This result, taken in connection with Table XIV, helps to explain why the correlation ratio in Table XII for 7 quarters is less than in Table XIII for five quarters. Hence the conclusion is reached that school preference, and time elapsed before enrolment are negatively correlated for a limited period of time up to two or three years though the correlation decreases numerically with the lapse of time. This chapter gives a true insight into the prospective student universe as represented by high school graduates, and furnishes a valuable standard of comparison. e. Table XII, 1921, extended to 9 quarters Under (c) as noted, Table XII was brought up to date by the addition of two more quarters, making nine quarters all told. For future reference Table XIIb is inserted as Table XII, extended to nine quarters. (Page 77) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 77 TABLE XIIb Table XII, extended to 9 quarters (1921) Preference for Registration at Kirksville Registration Non-registration Total Kirksville 177 260 437 No school 65 258 323 Other schools 47 346 393 Total 289 864 1153 V. SUMMARY AND CONCLUSIONS (1) Correlation between school preference and later residence registration is very high. Approximately two years after high school graduation 40.1 per cent of those with Kirksville preference, 15.7 per cent of those with no preference, and 9 per cent of those who prefer other schools enroll at Kirksville. Also it is found that 22.2 per cent of all high school graduates enroll. (2) School preference, and time from high school graduation to college registration are negatively correlated for a limited period of 2 to 3 years. The stronger the school preference, the sooner enrolment takes place. Students with Kirksville preference tend to enroll first; next, those with no preference; and last of all, those who prefer other schools. The results of this chapter enable school administrators to apply standards of recognized worth to problems of residence enrolment. These standards can be determined for each school, and then each universe of prospective students can be dealt with on the bases of merit, and of probable returns. The universe of high school graduates thus collected and classified represents a universe of prospective students available for residence enrolment in every state teachers college. High school graduates come well, come uniformly, and come quickly if a preference exists; therefore, they are used as a basis of comparison to determine whether extra-mural students who have had extra-mural study first, constitute a desirable prospective student universe. (Page 78) CHAPTER VI EXTRA-MURAL STUDENTS AS PROSPECTIVE COLLEGE STUDENTS In this chapter, for the universe of extra-mural students with extra-mural study first, the following questions are considered: (1) How do such extra-mural students compare, as prospective college students, with high school graduates who have no college preference? (2) How do such extra-mural students compare, as prospective college students, with high school graduates in general? (3) How do such extra-mural students compare, as prospective college students, with high school graduates having college preference? I. THE SCOPE OF STUDY EXTENDED The study is now extended so that it includes the three large teachers colleges of Missouri, and a teachers college of Illinois. Extra-mural students constitute the universe. Some of the questions involved were considered in Chapter IV, but now the problem is extended so as to include type of study, and order of enrolment over a period of several years in four different institutions. Evidently the order of enrolments in residence and in extra-mural study is the significant thing. As in Chapter IV, type of study means residence, correspondence, or extension study. In this chapter the last two are combined under the head of extra-mural study. Order of enrolment indicates the numerical sequence of type of study. II. THE MISSOURI STATE TEACHERS COLLEGES 1. Universe of extra-mural students with residence study a. Kirksville All extra-mural students, 1914-1922, who have had residence study also, are included. TABLE XVIII RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 818 65 883 Extra-mural 65 818 883 Total 883 883 1766 Qk = (818)(818) - (65)(65) / (818)(818) + (65)(65) = .983 (Page 79) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 79 b. Warrensburg All extra-mural students, 1915-1922, who have had residence study also, are included. TABLE XIX RELATION BETWEEN TYPE OF STUDY, AND ORDER, OF ENROLMENT Order of enrolment Type of study First Second Total Residence 652 63 715 Extra-mural 63 652 715 Total 715 715 1430 Qw = (652)(652) - (63)(63) / (652)(652) + (63)(63) = .982 c. Springfield All extra-mural students, 1918-1921, who have had residence study also, are included. TABLE XX RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 647 69 716 Extra-mural 69 647 716 Total 716 716 1432 Qs = (647)(647) - (69)(69) / (647)(647) + (69)(69) = .977 d. The three schools combined All extra-mural students, who have had residence study also, are included. TABLE XXI RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 2117 197 2314 Extra-mural 197 2117 2314 Total 2314 2314 4628 Qa = (2117)(2117) - (197)(197) / (2117)(2117) + (197)(197) = .983 (Page 80) 80 THE RELATION OF EXTRA-MURAL STUDY TO e. Interpretations and comparisons Table XVIII is used for purpose of illustration; it reads as follows: at Kirksville, 818 students enrolled first in residence; 65, second; 65, enrolled first in extra-mural study; 818, second. Total first enrolments, 883; total second, 883; total residence enrolments, 883; total extra-mural, 883; total enrolments of both types, 1766. However, 7 of the 65 who were enrolled first in extra-mural study, and entered later for residence study earned no credit in residence. Q represents the coefficient of association given by formula (VII) of Chapter I. The subscripts k, w, s, and a refer to Kirksville, Warrensburg, Springfield, and all schools combined respectively. We observe that Qk = .983, Qw = .982, Qs = .977, and Qa = .983. The values of these four coefficients of association are in remarkably close accord. They show that the data collected from the Missouri schools are homogeneous. They indicate that, in the universe of extra-mural students who have had residence study also, the association between residence study and first enrolment is nearly perfect. The approach to unity, or complete association, is the remarkable thing, not the fact that the association is positive; that much was to be expected. Of course in the above named universe the association between first enrolment and extra-mural study is just as strongly negative. Students with residence study first, furnish practically the only sources for securing extra-mural enrolments in this universe. Students with extra-mural study first, scarcely affect residence enrolments at all, and it takes such students to increase residence enrolments. Moreover, Qk = .996, in Table VIII, Chapter IV, for the Corresponding sets of facts in the year 1919-1920, while here Qk = .983. The strong positive association observed is a sufficient condition to show that extra-mural study is not appreciably affecting residence enrolment. But it does not at all follow that it is a necessary condition. This same statement applies to (b) below. In all cases it is evident that the association between residence study and second enrolment is the negative of the values found above. 2. Whole universe of extra-mural students a. Kirksville All extra-mural students, 1914-1922, are included. TABLE XXII RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 818 65 883 Extra-mural 244 818 1062 Total 1062 883 1945 (Page 81) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 81 Qk = (818)(818) - (244)(65) / (818)(818) + (244)(65) = .954 b. Warrensburg All extra-mural students, 1915-1922, are included. TABLE XXIII RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 652 63 715 Extra-mural 286 652 938 Total 938 715 1653 Qw = (652)(652) - (63)(286) / (652)(652) + (63)(286) = .919 c. Springfield All extra-mural students, 1918-1921, are included. TABLE XXIV RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 647 69 716 Extra-mural 319 647 966 Total 966 716 1682 Qs = (647)(647) - (69)(319) / (647)(647) + (69)(319) = .901 d. The three schools combined All extra-mural students are included. TABLE XXV RELATION BETWEEN TYPE OF STUDY, AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 2117 197 2314 Extra-mural 849 2117 2966 Total 2966 2314 5280 (Page 82) 82 THE RELATION OF EXTRA-MURAL STUDY TO Qa = (2117)(2117) - (849)(197) / (2117)(2117) + (849)(197) = .928 e. Interpretations and comparisons In the whole universe of extra-mural students we have: Qk = .954, Qw = .919, Qs = .901, and Qa = .928 In (2) also the association coefficients are very large, and in close accord. These coefficients show that, in the whole universe of extra-mural students as observed in the three largest teachers colleges of Missouri, the association between residence study and first enrolment is also but little short of complete association. 3. Observations and Comparisons (1) (a) Out of 1062 students who had extra-mural study at Kirksville, 65, or 1 out of 16.3, or 6.1 per cent, enter school for residence study after first having had extra-mural study; (b) out of 938 such students at Warrensburg, 63, or 1 out of 14.9, or 6.7 per cent, enter school for residence study after first having had extra-mural study; (c) out of 966 such students at Springfield, 69, or 1 out of 14, or 7.1 per cent, enter school for residence study after first having had extra-mural study. These figures are almost identical, and show that a uniform situation exists in the whole state. (2) (a) Out of 883 students who had both extra-mural and residence study at Kirksville 65, or 1 out of 13.5, or 7.4 per cent, enter school for residence study after first having had extra-mural study; (b) but of 715 such students at Warrensburg, 63, or 1 out of 11.4, or 8.8 per cent, enter school for residence study after first having had extra-mural study; (c) out of 716 such students at Springfield, 69, or 1 out of 10.4, or 9.6 per cent, enter school for residence study after first having had extra-mural study. (3) (a) Out of 1062 students who had extra-mural study at Kirksville, 244, or 22.5 per cent of them, had extra-mural study first, whereas 77.5 per cent of them had residence study first; (b) out of 938 such students at Warrensburg, 286, or 30.5 per cent of them, had extra-mural study first, whereas 69.5 per cent of them had residence study first; (c) out of 966 such students at Springfield, 319, or 33 per cent of them, had extra-mural study first, whereas 67 per cent had residence study first. Hence at Kirksville less than 1/4 of all extra-mural students begin college study with extra-mural enrolment, whereas more than 3/4 of them begin college study with residence enrolment. Almost identical results were found at Kirksville for the year 1919-1920. At Warrensburg 3/10 of all extra-mural students had their first connection with the college through extra-mural study, whereas 7/10 of them had their first connection with the college through residence study. At Springfield 1/3 of the extra-mural students had their first connection with the college through extra- (Page 83) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 83 mural study, whereas 2/3 of them had their first connection through residence study. (4) (a) Out of 244 extra-mural students at Kirksville who had their first connection with the college through extra-mural study, 179 of them, or 73.4 per cent, have never entered for residence study, whereas 26.6 per cent entered; (b) out of 286 such students at Warrensburg, 223 of them, or 78 per cent, have never entered for residence study, whereas 22 per cent entered; (c) out of 319 such students at Springfield, 250 of them, or 78.4 per cent, have never entered for residence study, whereas 21.6 per cent entered. The per cent of those having extra-mural study first, who enter school at Kirksville, is slightly greater than at either Warrensburg or Springfield. However, both of these schools have under (1) and (2) slightly greater per cents of the total number of extra-mural students entering for later residence study, and have under (3) a slightly greater per cent of extra-mural students who had their first connection with the college through residence study. But number (4) tests best the influence of extra-mural study on later residence enrolment. (5) Some results drawn from different universes of study at Kirksville are now compared, (a) Out of the 187 teachers (Chapter IV) who had both extra-mural and residence study, 14, or 1 out of 13.1, or 7.6 per cent, entered school for residence study after first having had extra-mural study. Under (2) at Kirksville 7.4 per cent entered, (b) Out of 187 teachers who had extra-mural study at Kirksville, 46, or 24.6 per cent, had extra-mural study first. Under (3) at Kirksville 22.5 per cent had extra-mural study first, (c) Out of 46 teachers who had their first connection with Kirksville through extra-mural study, 32, or 70 per cent, never entered for residence study. Under (4) at Kirksville 73.4 per cent never entered. For students of the year 1919-1920 (Chapter IV) 78.1 per cent never entered, (d) Out of 2664 public school teachers of northeast Missouri, 867, or 32.8 per cent had at Kirksville residence study as the first type of study there. But under (4) at Kirksville only 26.6 per cent of all extra-mural students, who had extra-mural study first, later entered Kirksville. In other words, in every comparison made under (5) the whole universe of teachers without any limitations furnishes better prospective students to the teachers college at Kirksville than does the universe of students whose first enrolment was extra-mural. 4. Other methods for determining relationship a. Mean square contingency However, as a check on the association between residence study and first enrolment, let us employ mean square contingency to Tables XXI and XXV, which involve a summary of data for (Page 84) 84 THE RELATION OF EXTRA-MURAL STUDY TO the three teachers colleges of Missouri. The independence values for Tables XXI and XXV respectively are given by Tables XXIa and XXVa. TABLE XXIa Independence values for Table XXI Order of enrolment Type of study (f) First (s) Second Residence (r) 1157 1157 Extra-mural (e) 1157 1157 By methods explained in Chapter I, we have: Sfr = 3873.5 Ssr = 33.5 Sfe = 33.5 Sse = 3873.5 Therefore S = 7814, N = 4628, S — N = 3186 Therefore C = √3186/7814 = .64 TABLE XXVa Independence values for Tables XXV Order of enrolment Type of study First Second Residence 1300 1014 Extra-mural 1666 1300 By methods explained in Chapter I, we have: Sfr = 3449.5 Ssr = 38.3 Sfe = 432.6 Sse = 3449.5 Therefore S = 7369.9, N = 5280, S — N = 2089.9 Therefore C = √2089.9/7369.9 = .53 In each case these coefficients of contingency denote, as observed in Chapter I, a very high degree of relationship, especially as shown in Table XXI which gets at the most important phase of the question. b. Tetrachoric functions Let us now compute by tetrachoric functions the coefficient of correlation, r, for Table XXI. We have a = 2117, b = 197, c = 197, d = 2117, and N = 4682. Therefore b + d = 2314; c + d = 2314; d/N = .4632; (b + d)/N = 1/2(1 — a) = .5; (c + d)/N = 1/2(1 — a') = .5 (Page 85) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 85 By formula (V) of Chapter I, 48r9 + 71r7 + 119r5 + 265r3 + 152r - 2074 = 0. Since, in this problem, a = a' and T = T' there arose the necessity of extending this equation three terms beyond that given by Everitt’s Tables. But by tables especially devised by Everitt, we calculated T7, T8, and T9 and obtained the above equation containing only odd powers of r. By Descartes’ rule of signs there is no negative root, and not more than one positive root. The positive root lies between 0 and 1. By Horner’s method r = .98, with probable error of .0003. This large coefficient indicates almost perfect correlation. 5. Summary By tests of highest efficiency we are forced to the conclusion that the correlation between residence Study and first enrolment in residence in the three largest teachers colleges in Missouri is practically perfect in the universe of extra-mural students who have had residence study also; and, as indicated earlier, the completeness of the association is the significant fact. We observe also that, in the whole universe of extra-mural students where 3/4 of the first enrolments in extra-mural study never enter at all for residence study, the association is still positive and very high. Moreover, we find that the condition observed at Kirksville in Chapter IV is not local, but statewide and remarkably uniform in every important particular. III. WESTERN ILLINOIS STATE TEACHERS COLLEGE, MACOMB, ILLINOIS 1. Introductory statement It has been shown that conditions are uniform over the state of Missouri. Let us now consider the influence of extra-mural study on residence enrolment in a teachers college of a neighboring state. The Macomb State Teachers College has been doing extra-mural work on a large scale since 1911. Originally part of the work was correspondence, but now it is almost entirely extension. The average enrolment for the first ten years was 519, and from 1913-1921, 2166 different individuals were enrolled. However, some variation from the results observed in Missouri may be expected, since extra-mural study in Illinois is favored, in that it meets certain requirements made of teachers as to position, salary, and certificate renewals, an advantage not enjoyed in Missouri. We quote from the Macomb Teachers College Quarterly: “These extension courses are accredited by county superintendents of schools for the renewal of certificates, by all normal schools, colleges and universities belonging to the North Central Association, and by other educational institutions of similar grade. Boards of education in our leading cities give credit for this work in the grading of teachers and their salaries.”1 1No. 49, March, 1921, p. 35. (Page 86) 86 THE RELATION OF EXTRA-MURAL STUDY TO We quote also from a Macomb extension class folder, 1923-1924: “The credits obtained in these courses (extension) are good in all the leading colleges and universities, and are accepted by the State Certification Board and by county superintendents for the renewal of certificates.” In Missouri, credits made in extra-mural courses are exactly on the same basis as are credits made in the three quarters of the regular school year. Residence credits made in summer quarters at the Missouri teachers colleges are accepted more liberally on state and county certificates than are any other credits. 2. Universe of extra-mural students with residence study At Macomb a sample of extra-mural students who had residence study also, was used. TABLE XXVI RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 250 132 382 Extra-mural 132 250 382 Total 382 382 764 Qm = (250)(250) - (132)(132) / (250)(250) + (132)(132) = .565 3. Whole universe of extra-mural students A sample of extra-mural students was used. TABLE XXVII RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Total Residence 250 132 382 Extra-mural 1034 250 1284 Total 1284 382 1666 Qm = (250)(250) - (132)(1034) / (250)(250) + (132)(1034) = -.372 4. Discussion of results In the discussion which follows, it should be kept in mind that under both (2) and (3) our universe involves only extra-mural students; and that, when the association between residence (Page 87) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 87 study and first enrolment is positive and approaches unity, it serves as a sufficient condition to show that extra-mural study, which comes first, is not appreciably resulting in later residence enrolment; but on the other hand, in no sense can it be considered a necessary condition to show that extra-mural study first, is leading to residence enrolment in case the association is positive and small, or even negative. Further investigation in such cases is necessary unless the association approaches near to —1. For instance if, in tables XXVI and XXVII, 250 were replaced by 1, then in each case the association would practically equal —1, and evidently extra-mural study first, would be leading to later residence enrolment; or the association between residence study and second enrolment would be nearly equal to 1. In universe (2) Qm is positive, but not so large as in the three Missouri teachers colleges. This coefficient shows that the association between residence study and first enrolment is strongly positive, or stated in another form the association between residence study and second enrolment is —.565, and strongly negative, but in neither case as strong as in the teachers colleges of Missouri. In universe (3) Qm is negative. This coefficient shows that residence study is negatively associated with first enrolment in the whole universe of extra-mural students, or stated in another form residence study is positively associated with second enrolment. It is evident, however, that (2) is a much better index of the influence of extra-mural study on residence enrolment than is (3). For in Table XXVII the negative association is due, to the large number of extra-mural students who never enter for residence study at all. But in Table XXVI, Q is positive and shows that residence study and first enrolment are strongly associated, or that residence study and second enrolment have strong negative association. However, thus far we are not able to speak so confidently of the situation in Illinois as we are in Missouri. The tests used are not nearly so decisive, and the problem requires further analysis and investigation. IV. MACOMB COMPARED WITH TEACHERS COLLEGES OF MISSOURI 1. Observation and comparisons (1) Out of 1284 students who had extra-mural study at Macomb, 132, or 1 out 9.7, or 10.3 percent enter school for residence study after first having had extra-mural study. The per cents at Kirksville, Warrensburg, and Springfield are respectively 6.1, 6.7, and 7.1. However, Macomb offers mainly extension courses. If only extension courses at Kirksville are considered the per cent is 9.3, nearly the same as at Macomb. Does this result indicate that extension study is more closely related to residence study than is correspondence study, and that it exerts a stronger influence in leading to residence enrolment? (Page 88) 88 THE RELATION OF EXTRA-MURAL STUDY TO (2) Out of 382 students who had both extra-mural and residence study at Macomb, 132, or 1 out of 2.9, or 34.6 per cent, enter school for residence study after first having had extra-mural study. The per cents at the Missouri teachers colleges are in the order used above: 7.4, 8.8, and 9.6. If only extension courses are used the per cent at Kirksville is 12.1. Macomb excels in this universe. (3) Out of 1284 students who had extra-mural study at Macomb, (a) 1034, or 80.5 per cent of them, had extra-mural study first; (b) 19.5 percent of them had residence study first. In the Missouri schools the per cents are: (a) 22.5, 30.5, and 33; (b) 77.5, 69.5, and 67. The size of per cents under (a) and (b) are just reversed at Macomb from what they are in the Missouri teachers colleges. At Macomb large numbers begin with extra-mural study. This situation is probably due to the position of advantage given extra-mural credits in Illinois, and also to the fact that Macomb has extension directors giving full time to the work. Neither of these conditions applies in Missouri. (4) Out of 1034 extra-mural students at Macomb who had their first connection with the school through extra-mural study, (a) 902, or 87.6 per cent of them, never have entered for residence study; (b) 12.6 per cent of them have entered. In the Missouri schools the per cents are respectively: (a) 73.4, 78, and 78.4; (b) 26.6, 22, and 21.6. But the universe in number (4) which consists of extra-mural students who had their first connection with the school through extra-mural study is the real universe of prospective students out of which residence enrolments must come if extra-mural study leads to residence enrolment. By this test applied in this universe, which represents the crux of the whole situation, Macomb stands at the foot of the list of schools studied, and Kirksville, at the head. The per cent of those who enter out of this universe of legitimate prospective students at Kirksville is more than twice as high as that at Macomb. 2. Universe of extra-mural students with extra-mural study first a. A new universe Comparison of facts in number (4) suggests a definite way out of a difficult situation. We now create the .universe of extra-mural students who had extra-mural study first,. We combine the data from the three Missouri teachers colleges, since they have been shown to be homogeneous in every respect, and compare them with similar data from Macomb, Illinois. We know definitely in Missouri that extra-mural study has a very minor influence on residence registration. We shall now find, in the universe designated above, the association between extra-mural study in Missouri and later residence registration when considered in connection with Illinois (Macomb) and later residence registration. (Page 89) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 89 TABLE XXVIII Relation between extra-mural study coming first, and later RESIDENCE REGISTRATION Residence registration Extra-mural study in Registration Non-registration Total Missouri 197 682 879 Illinois 132 902 1034 Total 329 1584 1913 Q = (197)(902) - (132)(682) / (197)(902) + (132)(682) = .323 b. Observations and conclusions Extra-mural students, with extra-mural study first, constitute a prospective student universe from which residence enrolments must come if extra-mural study leads to residence enrolment. Out of 879 extra-mural students, with extra-mural study first, in Missouri, 197 came into residence; out of 1034 such students in Illinois, 132 came into residence. We find that Q = .323. This coefficient shows that extra-mural study in Missouri has strong positive association with later residence registration when compared with extra-mural study in Illinois; therefore, students in Missouri with extra-mural study first, are considerably more likely to enroll for later residence study than they are in Illinois. Then, since extra-mural study has a very slight influence on residence enrolment in Missouri, it is clear that in Illinois, as represented by Macomb, the influence is still less. We have shown that this condition extends beyond Missouri. V. COMPARISON WITH A STANDARD 1. Another new universe Though the influence of extra-mural study on residence enrolment is indeed slight, still it may be argued that extra-mural students constitute the best universe for prospective college students. Let us examine this claim. Fortunately Chapter V provides a carefully worked out standard of comparison in a universe of prospective students which consists of high school graduates for the years 1920-1921 and 1921-1922. Since college entrance demands high school graduation, no one can dispute the validity of this universe of prospective students when taken as a whole. Moreover, there is good reason to believe that the prospective student universe of a teachers college should be limited to those who prefer that type of institution, for usually, they intend to teach. On the other hand it is certainly fair to consider a student who takes extra-mural study first, in a school as having a preference for that school, and, consequently, as being a prospective student. (Page 90) 90 THE RELATION OF EXTRA-MURAL STUDY TO 2. Standards used On this basis let us take, in the four teacher producing institutions combined, all the students who had their first connection with the schools through extra-mural study, and compare them: (a) with those high school graduates of Chapter V that preferred Kirksville; (b) with those who preferred Kirksville combined with those who had no preference; (c) with the whole universe of high school graduates regardless of any preference for any school. a. High school graduates who prefer Kirksville TABLE XXIX EXTRA-MURAL STUDENTS HAVING EXTRA-MURAL STUDY FIRST, COMPARED WITH HIGH SCHOOL GRADUATES HAVING KIRKSVILLE PREFERENCE Interest in school through Residence registration Registered Non-registered Total Extra-mural study 329 1584 1913 School preference 308 461 769 Total 637 2045 2682 Q = (329)(461) - (308)(1584) / (329)(461) + (308)(1584) = -.526 b. High school graduates having Kirksville preference and no preference combined TABLE XXX EXTRA-MURAL STUDENTS HAVING EXTRA-MURAL STUDY FIRST, COMPARED WITH HIGH SCHOOL GRADUATES HAVING KIRKSVILLE PREFERENCE AND NO PREFERENCE COMBINED Interest in school through Residence registration Registered Non-registered Total Extra-mural study 329 1584 1913 Preference and no preference 402 965 1367 Total 731 2549 3280 Q = (329)(965) - (402)(1584) / (329)(965) + (402)(1584) = -.335 c. All high school graduates (Page 91) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 91 TABLE XXXI EXTRA-MURAL STUDENTS HAVING EXTRA-MURAL STUDY FIRST, COMPARED WITH WHOLE UNIVERSE OF HIGH SCHOOL GRADUATES Interest in school through Residence registration Registered Non-registered Total Extra-mural study 329 1584 1913 High school graduation 469 641 2110 Total 798 3225 4023 Q = (320)(1641) - (469)(1584) / (329)(1641) + (460)(1584) = -.080 d. High school graduates with no school preference TABLE XXXII EXTRA-MURAL STUDENTS HAVING EXTRA-MURAL STUDY FIRST, COMPARED WITH HIGH SCHOOL GRADUATES HAVING NO COLLEGE PREFERENCE Interest in school through Residence registration Registered Non-registered Total Extra-mural study 329 1584 1913 No school preference 94 504 598 Total 423 2088 2511 Q = (329)(504) - (94)(1584) / (329)(504) + (94)(1584) = 0.22 Here Q is slightly positive, but almost zero. This coefficient locates the extra-mural student definitely. e. Observations and comparisons (1) From Table XXIX Q = -.526 which indicates very strong negative association between extra-mural study and later registration in a universe of prospective students composed of extra-mural students who had extra-mural study first, and of high school graduates who had a college preference. Extra-mural students in this universe are not nearly so likely to enter college as are high school graduates with a college preference. This comparison seems to be fair, and perhaps should constitute our standard. (2) In Table XXX a still more liberal attitude has been taken towards extra-mural study. Here Q = -.335, which also indicates strong negative association between extra-mural study and (Page 92) 92 THE RELATION OF EXTRA-MURAL STUDY TO later registration in a universe of prospective students composed of extra-mural students who had extra-mural study first, and of high school graduates who had either a college preference or no preference. Extra-mural students even in this universe are not nearly as likely to enter college as are those high school graduates having either a college preference or no preference at all. (3) In Table XXXI the greatest liberality was shown in the formation of a universe. Here again Q = -.080 which coefficient of association is negative. There is still a slight negative association between extra-mural study and later registration in a universe of prospective students composed of extra-mural students who had extra-mural study first, and of high school graduates en masse. Thus even in this universe extra-mural students are not as likely to enter college for residence study in a teachers college as are high school graduates taken at random. (4) This startling conclusion is drawn from large samples of material shown to be homogeneous over wide areas. However, as a check on Q=—.08 tetrachoric functions are applied to the data of Table XXXI. We obtain the equation r6 - .22r5 + .16r4 + 1.57r3 + .26r2 + 25.01r + 2.84 = 0. There is no positive root between 0 and 1. There are two negative roots, one of which is greater than 1; the other is between 0 and -1. By Horner’s method r = -.11. Thus the coefficient of correlation between interest in school through extra-mural study and later residence registration is negative, and supports the conclusion drawn from the fact in Table XXXI that Q = -.08. (5) These lists of high school graduates were obtained outside of Kirksville, and Adair county. They were collected hurriedly either by a Kirksville faculty member or by a senior college student who spent from one to two hours at most in each high school visited, and from 15 to 20 minutes with the senior class during which time the cards were filled out giving Kirksville preference, no preference, or preference for other schools. The different degrees of relationship involved in these three classes were definitely brought out in Chapter V in order to furnish a progressive standard of comparison. As seen in Table XXXII extra-mural students can be placed rather definitely in this scale by comparing them with high school graduates with no school preference. f. Percentage comparisons By referring in this chapter to comparison (4) under Missouri state teachers colleges and to (4) under Macomb Teachers College, we have at hand material for a new table which shows the per cent of enrolments out pf a universe of prospective students consisting of extra-mural students who had residence study first. By reference to Table XIV of Chapter V we have the per cent of high school graduates of each type of preference who enroll for (Page 93) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 93 residence study. In the following tabulation K, W, S, M, and A stand for Kirksville, Warrensburg, Springfield, Macomb, and all schools combined respectively: TABLE XXXIII RESIDENCE REGISTRATION OF EXTRA-MURAL STUDENTS WITH EXTA-MURAL STUDY FIRST, AND HIGH SCHOOL GRADUATES Per cent of extra-mural students with extra-mural study first who enrolled for residence study at Per cent of high school graduates of each type of preference, and per cent of all graduates who enrolled at Kirksville—1921 and 1922 visitations combined. K W S M A Kirksville preference No preference Other school preference All H. S. graduates 26.6 22.0 21.6 12.6 17.4 40.1 15.7 10.9 22.2 This table is self explanatory. It shows that the per cent of residence enrolments from extra-mural students with extra-mural study first, is highest at Kirksville, lowest at Macomb, and that the per cent for all combined is 17.4. In every case the per cent is much lower than the per cent for high school students who prefer Kirksville; the per cent of enrolment for all extra-mural students is considerably less than the per cent for all high school graduates; and is only slightly greater than the per cent for the “no preference” group of high school graduates. Had data for the visitation of 1921 alone been used the showing made by extra-mural students would be less favorable still. By reference to Table XIV of Chapter V each school can be placed, with reference to enrolment of extra-mural students, quite definitely in terms of enrolment of high school graduates. These percentage comparisons support in every detail the conclusions reached by more exact methods of study. VI. SUMMARY AND CONCLUSIONS The following results hold in the universe of extra-mural students having extra-mural study first: (1) Extra-mural students as prospective college students, are almost exactly on a par with high school graduates having no college preference, with the advantage perhaps a trifle in favor of the former. (2) Extra-mural students are not quite as good prospective college students as are high school graduates in general. (3) Extra-mural students when compared with high school graduates having college preference, are wholly outclassed as prospective college students. By applying the standards deduced, administrators of teachers colleges in Missouri will find that extra-mural students having (Page 94) 94 THE RELATION OF EXTRA-MURAL STUDY TO extra-mural study first, are on a par as prospective college students, with high school graduates having no college preference; that they are not quite so good as high school graduates in general; and that they are wholly out-classed by high school graduates with college preference. These facts stand out all the more prominently when it is recalled that these extra-mural students have had from 1 to 11 years in which to take up residence study, whereas about half of the high school graduates have had 2 1/4 years, and the other half, 1 1/4 years. It was found in Chapter IV that, in the universe of teachers of northeast Missouri, a teacher selected at random was a slightly better prospective residence student than was a teacher who first had been connected with the-school through extra-mural study. These remarkable conclusions are reached through investigation of extensive and widely distinct universes of material It is thus seen that public school teachers and high school graduates both furnish teachers colleges a more productive universe of prospective students than do extra-mural students. It is not the purpose in this study to argue for or against the value of extra-mural instruction in a teachers college. It may have a place. But no administrator of a teachers college should be deluded into the belief that he is adding to the prestige of his school through extra-mural study, and thereby increasing residence enrolment. (Page 95) CHAPTER VII RELATION BETWEEN TYPES OF STUDY AND ORDER OF ENROLMENT In this chapter the following questions are considered: (1) What is the strength of association between type of study and order of enrolment? (2) What relation exists between different types of enrolment as indicated by order of enrolment? I. PROBLEM AND PLAN OF APPROACH As yet no particular effort has been made to distinguish between residence, correspondence, and extension study in connection with order of enrolment where students have had at least one type of extra-mural study, and also residence study. This problem, aside from a mere inspection of table is, has two methods of approach. They are Pearson’s mean square coefficient of contingency and his new method of determining correlation when one variable is given by alternative, and the other, by multiple categories. Type of study and order of enrolment have the same meanings as in Chapters IV and VI. II. METHOD OF TREATMENT 1. Data treated by mean square contingency a. Kirksville We have from the universe of extra-mural students, 1914- 1922, the following table: TABLE XXXIV Relation between type of study and order of enrolment Order of enrolment* Type of Study First None Second Third Total Residence 818 179 65 0 1062 Extension 164 554 313 31 1062 Correspondence 86 369 538 69 1062 Total 1068 1102 916 100 3186 *When no-enrolment is included as an order of enrolment, the total enrolments equal 3 times the number of students. It is seen that the total of first enrolments exceeds the total number of students by 6. This situation is due to the fact that 6 students, who were registered simultaneously as first enrolment, were counted once under both correspondence and extension. (Page 96) 96 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXXIVa Independence values for frequencies in Table XXXIV Order of enrolment Type of study (f) First (n) None (s)Second (t)Third Residence (r) 356 367 306 33 Extension (e) 356 367 306 33 Correspondence (c) 356 367 306 33 The following formulae were developed in Chapter I: I = (Am)(Bn) / N; S = ∑ (AmBn)2/(AmBn)0; C = √S — N / S. When these formulae are applied, we have in terms of the notation adopted in Chapter I: Sfr = 1879.6 Snr = 87.3 Ssr = 13.8 Str = 00.0 Sfe = 75.5 Sne = 836.3 Sse = 320.1 Ste = 29.3 Sfc = 20.8 Snc = 371.0 Ssc = 945.9 Ste = 144.3 Therefore S = 4723.9, N = 3186, S — N = 1537.9 Therefore C = √1537.9/4723.9 = .57 This value of C shows that the order of enrolment among extra-mural students as a universe is highly dependent on the type of study, since even a small coefficient of contingency shows a high degree of relationship, but the nature of the relationship is not yet clear. If we now take in Table XXXIV rows (1) and (2), and form association ratios as we proceed from column marked “ first ” enrolment to column marked “third” enrolment, and then take rows (2) and (3) and proceed in the same manner we get two sets of ratios designated as sets (1) and (2). These ratios pass from tetrad to tetrad, each row containing three tetrads. Set (1) Set (2) (a) 818/982 = .833 164/250 = .656 (b) 179/633 = .283 554/923 = .600 (c) 65/378 = .172 313/851 = .368 (d) 0/31 = .000 31/100 = .310 (Page 97) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 97 We now observe, in both sets (1) and (2), as we pass from ratio (a) to (b), to (c), and to (d), that a > b > c > d. Or we may say that in passing from tetrad to tetrad in set (1) the signs are + + +. Also in set (2) the signs are + + +. So the distribution is completely isotropic, and set (1) shows that if we take the first two rows of Table XXXIV, that residence is positively associated with first enrolment when extension and no-enrolment are considered, positively associated with no-enrolment when extension and second enrolment are considered, and positively associated with second enrolment when extension and third enrolment are considered. If we take rows (2) and (3), extension and correspondence, set (2) shows that extension is positively associated with first enrolment when correspondence and no-enrolment are considered, positively associated with no-enrolment when correspondence and second enrolment are considered, and positively associated with second enrolment when correspondence and third enrolment are considered. Ratios in sets (1) and (2) show, as we pass from residence study through extension to correspondence, that the association in order of strength declines from first enrolment, through no-enrolment, through second enrolment to third enrolment. This relation indicates that “type of study” is a continuous function representing closeness of contact with the teacher, and that it increases in strength from correspondence, through extension to residence, and that order of enrolment is a continuous function of established relationships with a school, and since no-enrolments could be excluded, that it increases in strength from third enrolment, through second, to first enrolment. Therefore it is seen that contact with teacher, as represented by type of study, is highly correlated with relationship to school as evidenced in order of enrolments. These results seem to point to the conclusion that extension study is much more closely related to residence study than is correspondence study. Moreover, these data come from the Teachers College at Kirksville, a school that has put more energy into its correspondence department than into its extension department. These interesting results lead us to make similar studies dealing with the relation between the same three types of study and order of enrolment at Warrensburg and Springfield. b. Warrensburg We have from the universe of extra-mural students, 1915-1922, the following table: (Page 98) 98 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXXV RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First None Second Third Total Residence 652 223 61 2 938 Extension 236 456 215 31 938 Correspondence 50 359 478 51 938 Total 938 1038 754 84 2814 TABLE XXXVa INDEPENDENCE VALUES FOR FREQUENCIES IN TABLE XXXV Order of enrolment (f) (n) (s) (t) Type of study First None Second Third Residence (r) 313 346 251 28 Extension (e) 313 346 251 28 Correspondence (c) 313 346 251 28 Proceeding as explained in Chapter I, we have: Sfr = 1358.2 Snr = 143.7 Ssr = 14.8 Str = 0.1 Sfe = 177.9 Sne = 600.9 Sse = 184.1 Ste = 34.3 Sfc = 7.9 Snc = 372.5 Sse = 910.3 Ste = 92.9 Therefore S = 3897.6, N = 2814, S — N = 1083.6 Therefore C = √1083.6/3897.6 = .53 Just as in Table XXXIV, if we take rows (1) and (2)* we get ratios in set (1) and if we take rows (2) and (3), we get ratios in set (2) Set (1) Set (2) (a) 652/888 = .733 236/286 = .825 (b) 223/679 = .323 456/815 = .560 (c) 61/276 = .221 215/693 = .310 (d) 2/33 = .061 31/82 = .378 In set (1) a> b > c > d, and signs run + + +. In set (2) a> b > c, c < d, and signs run + + - (Page 99) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 99 Here the distribution lacks but little of being isotropic, and the frequencies are few in the third column where it falls short. A decrease of .07 in ratio (d) of set (2) would make the distribution isotropic, and then all that is said in dealing with Table XXXIV could be said in dealing with data from Warrensburg. To be specific, we should now say that set (1) shows, if we take the first two rows of Table XXXV, that residence is positively associated with first enrolment when extension and no-enrolment are considered, positively associated with no-enrolment when extension and second enrolment are considered, and positively associated with second enrolment when extension and third enrolment are considered. Set (2) shows, if we take rows (2) and (3), that extension is positively associated with first enrolment when correspondence and no-enrolment are considered, positively associated with no-enrolment when correspondence and second enrolment are considered, and slightly negatively associated with second enrolment when correspondence and third enrolment are considered. Hence Table XXXV supports well the conclusions reached in connection with Table XXXIV, and the strength of the association is about the same at Kirksville and Warrensburg since the coefficients of contingency in these schools are .57 and .53 respectively. c. Springfield Next we consider the same questions relative to extra-mural students at Springfield, 1918-1921. TABLE XXXVI Relation between type of study and order of enrolment Order of enrolment Type of study First None Second Third Total Residence 647 250 66 3 966 Extension 240 431 240 55 966 Correspondence 79 421 416 50 966 Total 966 1102 722 108 2898 TABLE XXXVIa Independence values for frequencies in Table XXXVI Order of enrolment (f) (n) (s) (t) Type of study First None Second Third Residence (r) 322 367 241 36 Extension (e) 322 367 241 36 Correspondence (c) 322 367 241 36 (Page 100) 100 THE RELATION OF EXTRA-MURAL STUDY TO Proceeding as explained in Chapter I, we have: Sfr = 1300.0 Snr = 170.3 Ssr = 18.0 Str = 0.3 Sfe = 178.8 Sne = 506.2 Sse = 239.0 Ste = 84.0 Sfc = 19.4 Snc = 482.9 Ssc = 718.0 Stc = 96.4 Therefore S = 3813.3, N=2898, S — N = 915.3 Therefore C = √915.3/3813.3 = .49 Just as in Table XXXIV, if we take rows (1) and (2), we get ratios in set (I), and if we take rows (2) and (3), we get ratios in set (2). Set (1) Set (2) (a) 647/887 = .730 240/319 = .753 (b) 250/681 = .367 431/851 = .506 (c)66/306 = .216 240/656 = .366 (d) 3/58 = .051 55/105 = .524 In set (1) a > b > c > d, and signs run + + + In set (2) a > b > c, c < d, and signs run + + — So again the distribution lacks but little of being isotropic, and the relations pointed out in Table XXV hold here also. C = .49 indicates a high degree of association between types of study and order of enrolment. d. Three schools, combined Let us now throw the tabulations of Kirksville, Warrensburg, and Springfield into a single table, and obtain the association between type of study and order of enrolment as it applies to extra-mural students in the three largest teachers colleges of the state of Missouri. TABLE XXXVII RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First None Second Third Total Residence 2117 652 192 5 2966 Extension 640 1441 768 117 2966 Correspondence 215 1149 1432 170 2966 Total 2972 3242 2392 292 8898 (Page 101) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 101 TABLE XXXVIIa INDEPENDENCE VALUES FOR FREQUENCIES IN TABLE XXXVII Order of enrolment (f) (n) (s) (t) Type of study First None Second Third Residence (r) 991 1081 797 97 Extension (e) 991 1081 797 97 Correspondence (c) 991 1081 797 97 Proceeding as explained in Chapter I, we have: Sfr = 4522.4 Snr = 393.1 Ssr = 46.3 Str = 0.3 Sfe = 413.3 Sne = 1920.8 Sse = 740.1 Ste = 141.1 Sfc = 46.6 Snc = 1221.1 Ssc = 2572.9 Ste = 297.9 Therefore S = 12315.9, N = 8898, S — N = 3417.9 Therefore C = √3417.9/12315.9 = .52 Just as in Table XXXIV, if we take rows (1) and (2), we get ratios in set (1), and if we take rows (2) and (3), we get ratios in set (2). Set (1) Set (2) (a)2117/2757 = .767 640/855 = .748 (b) 652/2093 = .311 1441/2590 = .556 (c)192/960 = .200 768/220 = .309 (d)5/122 = .041 117/287 = .407 In set (1) a > b > c > d, and signs run + + + In set (2) a > b > c, c < d, and signs run + + - Thus the table fails in the sign of a single tetrad of being isotropic and then by less than .1. Hence, in the whole universe of extra-mural students as represented by the three large teachers colleges of Missouri, the association between type of study and order of enrolment constantly increases as we pass from third enrolment, through second, through no-enrolment, to residence enrolment along one attribute, and from correspondence, through extension, to residence study along the other attribute. This result holds at Kirksville, but fails in a minor phase in one tetrad when the whole universe is considered. As extension study develops more (Page 102) 102 THE RELATION OF EXTRA-MURAL STUDY TO in these institutions, doubtless the distributions will be isotropic in each school. e. Three schools. combined, and no-enrolment column deleted The question naturally arises as to whether the association between types of study and order of enrolment is materially affected when the no-enrolment column is deleted. To answer this question the no-enrolment column is deleted in Table XXXVII. The resulting Table is numbered XXXVIII. This table was used in Chapter I to illustrate the finding and application of the mean square contingency coefficient. The reader is referred to Table XXXVIII of Chapter I for a full discussion of the relations involved. We find C = .57 and the association holds in the same manner as when the no-enrolment column is included; therefore, as we pass from residence study through extension, to correspondence, the association, in order of strength, declines from first enrolment, through second enrolment, to third enrolment with only a slight turning back for extension and correspondence when we come to third enrolment. 2. Data treated by Pearson’s new method of correlation The mean square coefficient of contingency shows a high degree of relationship between types of study and order of enrolments. We desire to know whether the same conclusions are borne out by Pearson’s new method of correlation. a. Kirksville (1) We shall apply this method to Table XXXIV where the three types of study with the four columns for enrolments are given. The table need not be repeated. By using the upper row and employing Sheppard’s Tables we obtain the array of means in set (1), and by using rows (1) and (2) combined we obtain set (2). The other sets of values are obtained as explained in Chapter I. Set (1) Set (2) Set (3) Set (4) x̄/σx = -.431 x̄'/σx = .431 h/σx = .862 x̄1/σ1 = .726 x̄1'/σ1 = 1.402 h/σ1 = .676 σ1/σx = 1.275 x̄2/σ2 = -.985 x̄2'/σ2 = .426 h/σ2 = 1.411 σ2/σx = .611 x̄3/σ3 = -1.469 x̄3'/σ3 = -.221 h/σ3 = 1.248 σ3/σx = .691 x̄4/σ4 = -6.000 x̄4'/σ4 = -.496 h/σ4 = 5.504 σ4/σx = .157 (Page 103) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 103 Using formula (II) of Chapter I, we have from sets (1) and (4), and from sets (2) and (4) respectively η1 = .743 and η2 = .962. Therefore at Kirksville there is a high degree of correlation between type of study and order of enrolment among extra-mural students. It is observed in both sets (1) and (2), always omitting the mean of the whole distribution, that the means of columns continuously decrease as we pass from residence, through extension, to correspondence, and at the same time pass continuously from first enrolment, through no-enrolment, through second enrolment, to third enrolment. (2) Let us now group in Table XXXIV all correspondence and extension enrolments as extra-mural enrolments, and use Pearson’s new method as given by formula (III) of Chapter I. TABLE XXXIX RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First None Second Third Total Residence 818 179 65 0 1062 Extra-mural 250 923 851 100 2124 Total 1068 1102 916 100 3186 If we take the upper row, x̄/σx = -.431, x̄1/σ1 = .726, x̄2/σ2 = -.985, x̄3/σ3 = -1.469, x̄4/σ4 = -6.000 By using formula (III) of Chapter I, we have η = .798. This value of η lies between the two values secured by formula (II). Beginning with the first column we see that the means of arrays of columns decrease continuously as we pass from residence to extra-mural study, and, at the same time pass from first to no-enrolment, to second and third enrolment along the enrolment variate. The graph is shown in the figure below for both Tables XXXIV and XXXIX since they have the same set of means of arrays of columns for the upper row. It is clear that the mean type of study, as indicated by means of arrays of columns, shifts continuously away from residence as we pass from first to third enrolment. In other words, the correlation ratio leads to the same conclusions reached by the mean square contingency coefficient. (Page 104) 104 THE RELATION OF EXTRA-MURAL STUDY TO FIG. 5 (3) We now take Table XXXIY and delete the no-enrolment column. The following table results: TABLE XL RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Third Total Residence 818 65 0 883 Extension 164 313 31 508 Correspondence 86 538 69 693 Total 1068 916 100 2084 From the upper row we have set (1), and from the two upper rows combined set (2). Set (1) Set (2) Set (3) Set (4) x̄/σx = -.193 x̄'/σx = .430 h/σx = .623 x̄1/σ1 = .726 x̄1'/σ1 = 1.402 h/σ1 = .676 σ1/σx = .922 x̄2/σ2 = -1.469 x̄2'/σ2 = -.221 h/σ2 = 1.248 σ2/σx = .499 x̄3/σ3 = -6.000 x̄3'/σ3 = -.496 h/σ3 = 5.504 σ3/σx = .113 (Page 105) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 105 By formula (PI) from Chapter I, we have from sets (1) and (4) and sets (2) and (4) respectively η1 = .671 and η2 = .824. The arrays are heteroscedastic, but in both set (1) and set (2) of means of arrays the values decrease continuously as we pass from residence in the first column through extension and correspondence of the alternate variate, and at the same time go from first enrolment through second and third enrolments of the categoric variate. This result agrees with the results found in Tables XXXIV and XXXIX when the no-enrolment column was included. It also agrees with the conclusions reached through mean square contingency methods both as to correlation and as to the possibility of deleting the no-enrolment columns. (4) Let us take Table XL, and combine the two lower rows into a single row representing extra-mural study. This tabulation follows: TABLE XLI RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Third Total Residence 818 65 0 883 Extra-mural 250 851 100 1201 Total 1068 916 100 2084 If we apply Sheppard’s Tables, we have: x̄/σx = -.144, x̄1/σ1 = .726, x̄2/σ2 = -1.469, x̄3/σ3 = -6.000 By formula (III), Chapter I, η = .861. This value is in close agreement with the values obtained in Table XL. It would evidently be repetition to apply Pearson’s method to the data from Warrensburg and Springfield. However, as a final check it is applied to the combined data from the three schools as found in Tables XXXVII, and XXXVIII. b. Three schools combined (1) We use Table XXXVII and obtain from the first row the means of arrays in set (1) ; from rows (1) and (2) combined, set (2). Set (1) Set (2) Set (3) Set (4) x̄/σx = -.4308 x̄'/σx = .4308 h/σx = .8616 x̄1/σ1 = .5600 x̄1'/σ1 = 1.4586 h/σ1 = .8986 σ1/σx = .9611 (Page 106) 106 THE RELATION OF EXTRA-MURAL STUDY TO x̄2/σ2 = -.8357 x̄2'/σ2 = .3738 h/σ2 = 1.2095 σ2/σx = .7123 x̄3/σ3 = -1.4033 x̄3'/σ3 = -.2498 h/σ3 = 1.1535 σ3/σx = .7469 x̄4/σ4 = -2.1100 x̄4'/σ4 = -.2025 h/σ4 = 1.9075 &sigma4/σx = .4517 By using formula (II), Chapter I, we have from sets (1) and (4), and from sets (2) and (4) respectively η1 = .60, and η2 = .71. (2) Next we use Table XXXVIII and, proceeding as before, obtain the following sets of values: Set (1) Set (2) Set (3) Set (4) x̄/σx = -.2300 x̄'/σx = .4642 h/σx = .6942 x̄1/σ1 = .5600 x̄1'/σ1 = .4642 h/σ1 = .8986 σ1/σx = .7727 x̄2/σ2 = -1.4033 x̄2'/σ2 = -.2498 h/σ2 = 1.1535 σ2/σx = .6018 x̄3/σ3 = -2.1100 x̄3'/σ3 = -.2025 h/σ3 1.9075 σ3/σx = .3639 By formula (II), Chapter I, we have from sets (1) and (4), and sets (2) and (4) respectively η1 = .61, and η2 = .68. By examining means of arrays of columns for both Tables XXXVII and XXXVIII, omitting, of course, the mean that applies to the whole distribution, we find that in set (1) the means decrease continuously as we pass from residence through extension to correspondence, while at the same time we go along the enrolment variate from first enrolment through no-enrolment, through second enrolment, to third enrolment. When set (2) of means is considered exactly the same thing happens except that in set (2) there is a slight increase in the mean of the last column over that of the preceding. Thus in both tables, between type of study and order of en-rolment, there is a very high degree of correlation which is scarcely affected by deleting the no-enrolment column. The values of η are in reasonably close agreement, and interpretations of the tables by mean square contingency methods, and by Pearson’s new method harmonize in every particular. III. SUMMARY AND CONCLUSIONS (1) In the universe of extra-mural students there is a very definite relation between type of study and order of enrolment. In the three large teachers colleges of Missouri, as has been shown for each separately and for all combined, there is strong positive (Page 107) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 107 correlation between type of study and order of enrolment as we pass from correspondence through extension to residence on study variate while at the same time we pass from third enrolment to first, along the enrolment variate. (2) From the standpoint of order of enrolment, it appears that extension study is much more closely related to residence study than is correspondence study. This fact suggests that type of study represents contact with teacher, and that different degrees of this contact in diminishing strength are represented by residence, extension, and correspondence; and that order of enrolment represents, established relationship with a school, and that different degrees of this relationship in diminishing strength are represented by first, second, and third enrolments; and that there is a strong correlation between contact with teacher and established relationship with a school. The close relationship noted between residence and extension study is suggestive. It would appear to have valuable implications for administrators, especially if this close relationship should be exhibited in other comparisons also. For instance, would it not be advisable to devote more of the energies of a faculty to extension rather than to correspondence instruction? (Page 108) CHAPTER VIII COLLEGE GRADUATES AND EXTRA-MURAL STUDY In this chapter the following questions are considered: (1) What is the influence of extra-mural study on residence enrolment among college graduates? (2) What is the relation between type of study and order of enrolment among college graduates? (3) How does the influence of extra-mural study on residence enrolment among college graduates compare with that among students in general? I. NUMBER AND ORDER OF ENROLMENT OF STUDENTS RECEIVING BACHELOR’S DEGREES 1. Introductory statement The purpose of this chapter is to consider the influence of extra-mural study on residence enrolment in the universe of graduates of three Missouri state teachers colleges and Macomb State Teachers College, Macomb, Illinois. If the extra-mural student is “serious minded, persistent and capable” as stated in so many extension course bulletins, surely the influences of extra-mural study will be at a maximum in the universe of college graduates, especially if the universe is further limited to a second universe of graduates who had extra-mural study. Data were secured relative to graduates at Kirksville, Warrensburg, Springfield, and Macomb. At Kirksville the tabulation extends from September, 1918 to September, 1923; at Warrensburg and Springfield, from September, 1919 to September, 1923; and at Macomb, from September, 1920 to September, 1923. Macomb has only recently offered four-year college curricula; consequently, the number of graduates from Macomb is too small to justify any well defined conclusions. 2. Tabulations by schools and years a. Data included The tabulations below show the number of persons receiving the bachelor’s degree by years, the order of enrolment in the different types of study, the number of students in each type, the per cent of the total number of students in each type, and the per cent of the total number of students in correspondence and extension combined, the total number of extra-mural studies, and the average number of extra-mural studies for all students and also for all extra-mural students alone. In the tables below, F stands for first enrolment, S for second enrolment, T for third enrolment, where a student may have one enrolment or no enrolment at all in each type of study—residence, correspondence, and extension. b. Kirksville, Warrensburg, Springfield, and Macomb (Page 109) TABLE XLII COLLEGE GRADUATES, ORDER OF ENROLMENT, AND EXTRA-MURAL STUDIES Residence Correspondence Extension B. S. graduates Students and per cent of all students having Extra-mural studies Correspondence Extension Correspondence or extension Total No. Average No. for all graduates Av. No. for extra-mural graduates alone Year F S T F S T F S T No. No. % No. % Kirksville 1922-1923 90 0 0 0 29 7 0 11 7 90 36 40.0 18 20.0 40 44.4 113 1.26 2.82 1921-1922 70 1 0 0 20 1 1 10 2 71 21 29.6 13 16.9 31 43.7 92 1.30 2.97 1920-1921 88 0 0 0 30 4 0 6 3 88 34 38.6 9 10.2 36 40.9 80 .91 2.22 1919-1920 74 0 0 0 23 1 0 11 3 74 24 32.4 14 19.0 34 45.9 59 .80 1.74 1918-1919 58 0 0 0 11 2 0 5 0 58 13 22.4 5 8.6 16 27.6 32 .55 2.00 Total 380 1 0 0 113 15 1 43 15 381 128 33.6 59 15.5 157 41.2 376 .99 2.33 Warremsburg 1922-1923 105 0 0 0 39 11 0 19 10 105 50 47.6 29 27.6 58 55.2 175 1.67 3.07 1921-1922 107 1 0 1 45 6 0 10 10 108 52 47.2 20 18.5 56 52.8 171 1.58 3.05 1920-1921 72 1 0 1 36 8 0 10 8 73 45 60.3 18 24.7 47 65.3 124 1.71 2.64 1919-1920 42 0 0 0 22 2 0 3 4 42 24 57.1 7 16.7 25 59.5 71 1.70 2.84 Total 326 2 0 2 142 27 0 42 32 328 171 52.1 74 22.6 186 56.7 541 1.65 2.92 Springfield 1922-1923 77 1 0 0 26 7 1 13 3 78 33 42.3 17 20.5 40 51.3 115 1.47 2.88 1921-1922 56 0 0 0 18 4 0 10 3 56 22 39.3 13 23.2 28 50.0 84 1.50 3.11 1920-1921 43 2 0 0 16 3 2 4 0 45 19 42.2 6 13.3 22 49.0 54 1.20 2.46 1919-1920 28 2 0 0 11 6 2 6 1 30 17 56.7 9 30.0 19 63.3 66 2.20 3.42 Total 204 5 0 0 71 20 5 33 7 209 91 43.5 45 21.5 109 52.1 319 1.52 2.95 Macomb 1922-1923 28 2 0 0 0 0 2 3 0 30 0 0 5 16.7 5 16.7 32 1.07 6.40 1921-1922 14 0 0 0 0 0 0 1 0 14 0 .0 1 7.1 1 7.1 214 2.00 1920-1921 7 1 0 0 0 1 1 3 0 8 1 25.0 4 50.0 4 50.0 26 3.25 6.50 Total 49 3 0 0 0 1 3 7 0 52 1 .2 10 19.2 10 19.2 60 1.16 6.00 Summary, totals—4 schools 959 11 0 2 326 63 9 125 54 970 391 40.3 188 19.4 462 47.5 1296 1.34 2.82 (Page 110) 110 THE RELATION OF EXTRA-MURAL STUDY TO c. Combined tabulation for schools of Missouri TABLE XLIII COLLEGE GRADUATES, ORDER OF ENROLMENT, AND EXTRA-MURAL STUDIES Students and per cent of all students having Extra-mural studies Residence Correspondence Extension B. S. graduates Correspondence Extension Correspondence or exsion Total No. Average No. for all graduates Average No. for extra-mural graduates alone Year F S T F S T F S T No. No. % No. % No. % 1922- 1923 272 1 0 0 94 25 1 43 20 273 119 43.6 64 23.4 138 50.5 403 1.11 2.94 1921- 1922 233 2 0 1 83 11 1 30 15 235 95 40.4 46 19.6 115 48.8 347 1.48 3.04 1920- 1921 203 3 0 1 82 15 2 20 11 206 98 47.6 33 16.1 105 50.9 258 1.25 2.46 1919- 1920 144 2 0 0 56 9 2 20 8 146 55 37.7 30 20.5 78 53.4 196 1.34 2.51 Total 852 8 0 2 315 60 6 113 54 860 367 42.7 173 20.1 436 50.7 1204 1.40 2.77 (Page 111) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 111 d. Observations and comparisons There are many interesting observations in connection with tables under (b) and (c). The following ones are noted: (1) At Kirksville, Warrensburg, and Springfield respectively 1 out of 2.6, 1 out of 1.9, and 1 out of 2.3 persons being graduated had correspondence study. Macomb offers but few correspondence courses. For all schools combined 1 out of 2.5 graduates has had one or more courses by correspondence. For the three Missouri schools during the last four years 1 out of 2.3 graduates had correspondence study. (2) At Kirksville, Warrensburg, Springfield, and Macomb respectively 1 out of 6.7, 1 out of 4.4, out of 4.7, and 1 out of 5.2 graduates had extension study. For all schools combined 1 out of 5.1 had one or more courses by extension study. For the three Missouri schools under (c) 1 out of 5 had extension study. (3) At Kirksville, Warrensburg, Springfield, and Macomb respectively 1 out of 2.4, 1 out of 1.8, 1 out of 1.9, and 1 out of 5.2 had either correspondence or extension study, or both. For all schools combined 1 out of 2.1 persons graduating had earned credit in some form of extra-mural study. For the three Missouri schools under (c) 1 graduate out of 2 had some form of extra-mural study. (4) At Kirksville, Warrensburg Springfield, and Macomb respectively the average number of extra-mural studies (2.5 semester hours each) is .99, 1.65, 1.52, and 1.16; for all schools combined it is 1.34; for the three Missouri schools under (c) it is 1.40. (5) At Kirksville, Warrensburg, Springfield, and Macomb respectively the average number of extra-mural studies for extra-mural students being graduated is 2.33, 2.92, 2.95, and 6.00; for all schools combined it is 2.82; and for three Missouri schools under (c) it is 2.77. (6) At Kirksville, Warrensburg, Springfield, and Macomb respectively 1 out of 381, 1 out of 162, 1 out of 42, and 1 out of 16 had extra-mural study first. For all schools combined 1 out of every 88 persons receiving a bachelor’s degree had extra-mural study before being enrolled in residence. For the three Missouri schools under (c) 1 person out of 106 had extra-mural study first. In other words, in the three large teachers colleges of Missouri, out of 852 persons being graduated in the last four years, only 8 had extra-mural study before enrolling for residence study. 3. Summary So we may say when we are thinking of the typical graduate of a teachers college, particularly in Missouri, that there are 2 chances out of 5 that he has had correspondence study; 1 out of 5 that he has had extension study; and 1 out of 2 that he has had some form of extra-mural study. If we know merely that he is a teachers college graduate, we may think of him as having completed 3.5 semester hours in extra-mural study, and 116.5, in resi- (Page 112) 112 THE RELATION OF EXTRA-MURAL STUDY TO dence. But, if we know that he is a graduate with, extra-mural study, we may think of him as having completed 7 semester hours in extra-mural study, and 113, in residence. If he comes from teachers colleges at large, there is 1 chance out of 88 that his first enrolment was in extra-mural study in the institution where he was graduated; but if he comes from a Missouri teachers college, there is 1 chance out of 106 that his first enrolment was in extra-mural study in the institution where he was graduated. II. Other methods of analysis 1. Type of study and order of enrolment A quantitative expression is now sought for the relationship between type of study and order of enrolment among the graduates of the three teachers colleges of Missouri for the four years 1919 to 1923. In fairness to extra-mural study it is necessary to exclude all students for these four years who did not also have extra-mural study of some type. This universe deals with graduates who have had both residence and extra-mural study. The two tables which follow can be deduced directly from Table XLIII. TABLE XLIV RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Residence 428 8 Extra-mural 8 428 Q = (428)(428) - (8)(8) / (428)(428) + (8)(8) = .9993 This coefficient shows that the association between, residence and first enrolment in the Missouri teachers colleges is practically perfect in the universe of graduates who have had extra-mural study also. It is evidently unnecessary to consider the whole universe of graduates. This coefficient of association shows that extra-mural study first, is also a negligible factor in leading to residence enrolment among graduates of teachers colleges. 2. Strength of association In order to find the strength of association between type of study and order of enrolment use is made of Pearson’s mean square contingency coefficient as explained in Chapter I. (Page 113) Residence Enrolment and Scholastic Standing 113 TABLE XLV RELATION BETWEEN TYPE OF STUDY AND ORDER OF ENROLMENT Order of enrolment Type of study First Second Third Total Residence 428 8 0 436 Extension 6 113 54 173 Correspondence 2 315 60 377 Total 436 436 114 986 TABLE XLVa INDEPENDENCE VALUES FOR FREQUENCIES IN TABLE XLV Order of enrolment (f) (s) (t) Type of study First Second Third Residence (r) 194 194 50 Extension (e) 75 75 20 Correspondence (c) 167 167 44 By methods explained in Chapter I, we have: Sfr = 944.25 Ssr = .33 Str = .00 Sfe = .48 Sse = 170.25 Ste = 145.30 Sfc = .02 Ssc = 549.16 Stc = 81.82 Whence S = 1891.61, N = 986, S — N = 905.61 C = √905.61/1891.61 = .69 If we take in Table XLV rows (1) and (2) and form association ratios and proceed from column marked first enrolment to column marked third enrolment, and then take rows (2) and (3). and proceed in the same manner, we get two sets of ratios designated as (1) and (2). These ratios pass from tetrad to tetrad, each row containing two tetrads. Set (1) Set (2) (a) 428/434 = .986 6/8 = .750 (b) 8/111 = .066 113/264 = .264 (c) 0/54 = .000 54/114 = .474 (Page 114) 114 THE RELATION OF EXTRA-MURAL STUDY TO 3. Interpretations and comparisons In set (1) a > b > c, and the signs run + +. In set (2) a > b, b < c, and the signs run + -. Thus, only in the last tetrad does the distribution fail to be isotropic, and it is significant that this place is the same one at which the distributions failed to be isotropic in Tables XXXV, XXXVI, and XXXVII of Chapter VII. We observe, therefore, that, if we take the first two rows of Table XLV, residence is positively associated with first enrolment when extension and second enrolment are considered, and positively associated with second enrollment when extension and third enrolment are considered. Set (2) shows, if we take rows (2) and (3), that extension is positively associated with first enrolment when correspondence and extension are considered, but negatively associated with second enrolment when correspondence and third enrolment are considered. These results show, with the exception noted in the last tetrad, as we pass, in type of study, from residence through extension to correspondence, that enrolments pass from first enrolment, through the second, to the third. However, there is a turning back in the fourth tetrad. But, in the whole distribution, if we consider residence as holding the extreme positive position in type of study, extension, an intermediate position, and correspondence as coming next in order; and, likewise, consider first enrolment as holding the extreme positive position in order of enrolment, while second and third enrolments follow in succession, we may then say that, as the type of study advances, the order of enrolment advances, too, and that there is a very strong positive association between type of study and order of enrolment. This fact is indicated by Q = .993 in Table XLIV, and C = .69 in Table XLV. When Pearson’s correction e = (m-1)(n-1)/N = .0041 is applied to C2, the value of C as given above is unchanged. The large value of C here, as also in Chapter VII, indicates that “type of study” represents contact with teacher, and, as contact increases as represented in succession by residence, extension, and correspondence, that order of enrolment increases in strength as represented by first, second, and third enrolments. III. SUMMARY AND CONCLUSIONS (1) The influence of extra-mural study in leading to residence enrolment is negligible among the graduates of teachers colleges, particularly those of Missouri. (2) Type of study appears to represent contact with teacher, and is highly correlated with order of enrolment. (3) The influence of extra-mural study on residence enrolment, and the relation of type of study to order of enrolment, as shown by coefficients of association and of mean contingency, are (Page 115) RESIDENCE ENROLMENT and SCHOLASTIC STANDING 115 about the same for college graduates as for students in general. However, in both respects students in general make the better showing. Instead of the influence of extra-mural study on residence enrolment being a maximum among college graduates, it is a minimum in comparison with its influence among students in general. This fact indicates that students who begin with extra-mural study quit school before graduation, and fail to meet the standards required of well prepared teachers. (Page 116) CHAPTER IX VIEWS OF STUDENTS AS TO INFLUENCES THAT LED TO RESIDENCE ENROLMENT In this chapter by means of consensus of opinion the following questions are considered: (1) How does extra-mural study rank among other influences leading to residence enrolment? (2) Do views of students, and statistical findings agree concerning the importance of extra-mural study as a factor in leading to residence enrolment? I. QUESTIONNAIRES AS TO REASONS FOR ENROLLING IN RESIDENCE 1. First questionnaire a. Purpose The views of students were obtained concerning influences and sources of information that led them to enroll for residence study. After consulting and advising with many students on this question, the following questionnaire was submitted to the students of the spring quarter of 1923 at Kirksville: b. Form Please indicate the three chief reasons why you entered this college instead of some other institution by placing the figures 1, 2, 3 in the parentheses after the statements which in order of importance express your first (1), second (2), and third (3) reasons respectively for coming here. 1. Near home and convenient ( ) 2. Home town ( ) 3. Less cost here ( ) 4. Advantages of town where school is ( ) 5. Reputation and high standing of school ( ) 6. Certain strong departments ( ) 7. Opportunity to pursue high school studies ( ) 8. Opportunity for student employment) 9. Personal influence of relatives ( ) 10. Personal influence of schoolmates and friends ( ) 11. Personal influence of home teachers ( ) 12. Personal influence of faculty members of the teachers college ( ) 13. Through correspondence and extension study ( ) 14. Through high school meets ( ) 15. Through public lectures and addresses of faculty mem-bers ( ) 16. Through visitation of high schools by faculty members and student representatives of college ( ) 17. Through bulletins and circulars ( ) 18. Through letters from college authorities ( ) (Page 117) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 117 19. Through newspaper articles and advertising ( ) 20..........................................( ) Other reasons Name.......................................... College classification........................ c. Tabulation of replies TABLE XLVI REASONS FOR ATTENDING THE KIRKSVILLE STATE TEACHERS COLLEGE First Second Third Total Near home and convenient 155 66 52 273 Home town 70 18 5 93 Less cost here 14 72 66 152 Advantages of the town 5 9 17 31 Reputation and high standing of the school 98 120 49 267 Strong departments 22 40 35 97 High school studies 29 21 18 68 Student employment 6 18 20 44 Influence of relatives 56 54 38 148 Influence of schoolmates and friends 28 45 39 112 Influence of home teachers 27 21 21 69 Influence of faculty members 4 6 14 24 Correspondence and extension courses 1 3 1 5 High school meets 2 4 11 17 Lectures and addresses 1 3 9 13 Visitation of high schools 1 1 6 8 Bulletins 2 6 21 29 Letters from college 1 1 2 4 Advertising 2 2 Total 522 508 426 1456 d. Interpretation of table A close examination of the replies received shows that the great majority of the total number of answers given, counting (Page 118) 118 THE RELATION OF EXTRA-MURAL STUDY TO first, second, and third reasons, can be grouped under three main headings as follows: (a) Economic considerations; (b) Accessibility; (c) Reputation and high standing of the school. Under Economic considerations can be placed the headings, "less cost” with 152 replies, and “student employment” with 44 replies, or a total of 196 replies. Under Accessibility can be placed the headings, “near home and convenient” with 273 replies, and “home town ” with 93 replies, or a total of 366 replies. Under Reputation and high standing of the school, can be placed “reputation and high standing of school” with 267 replies, “strong departments” with 97 replies, and “influence of faculty members” with 24 replies, or a total of 388 replies. Hence, 950 out of 1456 replies, or 65 per cent of the total number, can be grouped under these three main heads. If the first or chief reason for attending school at Kirksville is considered, 20 replies can be placed under Economic considerations; 225, under Accessibility; and 124, under Reputation and high standing of the school, or a total of 369 out of 522 replies making 70.7 per cent of all replies given as first or chief reason for attending school at Kirksville. The second and third columns make equally as good showings under these three main divisions. Under the heading, Economic considerations, the showing is better. Therefore students are attending school at Kirksville for three outstanding reasons: (a) Economic considerations, (b) Accessibility, (c) Reputation and high standing of the school. The first and second factors are mainly constant and beyond control of the school, but the third is not. So naturally it is desirable to know the most effective means whereby students learn of the reputation and high standing of the school they attend since this item is so influential in promoting residence enrolment and varies in proportion to the efforts put forth by the institution. 2. Second questionnaire a. Purpose All headings in the previous questionnaire, and answers written therein, were studied carefully, and a second questionnaire was prepared for finding out the sources of information that revealed the reputation, and high standing of the school and led. to residence enrolment. In this questionnaire economic considerations and accessibility were frankly admitted and excluded from the discussion since they were well known and mainly beyond the control of the institution. Wherefore all attention was centered on discovering the sources of information that revealed the reputation and high standing of the school. With this purpose in mind a second questionnaire of the following form was submitted: b. Form A recent study in a teachers college shows that (aside from economic considerations and accessibility) the principal reason why students enroll for residence study is the reputation and high standing of the school. (Page 119) Residence Enrolment and Scholastic Standing 119 Will you please indicate the four chief sources of information which revealed to you the reputation and high standing of this teachers college by placing the figures 1, 2, 3, 4 in the parentheses after the statements below, which in order of importance influenced you most towards enrolment; that is, place figure (1) after strongest influence, figure (2) after next strongest, etc. 1. Bulletins, circulars, and letters from the college ( ) 2. Newspaper articles and advertising ( ) 3. High school contests and spring athletic meets ( ) 4. Correspondence and extension study ( ) 5. Visitation of high schools by faculty members and other representatives of the college ( ) 6. Conferences with faculty members and lectures and addresses of faculty members ( ) 7. Parents and relatives ( ) 8. Friends and schoolmates ( ) 9. Teachers in home schools ( ) 10. Conferences with students of this college ( ) (Other statements may be written here) 11...............................( ) 12...............................( ) c. Nature of replies This questionnaire was answered by 446 students at Kirksville during the spring quarter of 1923 and by 709 students during the summer quarter of 1923. There are no duplications of answers for the quarters. The same questionnaire was answered, during the summer quarter of 1923, by 479 students at Warrensburg and 638 students at Cape Girardeau. There were relatively few persons who wrote answers in blank spaces (11), or (12); and, with not more than a half dozen exceptions, such answers either came under some one of the ten headings listed above or could be excluded because of being some economic consideration or some phase of accessibility. Where an answer was excluded, succeeding reasons were advanced accordingly in tabulating the data. d. Type of data At first it might be thought that the data involved in Table XLVII and subsequent tables constitute a mean square contingency distribution. But after a moment’s reflection it is clear that it is not such a distribution. The columns of order of influence 1, 2, 3, and 4 supplement or strengthen each other to make a totality of influences which give information that leads to enrolment. In a contingency, or association table the numbers along cross diagonals, in adjacent rows and columns, work against each other and reduce the association. Manifestly this condition does not hold in these tables. For instance, consider Table XLVII which follows in the next paragraph. The first tetrad in the upper left hand corner of the table is as follows: Bulletins and circulars, first, 54; second, 61 (Page 120) 120 THE RELATION OF EXTRA-MURAL STUDY TO Newspapers and advertising, first, 12; second, 11 Evidently bulletins and circulars are a much stronger influence than newspaper advertising in bringing students into residence. But if association formulae are employed Q = -.097, a negative association between bulletins and leading influence. Now suppose the frequency in the second order of influence under bulletins is decreased by 13, and becomes 48 instead of 61. Evidently the influence of bulletins is less in producing enrolment than it was before the change. But if association formulae are now employed Q = .016, a positive association between bulletins and first influence when compared with newspaper advertising and second order of influence. The two results are contradictory and impossible if interpreted as measures of influence leading to residence enrolment. Association formulae do not give in this instance what we wish to know. We wish to find the sum total of influence which bulletins exert on residence enrolment, and any increase in lower orders of influence must increase the total influence, provided higher orders of influence remain constant. Therefore association formulae do not apply to these tables. But the whole theory of mean square contingency depends upon the association of attributes with multiple classes; hence, it is evident that the mean square contingency coefficient is not applicable here. e. Tabulation of replies The following table is a tabulation of replies from the forms filled out at Kirksville during the spring quarter of 1923: TABLE XLVII SOURCES OF INFORMATION THAT INFLUENCED MOST TOWARDS RESIDENCE ENROLMENT Order of influence Sources of information First Second Third Fourth Total 1. Bulletins and circulars 54 61 60 74 249 2. Newspaper advertising 12 11 13 26 62 3. High school meets 13 39 28 45 125 4. Extra-mural study 1 7 6 4 18 5. Visitation of high schools 11 17 28 24 80 6. Conferences with faculty members 23 18 34 23 98 7. Parents and relatives 133 46 45 39 263 8. Friends and schoolmates 62 94 81 49 286 9. Teachers in home schools 103 77 58 51 289 10. Conferences with students of college 34 58 60 48 300 Total 446 428 413 383 1670 (Page 121) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 121 f. Interpretation of table Beginning at the left of the top row of the table we read as follows: 54 students state that bulletins and circulars furnished the information that influenced them most to enroll at Kirksville; 61, state that bulletins and circulars influenced them second only to some other source of information to enroll at Kirksville. The reading proceeds similarly under headings “third” and “fourth” in the next two columns. Finally, 249 students were influenced to some degree through bulletins and circulars to enroll at Kirksville. The same interpretation is to be applied to the nine remaining headings for sources of information. Under the last row marked “totals”, there were 446 students that gave first or leading influences, 428, influences of second rank; 413, influences of third rank; and 383, influences of fourth rank. A total of 1670 replies was given in which each student made from 1 to 4 replies. II. A METHOD DEVISED FOR DEALING WITH MATERIAL 1. General survey of material It is admitted, of course, that the type of data used in this chapter is largely a matter of opinion. On the other hand, the opinion comes from the only persons who have a right to advance it without proof. This chapter seeks to find whether the opinion of students as to leading influences which induced them to attend college accords with facts brought out in this study. 2. Strength of influence defined Attention is directed to the consideration of Table XLVII. Aside from a mere inspection of this table, and of those immediately following, difficulties are encountered in comparing sources of information and orders of influence because there is no common unit of measure. If it were known positively in Table XLVII that “bulletins and circulars” in the first column actually brought 54 students to school and that, “newspaper advertising” brought 12, we could say that “bulletins and circulars” bring into school 4.5 times as many students as does “newspaper advertising”. We could then say that the strength of an influence is proportional to its frequencies. In most cases, however, there are influences at work other than the first order influences. Then it appears that our best working assumption is that among first order influences, indicated by the first column, the strength of each particular influence of the first order is proportional to the number expressing its frequency. Likewise among second, third, and fourth orders of influence, indicated by second, third, and fourth columns respectively, we assume that the strength of each particular influence of second, third, and fourth orders is proportional to the number expressing its frequency. Thus strength of influence is defined. Evidently it can also be expressed as per cent of the total influence of the column to which it belongs. 3. Orders of influence We can now make comparisons of influences of the same order (Page 122) 122 THE RELATION OF EXTRA-MURAL STUDY TO in a column. But we cannot make comparisons as we pass from column to column, or to column of totals, since evidently these orders of influence are of different weights. For instance, if we used the first column alone to get an idea of the relative total strength of different types of influence such as that represented by “visitation of high schools” with a small number for its frequency in the first column and relatively large numbers in the remaining columns, it is clear that “visitation of high schools” would be underrated as an influence, whereas that represented by “teachers in home schools” with a large number in the first column and relatively small numbers in the remaining columns would be overrated. On the other hand if we use the ordinary arithmetic mean of columns, or its equivalent, the column of totals with units one fourth as large as in the column of means, all cases such as that cited above as being underrated are now in general overrated, since influences of second, third, and fourth orders are now counting on a par with first order influences, and their frequencies were assumed to be large; whereas those that were overrated are now in general underrated. Hence in general the first column and the column of means will give the upper and lower limits of the total strength exerted by various types of influences in producing enrolment. If we knew the weights to attach to the orders of influence, we should be able to assign to each particular influence a value expressed either as a number or a percent; and then the total strength of each influence could be compared with that of any other influence. Now the values of these weights can be determined by assuming, that the number of students brought in by fourth, third, second, and first order influences lies under the area included between the probability curve and the x-axis. This assumption is the only defensible one to make. 4. Determination of weights of orders of influence Let us break off our curve at 3σ on each side of the median. Then the total interval along the base line (x-axis) is 6σ, and we measure from the extreme left of this interval as origin to the right. The base line for the probability curve will be divided into 7 equal intervals, and we are concerned evidently with the first four as we pass from left to right. The argument is similar to that used in Part Two, Chapter I, for establishing proper numerical values to attach to a five point grading system where credit for quality of work is recognized by appropriate weights. If we divide 6σ by 7, we have .86σ as intervals. Since the outer intervals contain very few frequencies, and many writers break off the curve at 5σ let us take the two outer intervals as 1σ each and all intermediate intervals as .8σ. The following diagram will help to make the meaning clear: (Page 123) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 123 FIG. 6 Measuring from A, we have as abscissae of limiting ordinates 0, 1σ, 1.8σ, 2.6σ, 3.4σ, 4.2σ, 5σ, and 6σ measuring from () to the left, we have 0, -.4σ, -1.2σ, -2σ, -3σ; measuring to the right, we have .4σ, 1.2σ, 2σ, adn 37sigma;. From the probability curve, by use of Table III, page 389, of Rugg’s STATISTICAL METHOD APPLIED TO EDUCATION, the area (frequencies) between ordinates at e and f is 31 per cent of the whole area between the curve and the x-axis; the area between ordinates at d and e, 23 per cent of the whole area; the area between c and d, 9.3 per cent; and the area between A and c, 2.2 per cent of the whole area. The same per cents hold to the right. By means of Table VI, page 396, of Rugg’s Statistical Method Applied to Education, the abscissa of the median of the area under the curve from A to c is (for 1 /2 of 2.2 per cent of area = 1.1 per cent of area) M1 = .75σ, measured from A. The area from A to the second median = 2.2 per cent of area + 1 /2 of 9.3 per cent of area = 6.95 per cent of area. Measured from A, the abscissa of this, median for the area c to d is M2 = 1.53. Similarly for 23 per cent of the area which gives the abscissa of the median of the area from d to e, M3 = 2.27σ, and for 50 per cent of the area, which gives the abscissa of the median from e to f, M4 = 3σ. By additions of relative increases due to the symmetry of the curve M5 = 3.73σ, M6 = 4.47σ, and M7 = 5.25σ for the remaining intervals from left to right. But the order of influences, fourth, third, second, and first, as they lead to enrolments, are respectively represented by the intervals A-c, c-d, d-e, e-f along the base line. The strength or value of each order of influence in producing enrolment, as expressed in a common unit, is represented by the abscissa of the median of its interval. It is at once seen that if M1 = .75σ is taken as the standard of measure, each succeeding abscissa of medians of areas (enrolments) is obtained almost exactly by multiplying M1 = .75σ by 2, 3, 4, 5, 6, and 7 respectively. But this particular curve is taken only through the fourth interval from the left, therefore 2, 3, and 4 are used as multipliers of the value of the fourth order of influence taken as a standard, to give the medians of abscissae or values of the other influences. This result shows that if we multiply the values or strengths of influences in the first column by 4, those in the second column by 3, those in the third column by 2, and those in the fourth column by 1, they are all expressed in a common unit which has the strength of influence in (Page 124) 124 THE RELATION OF EXTRA-MURAL STUDY TO the fourth column as a standard.* But by our first assumption strength or value of influence in any column is proportional to the number expressing its frequency. Hence, if we multiply the frequencies in the first column by 4, those in the second, by 3, those in the third, by 2, and leave those in the fourth as they are, then the strength of influence in each column is proportional to these products, and is measured in terms of the same unit, and we may make comparisons of strength of influence as we pass from column to column. In a grading system the numbers 1, 2, 3, 4, 5, 6, 7 are weights to increase credit for quality of work; here they are weights to increase strength of influence because of order of influence, and extend only from 1 to 4 inclusive in this chapter. It is also interesting to note that the weights 1, 2, 3, 4 turned out to be the rankings applied in reverse order. 5. Total strength of influence determined The frequencies in each column may be taken as an observed value of a quantity (strength of influence), and by methods of least squares z = ∑pM/∑p, where z is the most probable value of the quantity (strength of influence), M, any observation (frequency), and p, its weight.1 It is evident, by applying this formula to the whole distribution, that a new column of weighted means is obtained where each frequency is one tenth as large as it is in a column of totals obtained after multiplying each frequency of the distribution by the weight of its column. This column is very important in tables of this chapter, and is referred to as the “weighted mean column". The method devised makes it possible to extend the tables dealing with views of students and to interpret results. III. COMPLETE TABULATIONS OF DATA 1. Tables—year, 1923 Influences leading to residence enrolment are shown in the following tables: *Instead of extending the curve four equal intervals to the right and distributing the frequencies of the three remaining intervals proportionally over the first four intervals as assumed above, the whole curve might be used by taking three equal intervals to the right and then by taking the fourth interval (Fig. 6) from 2.6σ to 6σ. This gives the abscissa of the median of this interval measured from e to B, M4 = 3.44σ. If M1 = .75σ is taken as the unit of measure, each succeeding abscissa of medians of areas is obtained by multiplying .75σ by 2, 3, and 4.6 respectively. Were this plan used the weighted mean column of succeeding tables would be obtained by multiplying frequencies in fourth, third, second and first columns by 1, 2, 3, and 4.6 respectively and by dividing the sum by 10.6. This plan causes the weighted mean column to conform somewhat more closely tp the first column than does the plan used. However, it complicates all computations considerably and changes results very slightly) hence, the simpler plan was chosen for the data of this chapter. 1Merriam’s Method of Least Squares, p. 95. (Page 125) a. Kirksville—spring quarter TABLE XLVIII INFLUENCES LEADING TO RESIDENCE ENROLMENT (a) Order of influence with frequencies or strength (b) Strength of influence in per cents (c) Rank order of frequencies or strength Types of influence First Second Third Fourth Total Mean Wt.*Mean First Col. Wt.* Mean Col. 1 Mean Col. First Col. Second Col. Third Col. Fourth Col. Total- Mean Col. Wt.* Mean Col. 1. Bulletins and circulars 54 61 60 74 249 62.2 59.3 12.1 13.8 14.9 4 3 2 1 4 4 2. Newspapers and advertising 12 11 13 26 62 15.5 13.3 2.7 3.1 3.7 8 9 9 7 9 9 3. High school meets 13 39 28 45 125 31.3 27.0 2.9 6.3 7.5 7 6 7 5 6 6 4. Extra-mural study 1 7 6 4 18 4.5 4.1 2 .9 1.1 10 10 10 10 10 10 5. Visitation of high schools 11 17 28 24 80 20.0 17.5 2.5 4.1 4.8 9 8 8 8 8 8 6. Conferences with faculty members 23 18 34 23 98 24.5 23.7 5.2 5.5 5.9 6 7 6 9 7 7 7. Parents and relatives 133 46 45 39 263 65.8 79.9 29.8 18.9 15.7 1 5 5 6 3 2 8. Friends and schoolmates 62 94 81 49 286 71.5 74.1 13.9 17.3 17.1 3 1 1 3 3 9. Teachers in home schools 103 77 58 51 289 72.2 81.0 23.1 18.9 17.3 2 2 4 2 1 1 10. Conferences with students of college 34 58 60 48 20 50.0 47.8 7.6 11.2 12.0 5 4 3 4 5 5 Total 446 428 413 383 1670 417.5 427.7 100.0 100.0 100.0 *Wt. = weighted and Col. = column in Tables XLVIII to LIII inclusive. (Page 126) b. Kirksville—summer quarter TABLE XLIX INFLUENCES LEADING TO RESIDENCE ENROLMENT (a) Order of influence with frequencies or strength (b) Strength of influence in per cents (c) Rank order of frequencies or strength Types of influence First Second Third Fourth Total Mean Wt. Mean First Col. Wt. Mean Col. Mean Col. First Col. Second Col. Third Col. Fourth Col. Total- Mean Col. Wt. Mean Col. 1. Bulletins and circulars 84 87 105 124 400 100.0 93.1 11.9 13.7 15.2 4 3 1 1 3 4 2. Newspapers and advertising 7 12 14 36 69 17.3 12.8 .9 1.9 2.7 10 10 10 8 10 10 3. High school meets 24 46 59 55 184 46.0 40.7 3.4 6.0 7.0 8 7 5 5 6 7 4. Extra-mural study 25 29 25 21 100 25.0 25.8 3.5 3.8 3.9 7 9 9 10 9 9 5. Visitation of high schools 20 46 53 56 175 43.7 38.0 2.8 5.6 6.7 9 8 7 4 8 6. Conferences with faculty members 40 52 49 35 176 44.0 44.9 5.7 6.6 6.7 6 6 8 9 7 6 7. Parents and relatives 178 69 54 37 338 84.5 106.4 25.1 15.7 12.5 1 5 6 4 3 8. Friends and schoolmates 112 141 99 57 409 102.3 112.6 15.8 16.6 15.6 3 1 3 3 2 9. Teachers in home schools 168 128 93 54 443 110.7 129.6 23.7 19.1 16.9 2 2 4 6 1 1 10. Conferences with students of college 51 80 100 101 332 83.0 74.5 7.2 11.0 12.8 5 4 2 2 5 5 Total 709 690 651 576 2626 656.5 678.4 100.0 100.0 100.0 (Page 127) c. Kirksville—spring and summer quarters combined TABLE L INFLUENCES LEADING TO RESIDENCE ENROLMENT (a) Order of influence with frequencies or strength (b) Strength of influence in per cents (c) Rank order of frequencies or strength Types of influence First Second Third Fourth Total Mean Wt. Mean First Col. Wt. Mean Col. Mean Col. First Col. Second Col. Third Col. Fourth Col. Total-Mean Col. Wt. Mean Col. 1. Bulletins and circulars 138 148 165 197 648 162.0 152.3 11.9 13.8 15.2 4 3 2 1 3 4 2. Newspapers and advertising 19 23 27 62 131 32.8 26.1 1.6 2.4 3.0 10 10 10 8 9 10 3. High school meets 37 85 87 101 310 77.5 67.8 3.2 6.1 7.2 7 6 6 5 6 7 4. Extra-mural study 26 36 31 25 118 29.5 29.9 2.2 2.7 2.7 9 9 9 10 10 9 5. Visitation of high schools 31 63 81 80 255 63.7 55.5 2.7 5.0 5.9 8 8 8 6 8 8 6. Conferences with faculty members 63 70 83 58 274 68.5 68.6 5.5 6.2 6.5 6 7 7 9 7 6 7. Parents and relatives 311 115 99 76 601 150.3 186.3 26.9 16.8 13.8 1 5 5 4 3 8. Friends and schoolmates 174 235 180 106 695 173.7 186.7 15.1 16.9 16.2 3 1 1 3 2 2 9. Teachers in home schools 271 205 151 105 732 183.0 210.6 23.5 19.0 17.1 2 2 4 4 1 1 10. Conferences with students of college 85 138 160 149 532 133.0 122.3 7.4 11.1 12.4 5 4 3 2 5 5 Total 1155 1118 1064 959 4296 1074 0 1106.1 100.0 100.0 100.0 (Page 128) d. Warrensburg—summer quarter TABLE LI INFLUENCES LEADING TO RESIDENCE ENROLMENT (a) Order of influence with frequencies or strength (b) Strength of influence in per cents (c) Rank order of frequencies or strength Types of influence First Second Third Fourth Total Mean Wt. Mean First Col. Wt. Mean Col. Mean Col. First Col. Second Col. Third Col. Fourth Col. Total-Mean Col. Wt. Mean Col. 1. Bulletins and circulars 74 55 86 68 283 70.7 70.1 15.4 15.0 15.5 4 3 1 2 3 3 2. Newspapers and advertising 4 15 27 26 72 18.0 14.1 .8 3.0 3.9 10 10 6 9 8 10 3. High school meets 7 19 20 23 69 17.3 14.8 1.5 3.2 3.8 8.5 7.5 8 10 9.5 8 4. Extra-mural study 13 22 25 30 90 22.5 19.1 2.7 4.1 4.9 7 6 7 6 6 7 5. Visitation of high schools 7 17 18 27 69 17.3 14.2 1.5 3.0 3.8 8.5 9 9.5 8 9.5 9 6. Conferences with faculty members 20 19 18 29 86 21.5 20.2 4.2 4.3 4.7 6 7.5 9.5 7 7 6 7. Parents and relatives 101 53 37 33 224 56.0 67.0 21.1 14.4 12.3 2 5 5 5 5 4 8. Friends and schoolmates 75 119 81 57 332 83.0 87.6 15.6 18.8 18.2 3 1 3 2 2 9. Teachers in home schools 144 99 66 41 350 87.5 104.6 30.1 22.4 19.2 1 2 4 4 1 1 10. Conferences with students of college 34 53 79 84 250 62.5 53.7 7.1 11.8 13.7 5 4 3 1 4 5 Total 479 471 457 418 1825 456.3 465.4 100.0 100.0 100.0 (Page 129) e. Cape Girardeau—summer quarter TABLE LII INFLUENCES READING TO RESIDENCE ENROLMENT Types of influence (a) Order of influence with frequencies or strength (b) Strength of influence in per cents (c) Rank order of frequencies or strength First Second Third Fourth Total Mean Wt. Mean First Col. Wt. Mean Col. Mean Col. First Col. Second Col. Third Col. Fourth Col. Total- Mean Col. Wt.Mean Col. 1. Bulletins and circulars 84 78 85 60 307 76.7 80.0 13.2 13.4 13.5 4 3 3 2 3 4 2. Newspapers and advertising 9 24 29 34 96 24.0 20.0 1.4 3.3 4.2 10 9 9 6.5 9 9 3. High school meets 24 37 39 29 129 32.3 31.4 3.8 5.3 5.7 8 8 7 8 8 8 4. Extra-mural study 21 22 19 23 85 21.3 21 3.2 3.5 3.7 9 10 10 10 10 10 5. Visitation of high school 48 55 49 46 198 49.5 50.1 7.5 8.4 8.7 5 6 5 5 6 6 6. Conferences with faculty members 45 39 38 34 156 39.0 40.7 7.1 6.8 6.9 6 7 8 6.5 7 7 7. Parents and relatives 148 72 42 24 286 71.5 91.6 23.2 15.3 12.6 1 4 6 9 4 3 8. Friends and schoolmates 94 130 92 57 373 93.2 100.7 14.7 16.8 16.5 3 1 2 3 2 2 9. Teachers in home schools 134 95 109 54 392 98.0 109.3 21.0 18.3 17.3 2 2 4 1 1 10. Conferences with students of college 31 65 60 92 248 62.0 53.1 4.9 8.9 10.9 7 5 4 1 5 5 Total 638 617 562 453 2270 567.5 598.0 100.0 100.0 100.0 (Page 130) f. Tables of the three schools combined TABLE LIII INFLUENCES LEADING TO RESIDENCE ENROLMENT (a) Order of influence with frequencies or strength (b) Strength of influence in per cents (c) Rank order of frequencies or strength Types of influence First Second Third Fourth Total Mean Wt. Mean First Col. Wt. Mean Col. Mean Col. First Col. Second Col. Third Col. Fourth Col. Total- Mean Col. Wt. Mean Col. 1. Bulletins and circulars 296 281 336 326 1239 309.8 302.5 13.0 13.9 14.8 4 3 2 1 3 4 2. Newspapers and advertising 32 62 83 122 299 74.7 60.2 1.4 2.8 3.6 10 10 9 8 9 10 3. High school meets 68 141 146 152 507 126.7 113.9 3.0 5.2 6.2 8 6 7 6 8 8 4. Extra-mural study 60 80 75 78 293 73.3 70.8 2.6 3.2 3.5 9 9 10 10 10 9 5. Visitation of high schools 86 135 148 153 522 130.5 119.8 3.8 5.6 6.2 7 6 5 6 7 6. Conferences with faculty members 128 128 139 121 516 129.0 129.5 5.6 5.9 6.1 6 8 8 9 7 6 7. Parents and relatives 560 240 178 133 1111 277.8 344.9 24.7 15.9 13.2 1 5 5 7 4 3 8. Friends and schoolmates 343 484 353 220 1400 350.0 375.0 15.1 17.3 16.7 3 1 1 3 2 2 9. Teachers in home schools 549 399 326 200 1474 368.5 424.5 24.2 19.6 17.6 2 2 -3 4 1 1 10. Conferences with students of college 150 256 299 325 1030 257.5 229.1 6.6 10.6 12.3 5 4 4 2 5 5 Total 2272 2206 2083 1830 8391 2097.8 2170.2 100.0 100.0 100.0 (Page 131) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 131 2. Comments Table X which consists of Tables XLVIII and XLIX combined, is a good sample of the whole year’s enrolment at Kirksville in as much as the number answering the questionnaire in Table XLVIII is approximately one half the number of different students for the fall, winter, and spring quarters; whereas the number answering the questionnaire in Table XLIX is approximately one half the number of summer term students. There are many interesting comparisons and deductions that can be drawn from these tables. In every item for each school there are similarities and contrasts. However, there was one leading purpose for securing these data and constructing these tables; namely, to find out how extra-mural study ranks as an influence leading to residence enrolment; and in the main the discussion which follows shall be in harmony with this purpose. IV. RELIABILITY OF NEW METHOD TESTED 1. Position of column of weighted means In the six tables where 60 comparisons are made, with only 5 minor exceptions, varying in amount from .2 to .7 of 1 per cent, each value in the column of weighted means, which expresses strength of influence, falls between the per cents in the first column and in the column of means as found under heading (b). This statement is also true under heading (a) of the tables. In other words, as was foreseen, the first column and the column of means will in general give upper and lower limits for the total strength of any type of influence listed in the tables. Moreover, under heading (c) of the tables, which deals with rank order of frequencies or strength of influence, the weighted mean column for each type of influence in the six tables coincides in rank with the first column or column of means or, lies between the two in every instance but one, where it fails by one half of the unit rank interval. 2. Coefficients of correlation between columns Further justification can be found for the use of the weighted mean as a measure of relationships in the foregoing tables. Let us use heading (c) which deals with rank order of columns, and find by Spearman’s rank order method the correlation between types of influence in the first column and the column of means, in the first column and the column of weighted means, and in the column of means and the column of weighted means. In the tabulations as they originally stood, doubtless, the first column and the column of means would be selected as the columns that would give the most valuable information. So we use these columns here and let r1m be the correlation of the column of means with the first column; r1w, the correlation of the column of weighted means with the first column; and rmw, the correlation of the column of means with the column of weighted means. When the calculations are made for each table, the following results are secured: (Page 132) 132 THE RELATION OF EXTRA-MURAL STUDY TO TABLE LIV CORRELATION COEFFICIENTS BETWEEN FIRST COLUMN AND COLUMN OF MEANS, FIRST COLUMN AND COLUMN OF WEIGHTED MEANS, AND COLUMN OF MEANS AND COLUMN OF WEIGHTED MEANS Correlation coefficients Tables of data r1m r1w rmw Kirksville, Table XLVIII .830 .915 .988 Kirksville, Table XLIX .867 .927 .976 Kirksville, Table L .909 .964 .964 Warrensburg, Table LI .885 .960 .936 Cape Girardeau, Table LII .879 .915 .988 Three schools combined, Table LIII .903 .909 .964 The column of weighted means in the six tables has a correlation of .909, or more, with the first- column and a correlation of .936 or more with the column of means. In either case the correlation is so high that if the column of weighted means were used as a measure instead of either of the other columns, the conclusions drawn could not go far astray even though it were granted that one of these columns represented absolutely the true situation. Also it is noted in every case that r1m lies between r1w and rmw; in other words, the correlation of the weighted mean, with both the first column and the column of means, is in each case higher than the correlation of the first column and the column of means with each other. These relations indicate that the column of weighted means is intermediate between the first column and the column of means. Also it is observed, in every case save one, rmw > r1w. Hence the column of weighted means conforms somewhat more closely to the column of means than it does to the first column. 3. Reliability of column of weighted means It has been shown not only by direct proof but by every test available in a concrete situation represented by six different universes of observation, that the column of weighted means takes an intermediate position between the two extremes represented by the first column and the column of means, and that it is the most reliable single statement of relations available for dealing with the data of this chapter. The foregoing considerations give assurance that the column of weighted" means can be used with great confidence for comparisons in the same and in different tables. (Page 133) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 133 V. Final expression for strength of influence 1. Tabulation of columns of weighted means Attention is now directed to a relatively simple tabulation for making comparisons and drawing conclusions. The following table shows the weighted means or strength of influence expressed in per cent for each type of influence for each table: TABLE LV STRENGTH OF TYPES OF INFLUENCES LEADING TO ENROLMENT Types of influences (1)Table XLVIII Kirksville, spring quarter % (2)Table XLIX Kirksville, summer quarter % (3)Table L- Kirksville, spring and summer quarters combined % (4) Table LI Warrensburg, summer quarter % (5) Table LII Cape Girardeau, summer quarter (6) Table LIII Three schools combined- summary % 1. Bulletins and circulars 13.8 13.7 13.8 15.0 13.4 13.9 2. Newspapers and advertising 3.1 1.9 2.4 3.0 3.3 2.8 3. High school meets 6.3 6.0 6.1 3.2 5.3 5.2 4. Extra-mural study .9 3.8 2.7 4.1 3.5 3.2 5: Visitation of high schools 4.1 5.6 5.0 3.0 8.4 5.6 6. Conferences with faculty members 5.5 6.6 6.2 4.3 6.8 5.9 7. Parents and relatives 18.9 15.7 16.8 14.4 15.3 15.9 8. Friends and schoolmates 17.3 16.6 16.9 18.8 16.8 17.3 9. Teachers in home schools 18.9 19.1 19.0 22.4 18.3 19.6 10. Conferences with students of college 11.2 11.0 11.1 11.8 8.9 10.6 Total of per cents 100.0 100.0 100.0 100.0 100.0 100.0 2. Interpretations and comparisons The first remarkable property of this table is the uniformity noticeable in rows and in columns. No such regularity could exist without well founded, underlying reasons. If column (1) be excluded, the agreement is still closer; and column (1), it will be (Page 134) 134 THE RELATION OF EXTRA-MURAL STUDY TO recalled, deals with spring term students at Kirksville, who are typical of the students for the regular school year, whereas the other columns deal chiefly or all together with summer term students. Column (3) is the summary of (1) and (2); column (6) is the summary of columns (3), (4), and (5). In every column “teachers in home schools" have an influence equal to or greater than that of any other enumerated influence in producing enrolment. Warrensburg stands at the head in this respect, and there is substantial justification in oft repeated assertions that Warrensburg students are loyal to their alma mater. However, the showings made by “visitation of high schools” and “high school meets” are not as good at Warrensburg as at Kirksville, and at Cape Girardeau. The differences noted are probably due to variations in methods of publicity. Extra-mural study as an influence leading to residence enrolment is now considered. In column (1) which is typical of three quarters of the year at Kirksville, the influence of extra-mural study in the free choice of an institution, aside from economic considerations and accessibility, stands lowest in the column, and is represented by a strength of .9 of 1 per cent; in other words, extra-mural study is the compelling reason for residence enrolment in less than 1 case out of 100. It is to be remembered that the spring quarter represents the three quarters of the regular school year, whereas the summer quarter represents no other quarter of the year. Unfortunately the replies from Warrensburg and Springfield came exclusively from summer term students; consequently, the samples from these schools are of a type to make the very best showing for extra-mural study since the extra-mural students are most numerous in summer quarters. For summer term students.at Kirksville the strength of influence of “extra-mural study” is 3.8 per cent which is less than that of any other type save “newspapers and advertising”. A like condition is found at Warrensburg and Cape Girardeau. But at Cape Girardeau the strength of “extra-mural study” is only .2 of 1 per cent higher than that of “newspapers and advertising”. Also in the summary of replies in column (6) “extra-mural study” is next to lowest, and exceeds “newspapers and advertising” by only .4 of 1 per cent. If we had had replies from the enrolment at Warrensburg and Cape Girardeau for the whole year instead of the summer alone, the indications are, because of the better showing made by “newspapers and advertising” in these schools, that “extra-mural study” as an influence leading to residence enrolment would fall below, or at most, equal “newspapers and advertising”. Therefore, the best that can be said for “extra-mural study” when all schools are considered, is that it ranks next to lowest in the ten influences leading to residence enrolment and that it has a strength of 3.2 per cent in the teachers colleges of Missouri, where (Page 135) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 135 2272 different students expressed their views, and that it is the leading influence in bringing 1 student out of 31 into residence. However, if the spring quarter at Kirksville is considered typical of the other teachers colleges for the three quarters of the regular school year, then “extra-mural study” stands lowest of all enumerated influences leading to residence enrolment, and has a strength of .9 of 1 per cent, and is the leading influence in bringing into residence 1 student out of 111. So the expressed views of students, in a universe most favorable to extra-mural study, coincide quite definitely with previous findings, and the conclusion is reached that “extra-mural study” exercises a very minor influence on residence enrolment. VI. SUMMARY AND CONCLUSIONS The position of extra-mural study as an influence leading to residence enrolment, as determined from Consensus of views of students, is as follows: (1) “Extra-mural study” ranks lowest among ten enumerated influences leading to residence enrolment for students of the regular school year at Kirksville. Next lowest are “newspapers and advertising”, whereas “teachers in home schools” stand highest. (2) “Extra-mural study” ranks next to lowest among ten enumerated influences leading to residence enrolment for students of the summer quarter at Kirksville, Warrensburg, and Cape Girardeau. “Newspapers and advertising” stand lowest, whereas “teachers in home schools” stand highest. (3) “Extra-mural study” exercises a very minor influence on residence enrolment, and the expressed views of students coincide quite definitely with the statistical findings of earlier chapters. It is significant that the consensus of opinion of students with reference to the influence of extra-mural study on residence enrolment is directly opposed to that of educators as noted in Chapter II, Part One, but coincides quite definitely with the findings of a study based on statistical data. (Page 136) PART TWO THE RELATION OF EXTRA-MURAL STUDY TO SCHOLASTIC STANDING CHAPTER I GRADES IN DIFFERENT TYPES OF STUDY In this chapter the grading system at Kirksville is explained and justified, and the following questions are considered: (1) When one group of students has a single type of study and another group has two or more types, which group makes the higher grades in a given type of study? (2) In what type of study are grades highest? (3) In what type of study is variability among grades greatest? (4) Which type of study furnishes grades that are the best criteria of the grades in other types of study? I. INTRODUCTORY STATEMENT Under scholastic standing are included both rank in grades, and advancement in terms of semester hours of credit. It is admitted that the ranking of students, as revealed by grades, varies widely from teacher to teacher, and from subject to subject, but it is our purpose to take these marks as they stand, and by applying to them the best methods available, find out what differences exist in the grades given to students in residence, in correspondence, and in extension study at the Teachers College at Kirksville. II. THE GRADING SYSTEM 1. Plan of grading at Kirksville The grading system at Kirksville makes use of five letters as follows: F, failing; P, passing; G, medium; S, superior; and E, excellent. Instead of attaching decimal values to these marks we assign values as follows: F = -10; P = —5; G = 0; S = 5; and E = 10. These values are called honor points. The question at once arises as to the validity of these numerically assigned values. 2. The system justified a. Proof It is easy to show that this system conforms well to the probability curve. Let us break off the probability curve at 3σ to the right and left of the median through the center of the curve. In a five point system of grading 6σ is divided by 5, and gives 1.2σ as length of intervals. (Page 137) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 137 Measuring from A, we have as abscissae of limiting ordinates 0, 1.2σ, 2.4σ, 3.6σ, 4.8σ, and 6σ. By means of the probability curve and Table III, page 389, of Rugg’s STATISTICAL METHOD APPLIED TO EDUCATION, we find that the area (frequencies) between ordinates at d and e is 45.14 per cent of the whole area between the curve and x-axis; the area between ordinates at e and f is 23.84 per cent of the whole area; and the area between f and B is 3.5 per cent of the whole area. When we measure from the median to the left, the areas are of course 23.84 per cent and 3.5 per cent respectively. By means of the probability curve we can find also the abscissa of the median of each area cut off by ordinates at the extremities of the intervals A-c, c-d, d-e, e-f, f-B. As we pass from ordinate to ordinate from the extreme left to the right, these areas indicate the per cent of failures. The median abscissae of intervals, from which the weight to be applied to credit for quality is determined, can be found from Table VI, page 396, of Rugg’s STATISTICAL METHOD APPLIED TO EDUCATION. This table is worked out where all measurements are from the y-axis at the extreme left of the figure. The abscissa of the median of the area under the curve from A to I (for 1/2 of 3.5 per cent of area = 1.75 per cent of area) is M1 = .92σ the abscissa of the median of the area under the curve from c to d (for 3.5 per cent of area + 1/2 of 23.84 per cent of area = (Page 138) 138 THE RELATION OF EXTRA-MURAL STUDY TO 15.42 per cent of area) is M2 = 1.99σ; the abscissa of the median of the area from d to e is 3σ; and the other two are in order 4.01σ and 5.08σ. It is sufficiently accurate to write these abscissae as 1σ, 2σ, 3σ, 4σ, and 5σ respectively. It is thus seen that if we take 1σ, which is the approximate abscissa of the median of the first interval, as a standard, the remaining abscissae of medians of intervals are obtained by multiplying 1σ by the weights 2, 3, 4, and 5 respectively, or by adding successively 1σ to the abscissa of the median of the preceding interval. The abscissae along the x-axis in the figure measured from left to right are positive and represent grades; and since credit for quality of work is assumed to be proportional to grades, the abscissae may be thought of as representing also credit for grades earned. The middle interval, or any other, could be used as a standard of comparison. Thus credit for quality of work in the five intervals as represented by grades F, P, G, S, and E from left to right is 1σ, 2σ, 3σ, 4σ, and 5σ respectively. If we transform axes to the point (3σ, 0), which is the center of the curve, the abscissae representing grades become respectively —2σ, —σ, 0, 1σ, and 2σ as shown in the figure. If σ = 5, credits for quality become —10, —5, 0, 5, 10 which are the actual values used at Kirksville in interpreting grades as honor points. These are very convenient values to use in averaging thousands of grades as was done in this study. After the average grade of each student was obtained, 10 was added to each average in order to avoid negative measures which are undesirable in tables. Then the values attached to the five point scale, as used in the tables of this chapter for purposes of computation, are 0, 5, 10, 15, 20. This procedure is equivalent to transforming axes from the center of the curve to (—2σ, 0), or (—10, 0) where σ = 5. It is well known, and is easily proved, that the addition of a constant to the measures or observations of a distribution leaves the coefficients of correlation and regression unchanged, but increases the central tendencies and measures of dispersion by this constant. Hence, to pass back to central tendencies and measures of dispersion in the original scale, we merely reverse the process and subtract the constant. The same reasoning applies when the measures are decreased by a constant. Hence, if we subtract 10 from all central tendencies and measures of dispersion as obtained from tables in Part Two, we shall have them reduced to the scale of values used in computing honor points at Kirksville. If we add 5 to all measures of central tendencies and dispersions, they will be reduced to a scale that exactly conforms to that of credit for quality, since 0, 5, 10, 15, 20, (the scale of our computation) then become 5, 10, 15, 20, 25 which are in proportion to the weights to be applied to give credit for quality. If 15 had been added to each value of the scale —10, —5, 0, 5, 10, as used at Kirksville, we should get as values of our five point scale 5, 10, (Page 139) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 139 15, 20, 25 also, and the scale would exactly conform to the abscissae of medians of intervals. But there was much advantage in finding the average of grades for each individual with the scale —10, —5, 0, 5, 10 and then adding 10 instead of 15, to make the final grade of each individual as it appears in the tables of this chapter and succeeding ones. b. Conclusions Any scale of grading may be used that is of the form a + d, 2a + d, 3a + d, 4a + d, 5a + d, where d is zero, positive, or negative, and in every such system of grading correlation and regression coefficients are unchanged, and measures of central tendency and dispersion can be reduced to the form a, 2a, 3a, 4a, 5a, as deduced from the figure in this chapter, by additions or subtractions of d. This fact completely justifies the numerical values assigned to grades at Kirksville, and the addition of 10 to each grade, and shows that, if we wish to pass back to the original values assigned, we subtract 10 from all measures of central tendency and of dispersion and leave coefficients of correlation and of regression unchanged, and that, if we wish to go to the scale of form a, 2a, 3a, 4a, 5a, we add 5 to all measures of central tendency and of dispersion and leave coefficients of correlation and of regression unchanged. The same procedure would apply if we wished to change all the measures in a frequency distribution back to the original scale, or to a scale of the form a, 2a, 3a, 4a, and 5a. Also attention is called to the fact that when F, P, G, S, and E are given values of 0, 5, 10, 15, and 20 in computations, these letters represent the intervals —2.5 to 2.5, 2.5 to 7.5, 7.5 to 12.5, 12.5 to 17.5, and 17.5 to 22.5. 3. Grades that were studied The grades of all students, residence, correspondence and extension, for the school year of 1919-1920 were considered. All grades for all quarters during which the student was at Kirksville were included, and as stated before, F, P, G, S, and E were assigned values of —10, —5, 0, 5, and 10 respectively. The arithmetic mean of all grades was taken as the most probable grade, and gave the rank of the student. The scale of values adopted made additions easy. This result was very desirable since there were, all told, grades for 3485 students many of whom had more than one type of study, and frequently as many as 48 courses or more. For tabular purpose 10 was added to each rank obtained by the law of averages and the sum gave the student’s rank as used for purposes of calculation. In nearly all instances residence, correspondence, and extension grades were treated separately, and were not averaged to make up a single grade or rank except in cases specifically mentioned where correspondence and extension grades were thrown together to make up a rank for extra-mural study. (Page 140) 140 THE RELATION OF EXTRA-MURAL STUDY TO III. COMPARISON OF GRADES AT KIRKSVILLE 1. Residence and correspondence grades, residence-correspondence universe a. Relations The grades of 340 students who have had both residence and correspondence study at Kirksville are considered. Comparisons of grades in different types of study are made by means of correlation and contingency tables. In the contingency table the intervals for F, P, G, S, and E are as indicated in II :2-b. Tables I and Ia which follow serve to show the facts concerning residence and correspondence study for this group of students. In these and succeeding tabulations A will be used to represent arithmetic mean, or mean; M, median; σ, standard deviation; r, coefficient of correlation; η, correlation ratio; and C, contingency coefficient. Subscripts r, c, e, and x are attached to indicate whether the foregoing measures apply to residence, correspondence, extension, or extra-mural study. Table I shows that for residence grades the mean is 13.1 and the median 13; for correspondence grades the mean is 14.6 and the median, 15.3. The standard deviation of residence grades is 2.33, that of correspondence grades is 4.03, and the correlation of residence grades with correspondence grades is r = .28 ± .04, and the correlation ratio is ηre = .34 ± .03. The correlation ratio is read, “the correlation of residence on correspondence grades”, and may differ considerably from the correlation of correspondence on residence grades. The well-known test of linear regression is √N/.67449 ‧ 1/2√η2 - r2 < 2.5.1 Here it gives 2.3 < 2.5 which shows that the regression is linear and that the coefficient of correlation is a reliable measure of the relationship. The coefficients of regression are: b1 = rσc/σr = .48; b2 = rσr/σc = .16. Therefore the regression equations are: c = b1R or c =.48R R = b2c or R = .16c From Table Ia the coefficient of contingency is C = .27. 1J. Blakeman, Biometrika, Vol. IV, p. 349. (Page 141) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 141 TABLE I RELATION BETWEEN RESIDENCE AND CORRESPONDENCE GRADES—CORRELATION Correspondence grades Residence grades 0-1 1-2 2-3 3-4 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 19-20 1 1 18-19 1 1 5 7 17-18 1 6 1 1 2 11 16-17 5 5 1 1 1 1 15 15-16 1 6 3 1 12 3 3 2 2 7 40 14-15 1 1 1 11 5 1 15 6 3 1 1 6 52 13-14 2 1 1 5 3 1 19 1 2 1 5 40 12-13 1 7 11 2 17 3 2 9 52 11-12 5 1 10 1 7 2 12 7 1 7 54 10-11 1 1 1 16 1 3 14 1 3 41 9-10 1 1 8 3 1 1 3 1 2 21 8-9 1 1 1 3 7-8 3 3 Total 3 0 0 1 0 11 0 5 1 0 67 2 41 7 3 10 6 12 21 5 8 47 340 r = .28 ηrc = .34 (Page 142) 142 THE RELATION OF EXTRA-MURAL STUDY TO TABLE Ia RELATION BETWEEN RESIDENCE AND CORRESPONDENCE GRADES— CONTINGENCY COEFFICIENT Correspondence Residence grades grades Pr Gr Sr Er Total Fe 0 1 3 0 4 Pc 0 12 4 0 16 Gc 3 68 46 1 112 Sc 0 65 82 1 148 Ec 0 24 29 7 60 Total 3 170 158 9 340 N = 340 S = 364 C = .27 b. Comparisons In terms of the notation adopted we have: (1) Ar = 13.1 Ac = 14.6 (2) Mr = 13.0 Mc = 15.3 (3) σr = 2.33 σc = 4.03 (4) r = .28 ± .04 ηrc = .34 ± .03 (5) R = .16c c = .48R (6) C = .27 The following observations are made: (1) The arithmetic mean of correspondence grades is 1.5 units higher than that of residence grades. This difference measured in terms of the standard deviation of residence grades is .63 of the standard deviation. (2) The median of correspondence grades is 2.3 units higher than the median of residence grades. This difference equals the standard deviation of residence grades. Thus in both tests of averages, correspondence grades are higher than residence grades at Kirksville. (3) The standard deviation of correspondence grades is larger than that of residence grades by 1.7 units, or it is 1.74 times the standard deviation of residence grades. (4) The coefficients of correlation and contingency show a moderate degree of relationship between residence and correspondence grades. (5) From the first regression equation in (5) we observe that for a student, whose correspondence grades vary a unit from the mean of the universe of correspondence grades, it is to be predicted that, on this account alone, his residence grades will vary from (Page 143) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 143 the mean of the universe of residence grades by .16 of a unit and in the same direction. From the second regression equation we observe that for a student, whose residence grades vary a unit from the mean of the universe of residence grades, it is to be predicted that, on this account alone, his correspondence grades will vary from the mean of the universe of correspondence grades by .48 of a unit and in the same direction. These results show that residence grades are a much better index of correspondence grades than correspondence grades are of residence grades. c. Conclusions The following conclusions are reached as to residence and correspondence grades at Kirksville: (1) Correspondence grades are appreciably higher than residence grades. (2) Variability among correspondence grades is much wider than that among residence grades. (3) Residence grades are a much better index of correspondence grades, than correspondence grades are of residence grades. 2. Residence and extension grades, residence-extension universe a. Relations The grades of 227 students who have had both residence and correspondence study at Kirksville are considered. Tables II and IIa which follow serve to show the facts relative to residence and correspondence study of this group. Table II shows that for residence grades the mean is 13.1 and the median, 12.9; for extension grades the mean is 13.9 and the median, 13.6 The standard deviation of residence grades is 2.29, that of extension grades is 3.56, and the correlation of residence grades with extension grades is r = .47 ± .03. This correlation is so high that there is no need to find the correlation ratio. The coefficients of regression are: b1 = rσe/σr = .72 and b2 = rσr/σe = .30. Therefore the regression equations are E = .72R, and R = .30E. From Table IIa the coefficient of mean square contingency is C = .51. b. Comparisons In our notation we have: (1) Ar = 13.1 Ae = 13.9 (2) Mr = 12.9 Me = 13.6 (3) σr = 2.29 σe = 3.56 (4) r = .47 ± .03 (5) R = .30E E = 72R (6) C = .51 (Page 144) 144 THE RELATION OF EXTRA-MURAL STUDY TO TABLE II RELATION BETWEEN RESIDENCE AND EXTENSION GRADES— CORRELATION Extension grades Residence grades 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 19-20 1 1 18-19 1 1 2 1 5 17-18 2 1 3 2 1 9 16-17 1 6 2 1 2 12 15-16 5 1 2 4 2 2 1 2 3 22 14-15 5 1 1 3 4 3 8 25 13-14 10 2 4 1 12 2 1 2 34 12-13 1 1 10 5 4 3 9 4 1 38 11-12 2 1 1 13 6 7 3 12 1 46 10-11 1 1 10 1 3 1 5 22 9-10 1 2 1 1 2 1 8 8-9 0 7-8 1 1 2 6-7 1 1 1 3 Total 6 0 2 1 1 56 14 24 16 1 59 5 14 4 5 19 227 r = .47 (Page 145) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 145 TABLE IIa RELATION BETWEEN RESIDENCE AND EXTENSION GRADES— CONTINGENCY COEFFICIENT Extension grades Residence grades Pr Gr Sr Er Total Pe 1 7 0 0 8 Ge 2 66 30 0 98 Se 1 41 51 1 94 Ee 0 2 20 5 27 Total 4 116 101 6 227 N = 227 S = 388 C = .51 The following observations are made: (1) The arithmetic mean of extension grades is .8 of a unit higher than that of residence grades. This difference equals .35 of the standard deviation of residence grades. (2) The median of extension grades is .7 of a unit higher than that of residency grades. This difference equals .3 of the standard deviation of residence grades. Thus in both tests of averages, extension grades are somewhat higher than residence grades. (3) The standard deviation of extension grades is greater than that of residence grades by 1.27 units, or is 1.55 times the standard deviation of residence grades. (4) The coefficients of correlation and contingency between residence and extension grades are high. (5) The first regression equation shows that for a student, whose extension grades vary a unit from the mean of the universe of extension grades, it is to be predicted that his residence grades will vary from the mean of the universe of residence grades by .30 of a unit and in the same direction. The second regression equation shows that for a student, whose residence grades vary a unit from the mean of the universe of residence grades, it is to be predicted that his extension grades will vary from the mean of the universe of extension grades by .72 of a unit and in the same direction. c. Conclusions The following conclusions are reached as to residence and extension grades at Kirksville: (1) Extension grades are somewhat higher than residence grades. (2) Variability among extension grades is considerably greater than that among residence (Page 146) 146 THE RELATION OF EXTRA-MURAL STUDY TO grades. (3) Residence grades are a much better index of extension grades than extension grades are of residence grades. At Kirksville both correspondence and extension grades are higher than residence grades, and correspondence grades are higher than extension grades. The mean of correspondence grades is .7 of a unit larger than the mean of extension grades, and the median of correspondence grades is 1.7 units larger than the median of extension grades. The standard deviation of both correspondence and extension grades is much larger than that of residence grades. Nor can this difference be explained on the ground of fewer studies making up the rank of students in extra-mural subjects, since it appears later that the standard deviation of grades of 253 entering freshmen who were in school from 1 to 3 quarters, was 2.55. The variability in correspondence grades is also considerably greater than that in extension grades since the standard deviation of the former is .47 greater than that of the latter. Furthermore, from both the coefficient of correlation and from the regression equations there is found a closer relationship between extension and residence grades than between correspondence and residence grades. It is clear that extension grades are a better index of residence grades than correspondence grades are. This conclusion bears out in a remarkable way a result commented upon in Part One in connection with type of study and order of enrolment. It was found that, in reference to first, second, and third enrolments, we pass from residence, through extension, to correspondence study. This result indicates that type of study represents contact with teacher, and that correspondence, extension, and residence represent three successive stages of this contact. The fact that extension grades are so much more closely related to residence grades than are (correspondence grades bears out this observation. These conclusions are drawn from homogeneous samples of students where each student had residence study in addition to correspondence or extension study. 3. Residence, correspondence, and extension grades— whole universe of each a. Relations Each student of 1919-1920 is now counted in each type of study in which he earned credit at Kirksville. A student may be counted 2 or even 3 times, but his grades in different types of work are kept separate. There were 1275 students, who had residence study; 359, had correspondence study; and 270, had extension study. The following tabulation gives the frequency distribution of grades of all students in the three types of study: (Page 147) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 147 TABLE III RELATION BETWEEN GRADES AND TYPE OF STUDY Grades Type of study 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total (1) Residence 1 0 1 2 1 14 13 24 27 77 192 190 208 140 133 124 50 45 16 3 14 1275 (2) Correspondence 3 0 0 1 0 13 0 5 1 0 73 2 41 7 3 112 12 22 5 9 50 359 (3) Extension 12 0 3 2 1 68 16 26 16 1 71 6 15 4 6 23 270 (Page 148) 148 THE RELATION OF EXTRA-MURAL STUDY TO For residence grades the mean is 12.7, the median, 12.5; and the standard deviation, 2.76. For correspondence grades the mean is 14.4; the median, 15.3; and the standard deviation, 4.05. For extension grades the mean is 13.4; the median, 13.4; and the standard deviation, 3.43. b. Comparisons When all grades in different types of study at Kirksville are considered, we have in terms of symbols introduced: (1) Ar < Ae < Ac (2) Mr < Me < Mc (3) σr < σe < σc Also when the whole universe of each type of study is considered, residence grades are lowest, extension grades, next, and correspondence grades, highest. Likewise residence grades are least variable, extension; grades, next, and correspondence grades, most variable of all. When comparisons are made with Tables I and II, it is found that both the mean and median of residence grades of all students are respectively less than the means and medians of residence grades of students who had both residence and correspondence study or residence and extension study. The residence grades of all students are also somewhat more variable than the residence grades of those who have had residence study and some other type of study also. These differences may be due to the fact that many of the 815 students are just beginning college study, and eliminations have not yet taken place on account of their inability to pursue college studies. In Table III there were only 19 students having correspondence study without residence study, and only 43, having extension study without residence study; hence, not much change could be expected in central tendencies and measures of dispersion. However, the mean of correspondence grades of all students is slightly less than it is for correspondence students having had residence study also; but the median remains the same, and the standard deviation is increased a trifle. The mean and median of extension grades of all students are perceptibly lower than these same measures are for the extension grades of students who have had residence study also. The standard deviation also is less than in Table II. c. Conclusions It therefore appears that students of a group which has had more than one type and also the same types of study, make somewhat higher grades in any one of the given types pursued than does the whole universe of students in any one of these types. 4. Residence and extra-mural grades-each universe excluding the other a. Relations Students with residence study only and students with extra- (Page 149) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 149 mural study only are now considered. Since the number of students in the year 1919-1920 who had either correspondence or extension study without residence study, is small, correspondence and extension students are treated as extra-mural students. The following tabulation gives the frequency distribution of grades for those who have had residence study only, and for those who have had extra-mural study only. TABLE IV RELATION BETWEEN GRADES AND TYPE OF STUDY Grades Type of study 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total Residence only 1 0 1 2 1 11 13 20 23 56 122 128 143 91 80 53 32 27 7 0 4 815 Extramural only 8 0 1 1 0 15 1 5 0 0 15 1 2 0 2 6 57 For residence grades the mean is 12.2 and the median, 12.3; for extra-mural grades the mean is 12.9 and the median, 12.5. The standard deviation of residence grades is 2.82; that of extra-mural grades is 4.52. b. Comparisons and conclusions The number of students in extra-mural study only, is smaller than is desirable for statistical work. However, both the mean and median of grades made by students with extra-mural study only, are larger than the mean and median of grades made by students who have had residence study only. Also the standard deviation of grades made by students with extra-mural study only, is larger than that of grades made by students with residence study only. By comparisons with Tables I, II, and III it is found that students who have had residence study without any extra-mural study make lower residence grades and grades of a wider range of variability than: (1) the residence grades of all students who have had residence study; (2) the residence grades of students who have had some form of extra-mural study also. The comparisons form an ascending series, and hold in the order made. When grades are judged by the median, it is found that the extra-mural grades of students, who have had no residence study, are lower and of a wider range of variability than: (1) the extra-mural grades of all students who have had extra-mural study; (2) the extra-mural grades (extension or correspondence) of students who have had residence study also. But, when grades are judged by the mean, it is found that the extra-mural grades of students (Page 150) 150 THE RELATION OF EXTRA-MURAL STUDY TO who have had no residence study, are higher than the extension grades of all other groups considered, but less than the correspondence grades of all other groups considered. These results are probably due to the combining of extension and correspondence grades into a single extra-mural grade, and also to the small sample available. 5. Residence grades of extra-mural students and grades of students with residence study only a. The problem stated An interesting question arises as to whether students who have had both residence and extra-mural study will make higher residence grades than do students of equal advancement who have had residence study only; in other words, is there some quality or attribute that goes with being a residence-extra-mural student that is conducive to higher grades? To answer this question the residence grades of 380 college graduates from 1918 to 1923 were studied. Central tendencies and measures of dispersion were found; also Pearson’s new method of correlation that is adapted to a variable and an attribute was used to find the correlation between being a student with both residence and extra-mural study and grades in residence. b. Relations The table which involves the facts relative to these four- year graduates follows: TABLE V RELATION BETWEEN TYPE OF STUDY AND GRADES OF STUDENTS WITH BACHELOR’S DEGREE Residence grades Type of study 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 Total (1) Number of students residence study only 2 4 16 40 39 32 36 22 16 7 9 223 (2) Number of students both residence, and extra-mural study 0 4 11 19 20 34 26 18 9 10 6 157 (3) Total number of students 2 8 27 59 59 66 62 40 25 17 15 380 For students with residence study only, the mean of residence grades is 13.54; the median, 13.33; and the standard deviation, 2.18. For students who have had both residence and extra-mural study, the mean of residence grades is 13.83; the median, (Page 151) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 151 13.76; and the standard deviation, 2.16. The correlation in this table was determined as an illustrative exercise involving Pearsons new method in Chapter I, Part One. The correlation between being a student with both residence and extra-mural study, and high residence grades is r = .086. c. Comparisons It is seen that the mean and median of grades of students who have had both residence and extra-mural study, are respectively .29 and .43 of a unit higher than the mean and median for students with residence study only. Measured in terms of the standard deviation of the whole distributions these differences are respectively .14 and .20 of the standard deviation. The standard deviation in row (1) is .02 greater than in row (2). The coefficient of correlation is r = .086. d. Conclusions These measures indicate that graduates of the Teachers College at Kirksville who have had both residence and extra-mural study make somewhat higher residence grades and grades of slightly less variability, than do graduates having residence study only. There also appears to be a small but sensible correlation between being a student with both residence and extra-mural study, and high residence grades. IV. COMPARISON OF GRADES AT MACOMB, ILLINOIS 1. General statement Due to the amount of labor in getting data relative to grades it was not possible to study in detail the grades and grading system of any school other than the Teachers College at Kirksville. However it was possible to secure the extension grades, at Macomb, Illinois, of 159 students who had had no residence study, both the extension and residence grades of 76 persons who had had both types of Study, and the residence grades of 324 students who had had residence study only. The grades at Macomb are evaluated on the same basis as are those at Kirksville It was not feasible to secure data concerning age and advancement of students, or to apply any of the tests as to mental ability and health as was done at Kirksville; moreover, it must be borne in mind that extra-mural study at Macomb, means extension study. All comparisons show that residence and extension study are more closely related than are residence and correspondence study. The courses in extension at Macomb are taught in the main by a few persons who devote full time to the work, whereas in Missouri the courses are generally offered by regular faculty members who devote their major energies to residence instruction. 2. Residence and extension grades a. Relations involved The relations between grades in different types of study at Macomb are shown by a conveniently arranged tabulation. In the sample secured the number of students who had pursued both types of study was too small to justify a correlation table (Page 152) 152 THE RELATION OF EXTRA-MURAL STUDY TO for residence and extension grades. Nor should too much weight be attached to central tendencies in this small group of 76 who had both types of study. TABLE VI RELATION BETWEEN GRADES AND TYPE OF STUDY AT MACOMB (a) (b) (c) Grades (1)Total no. residence students (2)Total no. extension students (3)Students with residence study only (4)Students with extension study only (5) Students with both types of study— residence grades (6) Students with both types of study— extension grades 20-21 12 13 6 9 6 4 19-20 3 1 2 0 1 1 18-19 10 6 5 0 5 6 17-18 19 6 14 5 5 1 16-17 16 7 9 3 7 4 15-16 45 65 34 49 11 16 14-15 13 5 10 3 3 2 13-14 16 11 11 7 5 4 12-13 32 21 26 12 6 9 11-12 16 4 11 1 5 3 10-11 76 69 65 50 11 19 9-10 18 1 15 1 3 0 8-9 16 0 15 0 1 0 7-8 35 6 33 4 2 2 6-7 12 0 11 0 1 0 5-6 29 10 28 7 1 3 4-5 8 1 7 1 1 0 3-4 3 0 3 0 0 0 2-3 8 3 8 2 0 1 1-2 1 0 1 0 0 0 0-1 12 6 10 5 2 1 Total 400 235 324 159 76 76 (Page 153) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 153 Let A stand for arithmetic mean; M, for median; and σ, for standard deviation; and the subscripts 1, 2, 3, 4, 5, and 6 denote the various columns of the table above. Then we have: (a) (b) (c) A1 = 11.13 A2 = 12.95 A3 = 10.54 A4 = 13.00 A6 = 13.64 M1 = 10.76 M2 = 12.80 M3 = 10.43 M4 = 12.70 M5 = 14.00 M6 = 13.00 σ1 = 4.64 σ2 = 4.17 σ3 = 4.50 σ4 = 4.03 σ5 = 4.36 σ6 = 4.19 In all cases the odd numbered subscripts refer to residence grades, and the even numbered to extension grades. The columns under (a), (b), and (c) are comparable. b. Comparisons and conclusions Both under (a) and (b) whether the comparison is made by the mean or median the extension grades are considerably higher than residence grades, but variability among residence grades is slightly greater than among extension grades. However, under (c) where the residence and extension grades of 76 persons who have had both types of study are compared, the residence grades when measured by mean or median, are slightly higher than extension grades, and the variability of residence grades is slightly greater than that for extension grades. However, this sample is inadequate. But when the residence and extension grades of those who have had but one type of study, are compared, extension grades are much higher than are residence grades; also when all residence grades are compared with all extension grades, the extension grades are much higher than are residence grades. Nevertheless, variability is slightly greater in every case for residence grades than it is for extension grades. This result is probably due to the fact that extension grades are made out by just a few persons at Macomb. The weight of evidence points to higher grades for extension study than for residence study at Macomb also. The lesser variability for extension grades can be explained, and shows that greater variability is not indigenous to extra-mural study as one might be led to believe. At Macomb as at Kirksville, higher grades appear to go with extension study. V. SUMMARY AND CONCLUSIONS 1. Summary of facts relative to grades at Kirksville Certain facts brought out in this chapter can be set forth concisely by a tabulation in terms of the symbols introduced under IIIa, where A represents arithmetic mean; M, median; σ, standard deviation; and subscripts r, c, and e represent respectively residence, correspondence, and extension study. (Page 154) 154 THE RELATION OF EXTRA-MURAL STUDY TO TABLE VII SUMMARY OF GRADES IN DIFFERENT STUDENT UNIVERSES AT KIRKSVILLE Measures used to interpret grades Unverse of students Ar Ae Ac Ax Mr Me Mc Mx σr σe σc σx No. Both residence and correspondence, Table I 13.1 14.6 13.0 15.3 2.33 4.03 340 Both residence and extension, Table II 13.1 13.9 12.9 13. 6 2.29 3.55 227 All residence students, Table III 12.7 12.5 2.76 1275 All correspondence students, Table III 14.4 15.3 4.05 359 All extension students, Table III 13.4 13.4 3.43 270 Residence study only, Table IV 12.2 12.3 2.82 815 Extra-mural study only, Table IV 12.9 12.5 4.52 57 2. Conclusions a. From data at Kirksville The tabulation above and proceeding tables warrant the following conclusions: (1) Students who have had both residence and extension study, or residence and correspondence study make higher grades in residence than do students with residence study only, higher grades in extension than do students with, extension, study only, and higher grades in correspondence than do students with correspondence study only. (2) When grades in the three types of study are compared, they are in every instance lowest in residence study, medium in extension study, and highest in correspondence study. (3) Variability is least among residence grades, medium among extension grades, and greatest among correspondence grades. (4) Residence grades are better criteria of either correspondence or extension grades, than correspondence or extension grades are of residence grades; and extension grades are better criteria of residence grades than are correspondence grades. (Page 155) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 155 (5) Extension and residence study appear to be more closely related than do correspondence and residence study. (6) Students who have had both residence and extra-mural study make slightly higher residence grades and grades of somewhat less variability than do students, of equal advancement, with residence study only. There is a small but significant positive correlation between being a student with both residence and extra-mural study, and residence grades. b. From data at Macomb (1) Extension grades are in general higher than residence grades; the only exception is in a small sample of 76 students with both types of study. (2) Variation is less among extension grades than it is among residence grades. c. Observations and comparisons It is significant that students having more than one type of study make higher grades in each type of study than do students having a single one of the given types of study. This fact means that students having two or more types of study make higher grades in general than do students having a single type of study. But this statement is just as true of students who have had both correspondence and extension study as it is of students who have had both residence and correspondence study, or both residence and extension study. It does not at all argue that there is any special merit in one type of study that is not found in the other types of study. In Chapters II and V which follow certain factors are considered which help to account for these differences in grades. Nevertheless, the administrator is still confronted with the fact that for all groups of students considered and even for the same group, correspondence grades are highest, extension, next, and residence, lowest. The further fact that variation is greatest for correspondence grades, next for extension grades, and lowest for residence grades is a strong indication that correspondence and extension grades are less efficiently administered at Kirksville than are residence grades. However, at Macomb where extension work is carried on by full time instructors, variability is less for extension than for residence grades. A full time extension faculty is probably a step in the right direction for better administration of extra-mural grades. Moreover, the fact that, when both rank of grades, and influence of type of study on residence enrolment are considered, extension grades are so much more closely related to residence grades than are correspondence grades, probably indicates that extension study is superior to correspondence study. The educational implication involved is in harmony with that pointed out at the close of Chapter VII, Part One. (Page 156) CHAPTER II RELATION OF GRADES TO AGE AND ADVANCEMENT In this chapter the following questions are considered: (1) Are age and advancement correlated with grades? (2) For what types of study is the correlation greatest? (3) For what groups of students is the correlation greatest? (4) For what groups of students are age and advancement greatest? I. INTRODUCTORY STATEMENT The purpose of this chapter is to find whether age and advancement affect grades in different types of study, and to determine the extent of relationship between age and grades, and advancement and grades. Results will be noted that help to explain why grades in certain types of study and among certain groups of students are higher than grades in other types of study and among other groups of students. Advancement means the number of semester hours completed. Since each study at Kirksville has a credit of 2.5 semester hours, advancement represents also the number of studies completed. II. ADVANCEMENT AND GRADES 1. Students with both residence and correspondence study a. Advancement and residence grades Let us take the 340 students, of the year 1919-1920, who had both residence and correspondence study, and arrange a correlation table for advancement (number of studies all told) and residence grades. The relations involved are shown in Table VIII. The mean of the number of studies is 26.3, where each study equals 2.5 semester hours; the standard deviation is 11.6 studies. All questions relative to grades in this table were answered under Table I of the preceding chapter. The coefficient of correlation is r = .316 ± .034. The correlation ratio of advancement on grades is ηag = .39 ± .032. The regression is practically linear since the test of linearity is short by only .5 of a unit. Hence there is a well marked correlation between advancement and age in this group which is slightly understated by r = .316. b. Advancement and correspondence grades Let us take the correspondence grades, used in Table VIII, of the same 340 students and arrange a correlation table for advancement and correspondence grades. This arrangement gives Table IX. The number of studies in this table, and the measures involved, are the same as in the preceding table. The coefficient of correlation is r = .212 ± .033. There is again a correlation between advancement and grades but it is not so high as when residence grades are used. (Page 157) Residence Enrolment and Scholastic Standing 157 TABLE VIII. RELATION BETWEEN ADVANCEMENT AND RESIDENCE GRADES Residence grades No. studies 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Total 48-up 1 1 3 3 1 9 46-48 5 4 2 1 12 44-46 1 2 3 3 1 10 42-44 1 4 2 1 2 2 12 40-42 2 1 2 2 2 2 2 13 38-40 1 1 2 2 1 2 1 10 36-38 1 1 2 1 5 2 1 13 34-36 3 1 2 3 3 3 1 1 17 32-34 1 3 3 2 9 30-32 1 1 1 1 5 28-30 1 2 2 3 3 5 2 1 2 21 26-28 3 2 1 5 2 5 7 1 26 24-26 1 3 5 0 8 1 8 2 1 34 22-24 3 7 9 3 1 3 26 20-22 1 1 6 5 1 1 1 1 17 18-20 1 4 2 3 3 3 3 2 21 16-18 1 1 9 1 1 4 17 14-16 3 2 1 5 11 12-14 2 2 5 5 1 1 16 10-12 2 3 2 1 1 2 1 1 13 8-10 2 3 1 1 1 1 1 10 6-8 1 2 2 1 1 1 8 4-6 1 1 3 1 2 1 9 2-4 1 1 Total 3 3 21 41 64 52 40 52 40 15 11 7 1 340 r = .316 ηag =.39 (Page 158) 158 THE RELATION of EXTRA-MURAL STUDY TO TABLE IX RELATION BETWEEN ADVANCEMENT AND CORRESPONDENCE GRADES Correspondence grades No. studies 0-1 1-2 2-3 3-4 4-5 5-6 6-7 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 48-up 1 6 2 9 46-48 1 1 1 2 1 2 1 3 12 44-46 1 1 3 1 1 3 10 42-44 2 7 1 1 1 12 40-42 1 2 2 3 1 1 1 2 13 38-40 4 1 3 2 10 36-38 3 1 2 2 1 4 13 34-36 1 1 6 1 2 1 5 17 32-34 1 2 1 4 1 9 30-32 1 1 2 1 5 28-30 1 1 4 3 7 1 1 3 21 26-28 1 1 8 2 6 3 1 3 26 24-26 1 4 5 1 17 1 2 3 34 22-24 1 7 5 3 5 1 1 3 26 20-22 1 1 1 5 3 4 1 1 17 18-20 2 4 6 6 1 1 1 21 16-18 1 1 1 4 2 4 1 3 17 14-16 4 1 5 1 11 12-14 1 1 4 2 1 5 2 16 10-12 1 1 1 3 1 2 22 13 8-10 2 1 4 1 2 10 6-8 4 2 2 8 4-6 3 4 2 9 2-4 1 1 Total 3 0 0 1 0 11 0 5 1 0 67 2 41 7 3 106 12 21 5 8 47 340 r = .212 (Page 159) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 159 2. Students with both residence and extension study a. Advancement and extension grades We now take the extension grades of the 227 students of the year 1919-1920 who had both residence and extension study. When the tabulation is made it gives Table X. The mean of the number of studies is 25.1, and the standard deviation is 11.2 studies. The coefficient of correlation is r = .267 ± .041. Here also there is considerable correlation between advancement and extension grades. There is no need to consider advancement, and residence grades here since this question was considered under Table VII, where a larger number of students was involved, and it is known that the residence grades and number of studies in the two groups run about the same. 3. Students with residence study only a. Advancement and residence grades Finally, we take the residence grades of the 815 students of the year 1919-1920 who had no extra-mural study. This tabulation gives Table XI. The mean of advancement is 20.6, and the standard deviation is 14.1. The coefficient of correlation is r = .283 ± .02. All facts relative to grades in this group appear under Table IV of the preceding chapter. 4. Summary (1) In each type of study there is a significant correlation between advancement and grades. (2) The correlation is greatest in the two tables which deal with residence study, next greatest in extension study, and least in correspondence study. These results support the conclusion that residence and extension study are more closely related than are residence and correspondence study when grades and advancement are considered. (3) The correlation between advancement and grades in the two groups of residence students is a little greater in the group which has had correspondence study also. (4) Advancement is greatest among students who have had both residence and correspondence study, one study less for those who have had both residence and extension study, and nearly six studies less for those who have had residence study only. III. AGE AND GRADES 1. Students with both residence and correspondence study a. Age and residence grades Let us take the 340 students of the year 1919-1920, who had both residence and correspondence study, and arrange a correlation table for age and residence grades. Table XII is obtained. (Page 160) 160 The Relation of Extra-mural Study to TABLE X RELATION BETWEEN ADVANCEMENT AND EXTENSION GRADES Extension grades No. Studies 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 48-up 1 4 1 2 1 9 46-48 3 1 1 5 44-46 3 1 1 5 42-44 1 5 1 1 8 40-42 3 1 1 5 38-40 1 1 2 36-38 1 2 3 1 7 34-36 2 2 1 1 1 2 9 32-34 1 1 2 2 1 1 8 30-32 2 2 28-30 4 1 2 2 1 10 26-28 3 1 2 5 2 1 1 15 24-26 1 1 9 1 3 1 5 1 1 2 2 27 22-24 8 3 2 1 3 17 20-22 2 1 1 1 2 1 1 2 11 18-20 1 2 3 2 1 1 1 11 16-18 2 7 3 2 1 4 1 1 21 14-16 1 1 6 1 2 2 1 1 15 12-14 2 1 1 2 3 2 1 3 15 10-12 1 3 1 1 2 8 8-10 3 2 3 8 6-8 1 1 3 5 4-6 1 1 1 1 4 Total 6 0 2 1 1 56 14 24 16 1 59 14 4 5 19 227 r = .267 (Page 161) Residence Enrolment and Scholastic Standing, 161 TABLE XI RELATION BETWEEN ADVANCEMENT AND RESIDENCE GRADES Residence grades No.Studies 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 48-up 4 12 4 7 5 1 3 2 1 39 46-48 4 8 8 3 2 4 3 2 34 44-46 4 5 2 6 1 1 4 23 42-44 1 1 2 2 1 7 40-42 1 1 1 1 3 5 2 2 16 38-40 1 1 2 1 3 1 9 36-38 3 4 7 2 1 17 34-36 1 1 1 3 3 2 3 1 1 16 32-34 2 2 2 3 4 1 14 30-32 2 2 4 5 5 3 3 1 25 28-30 1 1 2 2 5 2 2 1 1 17 26-28 2 6 2 4 6 3 3 2 1 29 24-26 2 4 8 4 6 5 8 6 2 45 22-24 1 1 9 5 10 6 6 1 2 1 42 20-22 2 3 3 4 9 5 4 1 1 31 18-20 2 3 6 5 8 1 2 1 28 16-18 1 1 6 7 12 2 3 4 2 2 40 14-16 2 6 6 8 9 6 8 2 1 2 50 12-14 1 1 1 1 3 8 11 5 10 3 3 1 1 49 10-12 3 4 5 10 6 7 5 4 1 1 46 8-10 1 2 3 5 8 5 9 2 5 3 1 44 6-8 2 2 6 3 7 7 5 2 2 1 37 4-6 4 9 8 12 16 21 20 2 7 5 5 1 2 112 2-4 1 1 2 5 4 2 13 1 2 2 4 1 4 3 45 Total 1 0 1 2 1 11 13 20 23 56 122 128 143 91 80 53 32 27 7 0 4 815 r = .283 (Page 162) 162 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XII RELATION BETWEEN AGE AND RESIDENCE GRADES Residence grades Age 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Total 54-56 1 3 4 52-54 2 1 1 4 50-52 1 1 48-50 1 1 2 46-48 1 1 44-46 1 1 2 42-44 2 1 1 1 5 40-42 1 38-40 1 2 1 2 6 36-38 1 4 2 7 34-36 2 1 3 1 2 3 12 32-34 1 1 1 2 2 2 1 3 13 30-32 1 2 3 4 2 4 3 1 1 21 28-30 3 2 4 2 1 4 16 26-28 3 5 8 5 4 2 3 1 2 33 24-26 3 3 8 2 2 10 4 1 1 2 36 22-24 4 9 10 13 7 7 9 2 62 20-22 1 5 6 11 14 11 15 2 3 1 1 70 18-20 3 1 3 8 8 3 4 2 5 2 1 40 16-18 1 1 2 4 Total 3 3 21 41 54 52 40 52 40 15 11 7 1 340 r = .201 ηar = .203 The mean of age expressed in years is 26.3, the median is 24, and the standard deviation is 7.6 years. The coefficient of correlation is r = .201 ± .035, and the correlation ratio is ηar = .203 ± .035, and the regression is linear. Hence there is a sensible correlation between age and residence grades in the universe of students who have had both residence and correspondence study. (Page 163) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 163 b. Age and correspondence grades Let us now take the correspondence grades of the same 340 students used in (a) above, and form the correlation table between age and correspondence grades. TABLE XIII RELATION BETWEEN AGE AND CORRESPONDENCE GRADES Correspondence grades Age 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 54-56 2 1 1 4 52-54 1 1 2 4 50-52 1 1 48-50 1 1 2 46-48 1 1 44-46 1 1 2 42-44 1 3 1 5 40-42 1 1 38-40 1 2 1 1 1 1 6 36-38 1 2 2 1 1 7 34-36 1 1 5 3 2 12 32-34 3 1 2 6 1 13 30-32 1 3 1 3 7 11 3 21 28-30 1 1 1 1 1 7 1 3 16 26-28 2 5 4 9 5 1 6 33 24-26 3 8 3 1 1 10 1 2 1 2 3 36 22-24 1 3 11 10 18 2 3 2 1 1 62 20-22 1 3 16 11 1 22 1 3 2 9 70 18-20 1 1 2 14 5 11 1 2 3 40 16-18 1 1 1 4 Total 3 0 0 1 0 11 0 5 1 0 67 2 41 7 3 106 12 21 5 8 47 340 r = .154 ηac = .284 (Page 164) 164 THE RELATION OF EXTRA-MURAL STUDY TO The mean of age, the median, and the standard deviation of age are the same as in the preceding table. The coefficient of correlation is r = .154 ± .036, and the correlation coefficient of age on grade is ηac = .284 ± .035. The distribution is practically linear; hence, the relationship is somewhat greater than r indicates. 2. Students with both residence and extension study a. Age and residence grades Let us take the 227 students of 1919-1920 who had both residence and extension studies, and form a correlation table. TABLE XIV RELATION BETWEEN AGE AND RESIDENCE GRADES Residence grades Age 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Total 54-56 3 3 52-54 1 1 50-52 1 1 1 3 48-50 1 1 46-48 0 44-46 1 1 42-44 1 1 1 1 5 40-42 1 1 3 2 1 8 38-40 1 2 1 3 1 1 2 11 36-38 2 2 1 5 34-36 3 2 6 32-34 1 1 1 2 1 6 30-32 2 1 2 1 3 1 1 1 12 28-30 1 4 2 2 1 10 26-28 1 1 6 2 2 3 2 2 2 21 24-26 2 5 5 3 5 5 25 22-24 3 8 14 9 1 4 2 1 2 44 20-22 1 4 8 9 10 1 3 37 18-20 1 1 5 8 2 5 1 2 1 26 16-18 1 1 2 Total 3 2 0 8 22 46 38 34 25 22 12 9 5 1 227 r = .327 (Page 165) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 165 The mean of age is 27.3 years, the median is 24.4, and the standard deviation is 8.2 years. The correlation is r = .327 ± .04. This coefficient shows a high degree of correlation between residence grades and age in the universe of students who have had both residence and extension study. b. Age and extension grades Let us now take the extension grades of the same 227 students, and form a correlation table between age and extension grades. TABLE XVI RELATION BETWEEN AGE AND EXTENSION GRADES Extension grades Age 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 54-56 2 1 3 52-54 1 1 50-52 1 1 1 3 48-50 1 1 46-48 0 44-46 1 1 42-44 1 1 1 1 5 40-42 3 4 1 8 38-40 4 1 1 1 1 2 1 11 36-38 1 2 5 34-36 1 1 1 2 1 6 32-34 3 1 1 1 6 30-32 5 1 4 1 1 12 28-30 1 2 1 4 1 1 10 26-28 3 3 4 5 1 2 21 24-26 1 4 1 1 3 6 2 2 1 4 25 22-24 2 11 6 7 2 11 1 3 1 44 20-22 1 11 13 3 4 3 11 1 37 18-20 1 1 11 1 4 5 1 2 26 16-18 1 1 2 Total 6 0 2 1 1 56 14 24 16 1 59 5 14 4 5 19 227 r = .195 ηac = .507 (Page 166) 166 THE RELATION OF EXTRA-MURAL STUDY TO The mean of age, the median, and the standard deviation of age were given in the preceding table. The correlation is r = .195 ± ,036, and the correlation ratio is ηac = .507 ± .033. The distribution is not linear, but the association is significant and understated by r. 3. Students with both residence and extra-mural study a. Age and residence grades In the spring of 1922, the Otis Tests of Mental Ability were given to a sample of 207 residence students who had some form of extra-mural study also. The correlation table for age and residence grades of this group is given below. TABLE XVI RELATION BETWEEN AGE AND RESIDENCE GRADES Residence grades Age 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 Total 48-up 2 1 4 1 6 46-48 1 1 1 4 44-46 1 4 1 3 42-44 1 1 1 1 4 40-42 1 2 3 38-40 0 36-38 1 1 2 1 1 6 34-36 2 2 1 1 1 7 32-34 1 2 1 2 1 7 30-32 3 1 1 1 2 9 28-30 1 1 1 2 2 1 2 10 26-28 4 3 1 5 2 1 13 24-26 1 5 5 13 6 8 2 2 2 2 47 22-24 1 6 12 14 4 9 2 1 1 47 20-22 1 2 2 5 5 5 3 1 1 1 1 1 28 18-20 2 1 4 3 2 1 13 Total 2 3 6 19 30 44 24 35 14 11 8 7 4 207 r = .420 (Page 167) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 167 The mean of age is 27.10 and the standard deviation of age is 7.42; the mean of residence grades is 12.38, and the standard deviation is 2.42. The coefficient of correlation between age and residence grades is r = .420 ± .038. 4. Students with residence study only a. Age and residence grades—students 1919-1920 We take the 815 students, of the year 1919-1920, who had residence study only, and form the correlation table between age and residence grades. TABLE XVII RELATION BETWEEN AGE AND RESIDENCE GRADES Residence grades Age 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total 54-56 1 1 1 1 4 52-54 1 1 50-52 1 1 48-50 1 1 1 3 46-48 1 1 1 44-46 1 1 42-44 1 1 2 4 40-42 1 1 1 38-40 1 1 1 1 1 1 1 7 36-38 1 1 2 1 2 1 8 34-36 1 2 1 1 1 1 2 4 14 32-34 1 1 1 1 1 1 1 1 10 30-32 2 4 1 7 3 3 2 2 26 28-30 1 5 4 7 8 1 3 2 1 38 26-28 1 3 6 8 9 9 5 8 2 6 57 24-26 2 3 5 10 15 11 7 8 5 3 2 2 73 22-24 1 2 4 6 7 17 20 39 21 9 8 2 3 139 20-22 1 1 3 4 6 5 20 46 36 26 22 21 14 7 2 214 18-20 2 1 5 6 5 6 11 28 33 41 20 11 9 8 186 16-18 1 1 2 2 2 4 3 3 1 2 1 2 25 Total 1 0 1 2 1 11 13 20 23 56 122 128 143 91 80 53 32 27 7 0 4 815 r = .203 (Page 168) 168 THE RELATION OF EXTRA-MURAL STUDY TO The mean of age is 23.5, the median is 21.8, and the standard deviation is 5.7 years. The coefficient of correlation is r = .203 ± .021. b. Age and residence grades—students who had mental tests. Here we take a sample of 145 students with residence study only, who took in the year 1922-1923 the Otis Tests of Mental Ability, and form a correlation table between age and residence grades. TABLE XVIII Relation between age and residence grades Residence grades Age 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 Total 42-up 1 1 40-42 1 1 38-40 1 1 36-38 1 1 34-36 0 32-34 1 1 2 8 30-32 1 1 1 1 1 1 7 28-30 1 1 2 26-28 1 1 2 1 3 1 3 1 1 14 24-26 2 1 1 2 2 1 1 1 1 12 22-24 2 2 1 5 6 3 4 2 2 27 20-22 15 6 4 7 8 4 4 1 3 42 18-20 4 3 2 9 4 4 3 2 1 1 1 34 Total 3 12 13 8 27 22 18 14 10 11 3 1 3 145 r = .204 The mean of age is 23.90, and the standard deviation of age is 4.74; the mean of residence grades is 11.72, and the standard deviation is 2.67. The correlation between age and residence grades is r = .204 ± .052. This coefficient is almost in exact agreement with that found in the preceding table. c. Age and residence grades—freshmen who had mental tests At the beginning of the fall term of 1921-1922, Otis Tests of (Page 169) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 169 Mental Ability were given to 253 entering freshmen. At the close of the school year a study was made of their grades. A correlation table between age and residence grades is given below. TABLE XIX RELATION BETWEEN AGE AND RESIDENCE GRADES Age Residence grades 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24 24-25 25-26 26-27 27-28 28-29 Total 17-18 1 1 16-17 1 3 1 5 15-16 2 1 2 1 1 7 14-15 1 1 2 2 1 1 1 9 13-14 1 2 3 1 2 1 10 12-13 1 5 8 5 4 1 4 1 29 11-12 1 7 6 5 5 1 2 1 1 29 10-11 1 6 11 10 1 5 5 3 1 1 1 1 45 9-10 4 2 12 14 6 4 1 1 41 8-9 3 14 6 8 2 1 2 1 37 7-8 2 6 5 5 2 2 22 6-7 1 3 2 1 1 8 5-6 1 1 4-5 3 3 1 1 1 9 Total 5 25 70 58 38 24 11 6 7 3 0 3 3 253 r = .098 The mean of age is 19.32, and the standard deviation is 2.19; the mean of residence grades is 10.14, and the standard deviation is 2.55. The correlation between age and residence grades is r = .098 ± .042. This result shows clearly that for the less mature, who have had residence study only, the correlation between age and residence grades steadily declines. 5. Summary a. General observations It is also worthy of note that age and advancement are correlated. In the tabulation involving 340 students who had both residence and correspondence study, the correlation between age and advancement is r = .166 ± .037, and the correlation ratio of age on advancement is η = .321 ± .033. (Page 170) 170 The Relation of Extra-mural Study To When it is said that grades and age are correlated, the distribution is taken as a whole. When, a certain point of the age scale is reached the correlation of age with grades is doubtless negative, but this condition applies only to a minor portion of the scale and is overbalanced by that portion of the scale where the correlation is positive. To test opt the truth of this assumption, the students above 30 years of age in the group of 340 students who had both residence and correspondence study, were divided into two groups. The first contains 59 students from 30 to 40 years of age; the second, 20 students from 40 years old and above. By Pearson’s new method of correlation it was found that “age above 40” when compared with “age from 30 to 40”, is negatively correlated with grades, and that the coefficient of correlation is r = -.167. The form of the age grade distributions indicates that this condition is common to all the tables. The arithmetic mean of the number of residence studies for students having both residence and correspondence study is 26.3; for those having both residence and extension study, 25.1; and for those having residence study only, 20.6 in one group and 22.7 in another group considered in Chapter III. b. A summarizing tabulation The following tabulation will help to summarize the relations between age and residence grades as it appears among different groups of students: TABLE XX MEASURES OF AGE, OF RESIDENCE GRADES, AND THEIR RELATIONS SUMMARIZED (a) Students with residence study only Mean Standard deviation Correlation Agem Grades Age Grades Coefficient Table XIX—253 freshmen, 19.3 10.1 2.19 2.55 .098 Tables IV and XVII—815 in year 1919-1920 23.5 12.2 5.70 2.82 .203 Table XVIII—145 who took mental tests 23.9 11.7 4.74 2.67 .204 (b) Students with residence study and some other form of study also Tables I and XII—340, residence and correspondence 26.3 13.1 7.60 2.33 .201 Tables II and XIV—227, residence and extension 27.3 13.1 .8.20 2.29 .327 Table XVI—207, residence and extra-mural 27.1 12.4 7.42 2.42 .420 (Page 171) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 171 c. Conclusions (1) From this table, for students who have had residence study only, it appears that the correlation between age and residence grades steadily increases as age increases. This statement also holds in the main for those who have had residence study with some other type of study since there is only .2 of a year’s difference between ages in the last two rows, and the correlation for each group is considerably greater than it is for the first group under (b). (2) The correlation between age and residence grades in the main is highest in the group that has had residence study and some form of extra-mural study. (3) Grades in each type of study are significantly correlated with age. (4) In all cases, if freshmen are excluded, the correlation between age and grades is greatest for residence grades, next largest for extension grades, and least, by a small margin, for correspondence grades. However, the correlation ratio of age on grades is very large for correspondence grades. The close relationship between residence and extension study is again evidenced. (5) When age is measured both in terms of mean and median, students having both residence and extension study are oldest, next are those Laving residence and extra-mural study, next, those having residence and correspondence study, whereas those having residence study only are youngest. (6) No doubt the correlation of grades with advancement and with age partially accounts for the fact that 815 students, who had no extra-mural study, made lower grades in residence than were made in residence study by those who had extra-mural study also. But in connection with the residence grades of the 380 students who are graduates of the Teachers College at Kirksville the question of advancement was eliminated, for they all had completed a minimum of 120 semester hours of credit. What causes the group which had both residence and extra-mural study to make the highest grades? Is it age, health, or mental ability? IV. SUMMARY AND CONCLUSIONS FOR THE CHAPTER (1) Advancement and age are both significantly correlated with grades at the Teachers College at Kirksville. (2) For both age and advancement this correlation is greatest for residence grades, medium for extension grades, and lowest for correspondence grades. (3) For both age and advancement the correlation with residence grades in general is greatest when the students have had some form of extra-mural study also. (4) Students having residence study and some form of extra-mural study are older and more advanced than are students having residence study only. (Page 172) 172 THE RELATION OF EXTRA-MURAL STUDY TO Residence grades are greatest when students have had some form of extra-mural study also; and extra-mural grades are greatest when students have had residence study also. The correlation of both age and advancement with residence grades is greatest when students have had some form of extra-mural study also. Students who have had both residence and extra-mural study are older and more advanced than those who have had residence study only. Therefore, it would appear that age and advancement are factors not only in determining higher grades in general but also in accounting for the making of higher residence grades by students with both residence and extra-mural study than are made by students having residence study only. Unfortunately, the records at Kirksville do not give the age of extra-mural students who have not come into residence; also the mean of the number of extra-mural studies of extra-mural students who have not come into residence is only 2.1. Hence it is impossible to find in this group of students the correlation between extra-mural grades and age, and between extra-mural grades and advancement. A study that would determine these relations would be valuable. However, the probability is that relations would be found similar to those just pointed out in connection with residence grades. Certain factors that affect grades will receive consideration in Chapter V. (Page 173) CHAPTER III RELATION OF HEALTH TO NUMBER OF STUDIES, GRADES, AND TYPE OF STUDY In this chapter the following questions are considered: (1) Are health and number of residence studies correlated? (2) Are health and number of extra-mural studies correlated? (3) Are health and grades correlated? (4) What type of students are most sensitive to health influence? (5) Do students in poor health show a tendency to earn credit through extra-mural study? I. INTRODUCTORY STATEMENT The State Teachers College at Kirksville has a strong and well equipped Department of Public Health which has kept for students accurate health and physical records as made in the physical examinations given each term for the past six years. Two lists of names selected as random samples were submitted to the Chairman of the Department of Public Health. The first consisted of 280 persons who had both residence and extra-mural study at Kirksville; the second, of 253 persons who had residence study only. Those who had extra-mural study only, did not take the physical examinations at Kirksville. The Chairman of the Department of Public Health, who knew nearly every student personally, examined the physical record cards kept of these students, and scored them as “good” or “poor”. The class records of each of these students for the whole time in school were then looked up. The arithmetic mean of all residence grades gave the student’s standing in residence study, and the arithmetic mean of all extra-mural grades gave the student’s standing in extra-mural study. Each list of names was further divided into two groups according to the health report, and arranged into various tabulations for purposes of study and comparisons. II. HEALTH AND NUMBER OF RESIDENCE STUDIES 1. Students with residence study only a. Relations involved We first consider health and number of studies of the 253 students who had residence study only. The relations involved are shown in Table XXI. By Pearson’s method, which applies to an attribute and a variable, and by use of Everitt’s Tables, the coefficient of correlation between health and number of studies can be found. The mean of the whole distribution is 22.732; mean for those in poor health, 21.216; standard deviation of total distribution, 13.106. (Page 174) 174 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXI RELATION BETWEEN HEALTH AND NUMBER OF RESIDENCE STUDIES Number of residence studies Health 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 Total Good 3 3 6 12 10 10 9 11 8 14 8 12 5 4 3 6 3 4 2 8 1 4 7 4 3 160 Poor 4 7 3 4 9 3 10 6 1 4 8 7 5 1 6 0 0 0 1 2 0 2 5 3 2 93 Total distribution 7 10 9 16 19 13 19 17 9 18 16 19 10 5 9 6 3 4 3 10 1 6 12 7 5 253 r = .112 TABLE XXII RELATION BETWEEN HEALTH AND NUMBER OF RESIDENCE STUDIES Number of residence studies Health 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 Total Good 1 1 1 2 6 8 9 10 7 10 25 15 9 12 4 6 2 9 10 5 7 8 2 0 3 172 Poor 1 2 4 4 4 7 9 8 4 9 8 7 7 1 6 3 2 6 1 4 7 2 1 1 108 Total distribution 1 2 3 6 10 12 16 19 15 14 34 23 16 19 5 12 5 11 16 6 11 15 4 1 4 280 r = .051 (Page 175) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 175 Therefore p̄/σn = —.116 1/2(1 — a) = .3652, 1/2(1 + a) = .6348, z = .3759 Therefore q̄/σp = 1.029 Therefore rpn = —.112 b. Interpretations This coefficient shows that the correlation between poor health and number of residence studies is negative. Then the correlation between good health (health) and number of residence studies is positive and just as strong numerically as that between poor health and number of residence studies. It may be represented by r = .112. In the universe of students with residence study only as health increases, the number of residence studies increases; as health declines, the number of studies declines. 2. Students with both residence and extra-mural study a. Relations involved We consider health and number of residence studies of the 280 students who had both residence and extra-mural study. The relations involved are shown in Table XXII. Mean of whole distribution is 24.528; mean for those in poor health, 24.00; standard deviation for whole distribution, 10.508. Therefore p̄/σn = —.0502 1/2(1 — a) = .3857, 1/2(1 + a) = .6143, z = .3824 Therefore q̄/σp = .9914 Therefore rpn = —.051 b. Interpretations The correlation between poor health and number of residence studies is negative; therefore, the correlation between good health and number of residence studies is positive. It may be represented by r = .051. Thus the coefficients of correlation show that health and advancement in residence studies are significantly and positively correlated. But the correlation is somewhat stronger in the group which has had residence study only. However, this circumstance does not in itself show that those with residence study only have the better health. It means only that good health and high grades, and poor health and poor grades are more often found together in the group of students who have had residence study only, than in the group of students who have had both types of study. III. HEALTH AND NUMBER OF EXTRA-MURAL STUDIES 1. Relations involved We take here the 280 students who had both residence and extra-mural study, and consider health and number of extra-mural studies. The relations involved are shown in Table XXIII. (Page 176) 176 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXIII RELATION BETWEEN HEALTH AND NUMBER OF EXTRA-MURAL STUDIES Number of extra-mural studies Health 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 Total Good 72 40 20 17 7 8 3 1 1 1 1 0 1 172 Poor 37 33 11 9 2 2 3 3 2 1 2 2 0 1 108 Total distribution 109 73 31 26 9 10 6 4 3 2 3 2 1 1 280 r = —.09 Mean of whole distribution is 2.721; mean for those in poor health, 2.935; standard deviation of whole distribution, 2.402. Therefore p̄/σn =.089 1/2(1 — a) = .3857, 1/2(1 + a) = .6143, z = .3824 Therefore q̄/σp = .9914 Therefore rpn = .09 2. Interpretations A sensible positive correlation is found between poor health and number of extra-mural studies completed. Then good health (health) and number of extra-mural studies are negatively correlated, and r = —.09; in other words, as the health of students declines the number of subjects pursued in extra-mural courses increases. This fact is significant; and from the results in sections II and III it is seen that students in poor health complete fewer studies in residence, but more in extra-mural work than do students in good health. IV. HEALTH AND RESIDENCE GRADES 1. Students with residence study only a. Relations involved We consider health and grades of the 253 students who had residence study only . TABLE XXIV RELATION BETWEEN HEALTH AND RESIDENCE GRADES Residence grades Health 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total Good 1 0 3 5 9 24 27 35 18 20 8 5 4 0 0 1 160 Poor 1 0 1 2 2 2 5 17 16 12 13 5 3 3 2 93 Total distribution 1 0 1 3 2 5 10 18 41 43 47 31 25 11 8 6 0 0 1 253 r = .238 (Page 177) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 177 Mean of whole distribution is 12.053; mean for those in poor health, 11.436; standard deviation for whole distribution, 2.516. 1 Therefore p̄/σn = —.2452 1/2(1 — a) = .3652, 1/2(1 + a) = .6348, z = .3759 Therefore q̄/σp = 1.029 Therefore rpn = —.238 b. Interpretations Thus poor health and residence grades have strong negative correlation. This coefficient which shows that good health (health) and residence grades have strong positive correlation, is represented by r = .238. In the universe of students with residence study only, as health increases grades increase significantly. 2. Students with both residence and extra-mural study a. Relations involved Next we consider health and residence grades of students who have had both residence and extra-mural study. TABLE XXV RELATION BETWEEN HEALTH AND RESIDENCE GRADES Residence grades Health 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 16-17 17-18 18-19 19-20 20-21 Total Good 1 2 2 8 16 33 27 22 21 21 6 10 2 0 1 172 Poor 1 1 7 9 24 16 18 20 7 4 0 1 108 Total distribution 1 3 3 15 25 57 43 40 41 28 10 10 3 0 1 280 r = .103 Mean of whole distribution is 12.989; mean for those in poor health, 12.769; standard deviation of whole distribution, 2.156. Therefore p̄/σn = —.1020 1/2(1 — a) = .3857, 1/2(1 + a) = .6143, z = .3824 Therefore q̄/σp = .9914 Therefore rpn = —.103 b. Interpretations For those who have had both residence and extra-mural study, poor health and residence grades are negatively correlated, or good health (health) and residence grades are positively correlated, which correlation is represented by r = .103. It is worthy of note that the correlation between health and grades among students with residence study only is about two times as high as that among those who have had both types of study. Nearly this same ratio is found between the two groups of students when correlations between health and advancement are compared. Here (Page 178) 178 THE RELATION OF EXTRA-MURAL STUDTY TO also, in conformity with earlier results, the mean residence grade of students with both types of study is higher than it is for the group with residence study only. A similar statement holds also for the number of residence studies completed. In all instances good health and high residence grades go together, also good health and number of residence studies completed go together, but in both instances the group with residence study only is the more sensitive to health influence. V. HEALTH AND EXTRA-MURAL GRADES Students with both residence and extra-mural study are considered. 1. Relations involved We now consider health and extra-mural grades of the 280 students who had both residence and extra-mural study. TABLE XXVI RELATION BETWEEN HEALTH AND EXTRA-MURAL STUDY Grades in extra-mural study Health 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 Total Good 2 1 0 9 0 3 2 2 33 6 15 5 7 47 6 10 2 3 19 172 Poor 1 0 0 5 0 3 1 1 28 2 15 9 1 24 5 7 1 1 4 108 Total distribution 3 1 0 14 0 6 3 3 61 8 30 14 8 71 11 17 3 4 23 280 r = .119 Mean of whole distribution is 13.493; mean for students in poor health, 13.02; standard deviation of whole distribution, 3.993. Therefore p̄/σn = —.1184 1/2(1 — a) = .3857, 1/2(1 + a) = .6143, z = .3824 Therefore q̄/σp = .9914 Therefore rpn = —.119 2. Interpretations It follows that poor health and extra-mural grades are negatively correlated; therefore, good health (health) and extra-mural grades are positively correlated, which correlation is represented by r = .119. Thus in both residence and extra-mural study health and grades are quite significantly correlated. VI. HEALTH AND TYPE OF STUDY 1. Relations involved Last we consider health and type of study. It is to be regretted that it is impossible to have the health records of extra-mural students who have never enrolled for residence study. However, health records are available for two groups of students, one consisting of 280 students who had both residence and extra- (Page 179) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 179 mural study, the other consisting of 250 students who had residence study only. It is possible to divide each of these two groups into two other groups according to health records and to form association or fourfold correlation tables. TABLE XXVII RELATION BETWEEN HEALTH AND TYPE OF STUDY Health Type of study Good health Poor health Total Residence and extra-mural both (AB) = 172 (aB) = 108 (B) = 280 Residence only (Ab) =160 (ab) = 90 (b) = 250 Total (A) = 332 (a) = 198 N = 530 The coefficient of association is Q = (90)(172) — (160)(108) / (90)(172) + (160)(108) = —.055 2. Interpretations To check this result, Yule’s formula for correlation of a fourfold table is used.1 The formula in terms of elements of Table XXVII is r = Nd/(A)(a)(B)(b), where Nd = (AB)(ab) — (Ab)(aB). By this formula, r = —.027. The values of both Q and r indicate a slight negative association or correlation between good health and having both residence and extra-mural study. These coefficients show that there is a slight positive association between good health and residence study only. The result can hardly be considered as very significant, but it probably indicates an actual tendency on the part of those in poor health to get into the residence-extra-mural group of students. VII. SUMMARY AND CONCLUSIONS (1) Health and number of residence studies are positively correlated; therefore, students in good health attend school longer and complete more studies in residence than do those in poor health. (2) Health and number of extra-mural studies are negatively correlated; therefore, students in poor health complete more hours of credit in extra-mural study than do those in good health. (3) Health and grades are significantly correlated in every type of study. It is interesting to note that health affects achievement of students in the college just as certainly as it does in the 1Yule, An Introduction to the Theory of Statistics, p. 216. (Page 180) 180 THE RELATION OF EXTRA-MURAL STUDY TO elementary schools. These results fully support conclusions reached by Dr. Jasper N. Mallory in his dissertation on THE RELATION OF SOME PHYSICAL DEFECTS TO ACHIEVEMENT IN THE ELEMENTARY SCHOOL. (4) Students with residence study only are more sensitive to health influence in respect to both advancement and grades than are students with both residence and extra-mural study. (5) There is a slight tendency on the part of students in poor health to earn credit through extra-mural study. The educational implications of this chapter are very important to school administrators. As health improves, students complete more studies in residence; as it declines, they complete fewer studies in residence. This fact indicates that teachers colleges should establish departments of health and utilize them for correcting defects and minor ailments, and for improving the health of students at large. However, students in poor health not only complete fewer studies in residence, but actually turn to extra-mural work, and complete more extra-mural studies than do students in good health. It turns out that extra-mural instruction is provided for persons who are less physically fit than are residence students. It is therefore appropriate to ask what effect extra-mural instruction has in keeping teachers in service who are not up to the standard of health needed for efficient teaching. It also appears that students in good health make higher grades both in residence and in extra-mural studies than do students in poor health. This fact is an additional reason why the school should safeguard the health of its students. (Page 181) CHAPTER IV RELATION BETWEEN MENTAL ABILITY, AGE, ADVANCEMENT, GRADES, AND TYPE OF STUDY In this chapter the following questions are considered: (1) Are mental ability and age of college students correlated? (2) Are mental ability and advancement correlated? (3) Are mental ability and residence grades correlated? (4) Are mental ability and type of study correlated? I. INTRODUCTORY STATEMENT During the year 1922-1923, Otis S-A Tests of Mental Ability, Higher Examination, Form A, were given to 207 persons who were in school and had pursued some form of extra-mural study at Kirksville. At about the same time they were given also to a random sample of 145 persons who had not pursued extra-mural study. The group with residence study only, had a much higher per cent of freshmen than had the other group; however, there is not much difference in the relative numbers of students in the remaining years of college work. The freshmen in both groups were not entering freshmen; all of them had been in school six months or more. These tests were given also to 253 entering freshmen at the beginning of the fall quarter, 1922-1923. The tests were given by trained instructors under almost identical conditions. The highest score possible with the Otis Tests is 75. II. MENTAL ABILITY AND AGE 1. Students with both residence and extra-mural study We consider mental ability and age of 207 students who had both residence and extra-mural study. Each year of the college was represented in this group. Table XXVIII contains the tabulated data. The mean score is 52.60, and the median score is 51.48; the mean age, 27.10; the standard deviation of score, 9.45; the standard deviation of age, 7.42; and the range of score is from 30 to 74, and the range of age, from 18 to 52. The coefficient of correlation by the product moment method is r = —.096 ± .047. The correlation between score and age is slightly negative, and probably not very significant. 2. Students with residence study only a. A sample from a four-year college We consider mental ability and age of 145 students who had residence study only, at Kirksville. Each year of the college was represented in this sample. Table XXIX contains the tabulated data. The mean score is 52.20, and the median score is 52.42; the mean age, 23.90; the standard deviation of score, 9.56; the standard deviation of age, 4.74; and the range of score is, from 32 to 74, and (Page 182) 182 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXVIII RELATION BETWEEN MENTAL SCORE AND AGE Score Age 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-up Total 72-74 1 1 2 70-72 2 1 3 68-70 1 1 5 1 1 9 66-68 4 2 2 1 9 64-66 2 1 1 1 1 6 62-64 1 2 1 4 1 1 10 60-62 1 1 2 1 1 1 1 8 58-60 1 6 2 1 1 1 1 13 56-58 2 2 5 3 2 1 15 54-56 2 1 3 2 1 1 1 11 52-54 1 4 3 2 1 1 1 13 50-52 1 3 3 4 4 1 1 17 48-50 2 1 5 7 2 1 1 1 1 1 1 23 46-48 3 3 2 1 1 4 2 16 44-46 3 4 5 1 1 1 1 1 17 42-44 3 4 2 1 1 11 40-42 2 1 1 1 1 1 7 38-40 1 1 1 1 1 5 36-38 1 1 1 1 4 34-36 1 1 2 32-34 1 1 1 1 4 d-32 1 1 2 Total 13 28 47 47 13 10 9 7 7 6 0 3 4 3 4 6 r = —.096 (Page 183) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 183 TABLE XXIX RELATION BETWEEN MENTAL SCORE AND AGE Age Score 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 Total 72-74 1 1 70-72 1 2 1 4 68-70 2 2 4 66-68 2 2 64-66 1 1 1 1 1 5 62-64 2 3 2 2 1 10 60-62 1 3 1 1 2 8 58-60 5 1 2 8 56-58 2 1 2 1 2 1 9 54-56 3 4 2 1 1 1 12 52-54 5 1 3 1 1 1 12 50-52 1 8 4 13 48-50 2 3 1 1 1 1 9 46-48 1 2 2 3 1 9 44-46 4 2 1 2 9 42-44 1 2 2 5 40-42 3 2 1 1 7 38-40 2 1 2 1 6 36-38 2 2 1 1 1 7 34-36 1 1 d-34 2 1 1 4 Total 34 42 27 12 14 2 7 2 0 1 1 1 2 145 r = .034 (Page 184) 184 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXX RELATION BETWEEN MENTAL SCORE AND AGE Age Score 16-17 17-18 18-19 19-20 20-21 21-22 22-23 23-24 24-25 25-26 26-27 27-28 28-29 Total 62-up 1 1 1 1 1 1 6 60-62 1 2 3 58-60 1 2 3 56—58 1 2 1 3 1 8 54-56 3 8 2 1 2 2 18 52-54 1 2 2 5 1 1 12 50-52 1 5 2 6 1 1 1 1 1 19 48-50 3 5 1 10 46-48 4 6 5 1 1 1 2 20 44-46 1 12 2 3 1 2 1 1 23 42-44 5 7 7 4 3 1 1 2 1 31 40-42 7 2 2 1 1 13 38-40 4 5 3 5 1 18 36-38 1 2 6 5 1 1 1 1 1 19 34-36 1 5 2 3 1 1 13 32-34 1 3 5 3 1 1 14 30-32 3 1 2 1 7 28-30 2 3 2 7 26-28 1 1 2 4 24-26 1 1 22-24 1 1 20-22 1 1 d-20 1 1 2 Total 5 25 70 58 38 24 11 6 7 3 0 3 3 253 r = —.049 (Page 185) Residence Enrolment and Scholastic Standing 185 the range of age, from 18 to 44. The coefficient of correlation is, by the product moment method, r = .034 ± .055. This correlation is slightly positive, but is so small that it indicates practical independence between mental score and age. b. Entering freshmen We next consider mental ability and age of 253 entering freshmen. Table XXX contains the tabulated data. The mean score is 43.76, and the median score is 43.71; the mean age, 19.32; the standard deviation of score, 9.80; the standard deviation of age, 2.19; the range in score, 18 to 65; in age, 16 to 28. The correlation coefficient by the product moment method is r =—.049 ± .042. Again it is observed in a group where no elimination has taken place, that age and mental ability measured by the Otis Tests are practically independent. 3. Conclusions (1) Age and mental ability are practically independent in each group. In the youngest group there was a slight negative correlation; in the medium age group, a very slight positive correlation; and in the oldest group, a somewhat stronger negative correlation. These results show that the age factor is practically eliminated in Otis Higher Examination, Form A. The outcome is as it should be if the tests are to measure mental ability. (2) The mental score in each of the two samples taken from the college as a whole is practically the same. The mean score for entering freshmen is 8.85 points less than it is for those students with both residence and extra-mural study. (3) The standard deviation of score is practically the same in all groups. III. MENTAL ABILITY AND ADVANCEMENT 1. Students with both residence and extra-mural study We next consider mental ability and advancement of those who have had both residence and extra-mural study. Advancement as used in this chapter refers to college classification or the number of years of college work completed. Table XXXI contains the tabulated data. By the product moment method r = .162 ± .046. 2. Students with residence study only Table XXXII contains the tabulated data. By the product moment method r=.116±.054. (Page 186) TABLE XXXI RELATION BETWEEN MENTAL SCORE AND ADVANCEMENT Otis score of mental ability College credit-years 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 52-54 54-56 56-58 58-60 60-62 62-64 64-66 66-68 68-70 70-72 72-74 Total 3-4 1 3 3 2 4 3 2 3 2 1 2 3 4 2 1 36 2-3 1 1 1 1 2 3 8 2 3 2 3 4 1 2 1 1 2 1 39 1-2 1 2 2 1 3 4 5 8 4 6 4 3 4 6 3 4 5 1 4 4 1 75 0-1 1 9 2 2 5 4 6 7 7 4 3 3 4 2 1 1 1 2 57 Total 1 0 1 4 2 4 5 7 11 17 16 23 17 13 11 15 13 8 10 6 9 9 3 2 207 r = .162 TABLE XXXII RELATION BETWEEN MENTAL SCORE AND ADVANCEMENT Otis score of mental ability College credit-years 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 52-54 54-56 56-58 58-60 60-62 62-64 64-66 66-68 68-70 70-72 72-74 Total 3-4 1 1 1 1 1 1 2 2 1 4 1 1 1 1 1 19 2-3 1 1 1 2 1 2 2 4 2 2 3 1 3 1 1 1 2 30 1-2 1 1 1 1 2 1 4 3 1 3 4 4 1 1 2 5 2 1 38 0-1 1 1 4 3 4 2 3 3 5 4 4 5 1 6 3 3 2 1 2 58 Total 1 1 1 0 1 1 7 6 7 5 9 9 9 13 12 12 9 8 8 10 5 2 4 4 1 145 r = .116 (Page 187) Residence Enrolment and Scholastic Standing 187 3. Conclusions For both types of students there is a small but doubtless significant correlation between mental score and advancement. The more advanced students, for some reason, make higher mental scores than do the less advanced. IV. MENTAL ABILITY AND RESIDENCE GRADES 1. Students with both residence and extra-mural study We first consider mental ability and residence grades of students who have had both residence and extra-mural study. Table XXXIII contains the tabulated data. The central tendencies and standard deviations have been given in other tables. The coefficient of correlation between mental ability and residence grades is r = .303 ± .043. 2. Students with residence study only a. A sample from a four-year college We consider mental ability and grades of the 145 students who had residence study only. Table XXXIV contains the tabulated data. The coefficient of correlation between mental score and residence grades is r = .449 ± .043. b. Entering freshmen Finally, we consider mental ability and residence grades of 253 entering freshmen. The grades were taken after these freshmen had been in school nine months. Table XXXV contains the tabulated data. The coefficient of correlation between mental score and residence grades is r = .530 ± .030. 3. Conclusions (1) There is strong positive correlation between mental score and residence grades. (2) The correlation between mental score and residence grades increases decidedly as we pass from the most mature group with both residence and extra-mural study, to the group next in maturity with residence study only, and to the least mature represented by entering freshmen. The mean of age and the coefficients of correlation of these groups in the order mentioned above are: 27.10, 23.90, 19.32; and .303, .449, .530. V. MENTAL ABILITY AND TYPE OF STUDY 1. Relations involved We now make direct comparison of the two groups from the college, one of which had both residence and extra-mural study and the other, residence study only. It was found under section II: 3, that the central tendencies of the two groups were practically the same. Those who had both residence and extra-mural study had a higher mean score than did those who had residence study only, whereas those who had residence study only had the higher median score. Table XXXVI contains the tabulated data. (Page 188) 188 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXXIII RELATION BETWEEN MENTAL SCORE AND RESIDENCE GRADES Residence grades Score 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 Total 72-74 1 1 2 70-72 1 1 1 3 68-70 2 1 2 2 1 1 9 66-68 1 1 1 1 4 1 9 64-66 1 1 2 1 1 6 62-64 1 1 1 2 1 1 1 2 10 60-62 1 4 1 1 1 8 58-60 2 1 2 2 3 1 1 1 13 56-58 3 1 2 3 2 1 2 1 15 54-56 1 6 2 1 1 11 52-54 1 2 1 3 1 4 1 13 50-52 2 1 5 5 2 1 1 17 48-50 3 5 5 2 3 1 23 46-48 2 1 3 2 2 2 16 44-46 2 1 7 2 1 2 1 1 17 42-44 1 1 3 3 1 1 1 11 40-42 1 3 2 1 7 38-40 1 1 1 1 1 5 36-38 1 1 1 1 4 34-36 1 1 2 32-34 1 1 4 d-32 1 1 2 Total 2 3 6 19 30 44 24 35 14 11 8 7 4 207 r = .303 (Page 189) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 189 TABLE XXXIV RELATION BETWEEN MENTAL SCORE AND RESIDENCE GRADES Residence grades Score 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 Total 72-74 1 1 70-72 1 2 1 4 68-70 1 1 1 1 4 66-68 1 1 2 64-66 2 1 2 5 62-64 1 1 2 2 3 1 10 8 60-62 1 2 1 1 1 1 1 58-60 1 2 2 1 1 1 8 56-58 1 1 2 2 2 1 9 54-56 1 2 1 1 2 3 1 1 12 52-54 5 3 1 2 1 12 50-52 1 2 1 3 2 1 2 1 13 48-50 1 2 1 2 2 1 9 46-48 2 3 2 2 9 44-46 1 1 2 1 1 1 2 9 42-44 1 1 1 2 5 40-42 2 1 3 1 7 38-40 1 2 2 1 6 36-38 1 2 1 1 1 1 7 34-36 1 1 d-34 1 1 1 1 4 Total 3 12 13 8 27 22 18 14 10 11 3 1 3 145 r = .449 (Page 190) 190 THE RELATION OF EXTRA-MURAL STUDY TO TABLE XXXV RELATION BETWEEN MENTAL SCORE AND RESIDENCE GRADES Residence grades Score d-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 Total 62-64 1 1 1 1 1 1 6 60-62 1 1 1 3 58-60 2 1 3 56-58 1 1 2 1 1 1 1 8 54-56 1 2 3 3 2 1 1 1 2 2 18 52-54 1 1 3 3 1 1 2 12 50-52 1 2 4 2 5 2 3 19 48-50 1 1 1 1 3 2 1 10 46-48 3 1 2 5 4 4 1 20 44-46 1 4 5 5 4 2 1 23 42-44 1 3 6 3 6 5 5 1 1 31 40-42 1 1 3 3 2 1 1 1 13 38-40 3 3 2 4 2 1 1 2 18 36-38 1 3 7 3 2 2 1 19 34-36 1 3 6 1 1 1 13 32-34 1 2 2 4 3 1 1 14 30-32 2 1 1 1 1 1 7 28-30 1 2 1 2 1 7 26-28 1 2 1 4 24-26 1 1 22-24 1 1 20-22 1 1 d-20 1 1 2 Total 9 1 8 22 37 41 45 29 29 10 9 7 5 1 253 r = .530 (Page 191) RESIDENT ENROLMENT AND SCHOLASTIC STANDING 191 TABLE XXXVI RELATION BETWEEN MENTAL SCORE AND TYPE OP STUDY Otis score Type of study 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 52-54 54-56 56-58 58-60 60-62 62-64 64-66 66-68 68-70 70-72 72-74 Total Residence and extramural 1 0 1 4 2 4 5 7 11 17 16 23 17 13 11 15 13 8 10 6 9 9 3 2 207 Residence only 1 1 1 0 1 1 7 6 5 9 9 9 13 12 12 9 8 8 10 5 2 4 4 1 145 Total distribution 1 2 1 1 5 3 11 11 14 16 26 25 32 30 25 23 24 21 16 20 11 11 13 7 3 352 r = .029 (Page 192) 192 THE RELATION OF EXTRA-MURAL STUDY TO Mean of total distribution is 52.352; mean of those with residence study only, 52.2; standard deviation of total distribution, 9.634. Therefore p̄/σn = —.0159 1/2(1 — a) = .4119, 1/2(1 + a) = .5881, z = .2226 Therefore q̄/σr = .5409 Therefore rrn = —.029 2. Comparisons The correlation between mental score and being a student with both residence and extra-mural study is r = .029. This coefficient indicates that mental score and type of study, as represented by those having residence study only, and by those having both residence and extra-mural study, are practically independent. As noted earlier, the mean of score for those with both residence and extra-mural study is 52.60. It is seen that the mean score of the group that had residence study only is .4 of a unit less than that of the group that had both types of study. On the other hand, the median of this group is .94 of a unit larger than the median of the group that had both residence and extra-mural study. The medians of freshman, sophomore, junior, and senior students who come from the group with residence study only, are respectively: 51.00, 52.25, 53.00, and 56.25, whereas the median of the total distribution is 52.42. The medians of the other group by years are in the order named above: 49.90; 50.75, 52.30, and 56.00, whereas the median of the total distribution is 51.48. Thus, in every year, and in total distributions the medians of the group that had residence study only, are the larger. It therefore appears, though the mean of scores made by those with residence study only is a trifle smaller than the mean of scores made by the other group, that, when the scores are considered in the light of all central tendencies, the advantage in score is not against those who had residence study only. This fact is true in spite of a considerable correlation between advancement and score, and in spite of too large a proportion of freshmen in the group with residence study only. But because the mean of the residence group is a little smaller than that of the other group the correlation between being a student with both residence and extra-mural study, and mental score is positive. However, this correlation is extremely small, and we are certainly justified in concluding that mental score is independent of type of study. VI. SUMMARY AND CONCLUSIONS (1) Mental ability and age are independent. (2) Mental ability and advancement are significantly correlated. This fact is shown both by central tendencies and by the coefficient of correlation. (3) Mental ability and residence grades are strongly correlated which correlation increases sharply as we pass from the residence extra-mural group, through the group with residence (Page 193) Residence Enrolment and Scholastic Standing 193 study only, to the entering freshman group. Accordingly the correlation increases as age or maturity decreases. (4) Mental ability and type of study, as represented by those with both residence and extra-mural study and by those with residence study only, are independent. These results show that the tests used are valid since the scores made do not depend upon age. They show also that difference in grades between the two groups of college students, one group with residence and extra-mural study, and the other with residence study only, cannot be explained on the ground of superior mental ability in one group. These facts are made use of in the following chapter. (Page 194) CHAPTER V FACTORS THAT ACCOUNT FOR HIGH GRADES In this chapter the following questions are considered: (1) Is age responsible for the fact that graduates with both residence and extra-mural study make somewhat higher grades than do graduates with residence study only? (2) Are age and advancement combined, responsible for the fact that students with both residence and extra-mural study make higher grades than do students with residence study only? (3) Is there an art of making grades? I. COMPARISONS OF GRADES IN DIFFERENT TYPES OF STUDY When students at large, or when students who have had both correspondence and residence study, or, when students who have had both correspondence and extension study are considered, it is seen that correspondence grades are higher than residence or extension grades.1 Moreover, extension grades under all conditions are higher than are residence grades. These differences may be due to different standards of grading in the different types of study, or to certain other factors such as advancement and age, since it was found that advancement and age are strongly correlated with grades of all kinds, and since it was also found that students with extra-mural study are older and more advanced than are students with residence study only. However, when the same students are considered and still correspondence grades are highest, extension grades, next, and residence grades, lowest, it would seem that the standards of grading are different. In other words, the student in residence is probably held to a stricter accounting when grades are reported. II. COMPARISONS OF RESIDENCE GRADES FOR DIFFERENT TYPES OF STUDENTS It is seen also that the residence grades of 223 college graduates who had both, residence and extra-mural study are somewhat higher than the residence grades of 157 graduates who had residence study only. Although in the selection of this sample difference in advancement is eliminated since all had completed 120 semester hours or more of credit; and although difference in mental ability is eliminated since we found that mental ability is independent of being a student with both residence and extra-mural study and being a student with residence study only and although slightly poorer health on the part of the group having both types of study is somewhat opposed to higher residence grades for this group than for the one having residence study only, those having both residence and extra-mural study make the higher residence grades. Now there is only one outstanding factor left that has 1Table VI, Chapter 1, Part Two. (Page 195) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 195 appeared in this study that will account for the fact that graduates with residence and extra-mural study receive higher residence grades than do those with residence study only. That factor is maturity or age. The group with both types of study is older; hence, maturity seems to account for the higher residence grades. III. INFLUENCE OF AGE AND ADVANCEMENT ON RESIDENCE GRADES Age or maturity does not influence grades quite so much as does advancement. But even after advancement is eliminated by partial correlations, age is a sensible factor in determining residence grades as the following sample shows: Let the subscripts 1, 2, 3 used with r, the coefficient of correlation, stand respectively for residence grades, age, and advancement. But for the 340 students who had both residence and extra-mural study r12 = .20, r13 = .32, r23 = . 16. Then by the well known formula for partial correlation r12.3 = r12 — r13r23 / √(1 — r23)(1 — r13)..........(VIII), we find r12.3 = .16. This coefficient is read the correlation of residence grades and age, with advancement out. Likewise we find that r13.2 = .30. This result shows that the correlation of residence grades and advancement, with age out, is a rather marked correlation, and that it is considerably higher than the correlation of residence grades and age. Also when residence grades, age, and advancement of students with residence study only, are considered, we get practically the same results. IV. SUMMARY AND CONCLUSIONS (1) Age and advancement combined are chiefly responsible for the fact that students with both residence and extra-mural study make considerably higher grades than do students with residence study only, though the two groups have the same mental ability, and the residence group is favored by somewhat better health. (2) Age and advancement may account in part for the fact that extra-mural grades are higher than residence grades, but not entirely, by any means, since extra-mural grades are higher than residence grades for the same students. (3) Age is chiefly responsible for the fact that graduates with both residence and extra-mural study make somewhat higher residence grades than do graduates with residence study only. (4) There appears to be an art of making grades. The facts brought out in the preceding paragraph lead us to ask if there is not an art of making grades. The more advanced and mature students may be more diligent and serious minded than are the less advanced and younger students, which quali- (Page 196) 196 THE RELATION OF EXTRA-MURAL STUDY TO ties may explain why students with both residence and extra-mural study make not only higher grades in general, but also higher residence grades, than do students with residence study only. Also this older and more advanced group of students may know better how to study than does the younger and less advanced group, which aptitude may account for the higher grades received by those having both residence and extra-mural study. On the other hand, the older and more advanced students may know better how to please, the teacher and how to fall in with the teacher’s notion of a good recitation than do the younger and less advanced students, or they may be more self-assertive and dogmatic than are the younger and less advanced students, which attitudes may account for the higher grades received by those having both residence and extra-mural study. Boldness accompanied by maturity of manners and physical appearance may be accepted by the teacher as an index of knowledge and understanding; consequently, the mature and self assertive students may receive higher grades than do the youthful and less assertive ones. The fact that mental ability and grades are much more highly correlated in the entering freshman group and in the group having residence study only, than in the group having both residence and extra-mural study, seemingly indicates that students having both types of study are receiving grades beyond those warranted by their mental ability. Thus it is fitting to ask: “Is there an art of making grades?” The problems arising out of this question are interesting, and their solutions are vital to successful grading. To find these answers now would divert us from our original purpose, but they will doubtless be found by trained investigators who have at hand facilities for controlled experiments. (Page 197) CHAPTER VI RELATIONS INVOLVING NUMBER OF STUDIES, ORDER OF ENROLMENT, AND GRADES In this chapter, for extra-mural students with residence study also, the following questions are considered: (1) Do those who begin with extra-mural study complete more or less residence work than those do who begin with residence study? (2) Do those who begin with extra-mural study complete more or less extra-mural work than those do who begin with residence study? (3) Do those who begin with extra-mural study make higher or lower residence grades than those do who begin with residence study? (4) Do those who have had both residence and extra-mural study complete more work in residence than those do who have had residence study only? I. STATEMENT OF QUESTION AT ISSUE The effect of order of enrolment among extra-mural students upon number of studies completed in residence and upon residence grades has yet to be considered. When an extra-mural student has first connection with a school through extra-mural study, that person is said to have extra-mural study first, but if the first connection with the school is through residence study, that person is said to have residence study first or extra-mural study second. The question now arises, since extra-mural enrolments coming first, do not exert any appreciable influence upon later residence enrolments, whether those students who have had extra-mural study first, and later enroll in residence, show more perseverance than other students do; and whether in consequence they complete more studies in residence and in extra-mural work, and make higher residence grades than other students do. If they do complete more studies and make higher grades these facts might in a measure compensate the school for the small influence extra-mural study has in leading to residence enrolment; for then, although the number of residence registrations from the extra-mural study group might be small, these enrolments would be repeated from quarter to quarter, and would add consistently to the sum total of attendance. Moreover, superior scholarship would serve as further compensation for the small residence enrolment coming from students having had extra-mural study first. Finally, the effect of extra-mural study upon residence attendance is considered. It is sometimes asked whether students who have had both residence and extra-mural study do not con- (Page 198) 198 THE RELATION OF EXTRA-MURAL STUDY TO tinue longer in school, because of their extra-mural study, than do those who have had residence study only. If it can be shown that they remain appreciably longer in school than do those with residence study only, there may be some compensation for the slight influence extra-mural study has on residence enrolment. II. RELATION BETWEEN NUMBER OF RESIDENCE AND NUMBER OF EXTRA-MURAL STUDIES 1. Kirksville We take, for the year 1919-1920, 470 students who had both extra-mural and residence study and find whether or not an increase in number of studies for one type means an increase for the other type also. Table XXXVII contains the tabulated data. By the product moment method r = —.047. There is a slight negative correlation between the number of residence and of extra-mural studies in a universe where students have had both types of study. To say the least there is substantial justification for concluding that the number of studies in the two types of study are independent, and that the number of residence studies completed does not increase as the number of extra-mural studies increases but actually tends to decrease. 2. Warrensburg and Springfield At Warrensburg, between 1915-1922, 715 different students had both residence and extra-mural study. At Springfield, between 1918-1921, 716 different students had both residence and extra-mural study. These 1431 students furnish material for a single correlation table between number of residence and of extra-mural studies. Table XXXVIII contains the tabulated data. The coefficient of correlation between number of residence and of extra-mural studies is r = .017. The correlation is very slightly positive, and indicates as near an independence between number of studies in the two types of work as could be expected. 3. Conclusions The result accords well with that found at Kirksville. As extra-mural courses increase, nothing is added to the number of residence courses. If extra-mural courses actually keep up school interest, and hold students in school as some maintain, there should be a strong positive correlation in the foregoing tables. But instead one coefficient is slightly negative, and the other is positive by a very small margin. III. ORDER OF ENROLMENT AND NUMBER OF RESIDENCE STUDIES 1. Kirksville a. Whole universe of extra-mural students Let us take, for the years 1914-1922, all students who had extra-mural study. Of this number 179, had no residence study. Table XXXIX contains the tabulated data. (Page 199) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 199 TABLE XXXVII RELATION BETWEEN NUMBER OF RESIDENCE AND OF EXTRA-MURAL STUDIES Number residence studies No. extra- mural studies 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-up Total 13-14 1 1 12-13 1 1 1 3 11-12 1 1 1 3 10-11 1 1 1 1 1 5 9-10 1 1 8-9 1 3 3 1 2 1 11 7-8 1 1 2 2 2 2 1 1 12 6-7 1 1 3 1 1 4 2 2 1 1 20 5-6 1 3 4 1 1 1 2 1 1 1 1 17 4-5 2 1 2 4 5 4 1 3 5 3 3 1 1 1 1 5 3 45 3-4 1 1 5 4 1 4 3 9 4 4 1 2 2 2 3 2 4 1 4 1 60 2-3 1 3 2 5 4 4 7 6 6 9 7 10 6 5 3 4 4 3 5 6 4 2 1 107 1-2 2 13 5 9 9 13 10 10 1 5 12 22 18 10 3 6 1 6 7 3 5 5 2 4 5 185 Total 6 21 10 24 26 29 28 27 24 42 41 36 20 10 19 7 15 17 11 13 21 7 7 9 470 r = —.047 (Page 200) THE RELATION OP EXTRA-MURAL STUDY TO 200 TABLE XXXVIII RELATION BETWEEN NUMBER OF RESIDENCE AND OF EXTRA-MURAL STUDIES Number of extra-mural studies Number of residence studies 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 Total 48-up 22 11 7 11 2 53 46-48 3 6 1 3 1 14 44-46 6 6 4 16 42-44 7 6 1 1 1 2 18 40-42 6 5 2 1 1 15 38-40 5 3 1 2 1 1 1 14 36-38 7 1 3 1 1 2 15 34-36 8 3 3 3 2 1 20 32-34 9 12 4 1 1 27 30-32 5 2 3 2 1 3 16 28-30 10 8 5 2 25 26-28 10 7 8 2 3 2 32 24-26 25 24 5 7 2 8 3 74 22-24 29 21 5 4 2 1 62 20-22 24 30 17 24 9 2 1 1 108 18-20 23 15 9 3 2 1 1 54 16-18 33 29 12 8 5 5 3 1 96 14-16 18 24 5 8 4 5 1 65 12-14 42 32 15 17 6 6 3 1 1 123 10-12 24 23 11 3 5 2 68 8-10 55 45 24 14 4 11 2 1 1 1 158 6-8 26 14 5 2 3 1 51 4-6 96 98 19 26 8 8 1 2 258 2-4 1 25 13 1 3 1 43 0-2 1 3 1 1 6 Total 519 438 168 151 67 60 6 11 2 3 4 2 1431 r = .017 (Page 201) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 201 TABLE XXXIX RELATION BETWEEN ORDER OF, ENROLMENT AND NUMBER OF RESIDENCE STUDIES Number of residence studies Type of student 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 Total No. students residence first 7 29 77 37 74 40 63 32 54 25 61 60 43 24 13 22 12 22 23 15 22 20 15 1 7 6 818 No. students extra-mural study first 183 7 15 3 11 2 6 1 1 2 4 1 0 2 1 1 0 1 1 0 0 1 1 0 0 0 244 Total distribution 190 36 92 40 85 42 69 33 55 27 65 61 43 26 14 23 12 23 24 15 22 21 16 15 7 6 1062 ren = —.693 TABLE XL RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF RESIDENCE STUDIES Number of residence studies Type of student 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 Total No. students residence first 7 29 77 37 74 40 63 32 54 25 61 60 43 24 13 22 12 22 23 15 22 20 15 15 7 6 818 No. students extra-mural study first 4 7 15 3 11 2 6 1 1 2 4 1 0 2 1 1 0 1 1 0 0 1 1 0 0 0 65 Total distribution 11 36 92 40 85 42 69 33 55 27 65 61 43 26 14 23 12 23 24 15 22 21 16 15 7 6 883 ren = —.317 (Page 202) 202 THE RELATION OF EXTRA-MURAL STUDY TO Pearson’s new method of correlation is used. Mean of whole distribution is 16.655; mean for those who had extra-mural study first, 3.994; standard deviation of whole distribution, 13.412. Therefore p̄/σn = —.9440 1/2(1 — a) = .2298, 1/2(1 + a) = .7702, z = .3032 Therefore q̄/σe = 1.3629 Therefore ren = —.693 This coefficient shows that the correlation of extra-mural study first, with number of residence studies is negative and very high. When a student has his first registration in extra-mural work, he seldom takes many studies in residence. Here, however, it may be said that the 179 extra-mural students who had no residence study at any time, should be excluded from the table since they evidently increase the negative correlation. Because there seems to be some merit in this contention, henceforth all extra-mural students who have had no residence study will be excluded. Also in the tabulations which follow for Warrensburg, Springfield, and Macomb, students who have not had residence study also, will be excluded since they serve only to increase numerically a negative correlation, or to reduce it if it is positive. So hereafter the universe will consist of students who have had both residence and extra-mural study. b. Universe of extra-mural students with residence study Table XL contains the tabulated data. Mean of whole distribution is 19.414; mean for those who had extra-mural study first, 11.862; standard deviation for whole distribution, 12.602. Therefore p̄/σn = —.5993 1/2 (1 — a) = .0736, 1/2(1 + a) = .9264, z = .1394 Therefore q̄/σe = 1.894 Therefore ren = —.317 This coefficient shows that, even after the extra-mural students who had no residence study are excluded, there is still a strong negative correlation between extra-mural study first, and the number of studies completed in residence. In other words, the fact that a student pursues extra-mural study first, is a good indication that, under most favorable conditions, he will complete but little residence study. At Kirksville students of the whole universe average a little less than 5 quarters in residence; those with residence study first, average 5 quarters; but those with extra-mural study first, average slightly less than 3 quarters. Moreover, the average time in residence, for students with residence study only, is, in two different universes studied, from 5 to 5.7 quarters.1 1Part Two; Chapter II, Table XI; Chapter III, Table XXI. (Page 203) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 203 TABLE XLI RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF RESIDENCE STUDIES Number of residence studies Type of student 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50-52 Total No. students residence first 1 13 75 14 74 27 60 29 53 17 75 36 39 18 16 12 11 16 14 9 6 8 5 6 7 11 652 No. students extra-mural study first 0 1 40 2 9 3 4 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 63 Total distribution 1 14 115 16 83 30 64 29 54 18 76 36 39 19 16 12 11 16 14 9 6 8 5 6 7 11 715 ren = —.670 TABLE XLII RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF RESIDENCE STUDIES Number of residence studies Type of student 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 50 up Total No. students residence first 4 26 109 31 65 29 51 36 42 33 31 27 31 17 6 7 15 3 2 6 9 12 10 9 5 31 647 No. students extra-mural study first 0 6 32 4 11 7 4 1 2 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 69 Total distribution 4 32 141 35 76 36 55 37 44 33 32 27 32 17 6 7 15 3 2 6 9 12 10 9 5 31 716 ren = —.431 (Page 204) 204 THE RELATION OF EXTRA-MURAL STUDY TO 2. Warrensburg a. Universe of extra-mural students with residence study Let us take for the years 1915-1922, all students who had both residence and extra-mural study. Table XLI contains the tabulated data. Mean of the whole distribution is 17.788; mean for those who had extra-mural study first, 4.232; standard deviation of whole distribution, 11.166. Therefore p̄/σn = —1.2140 1/2(1 — a) = .0881, 1/2(1 + a) = .9119, z = .1598 Therefore q̄/σe = 1.813 Therefore ren = —.670 At Warrensburg also the correlation between extra-mural study firsthand the number of residence studies completed is negative and very strong. This result shows that students who enroll in residence after first having extra-mural study are not likely to complete many studies in residence. At Warrensburg students of the whole universe average a little more than 4 quarters in residence; those with residence study first, average nearly 5 quarters; but those with extra-mural study first, average only 1 quarter. 3. Springfield a. Universe of extra-mural students with residence study We take, for the years 1918-1921, all students who had both residence and extra-mural study. Table XLII contains the tabulated data. Mean of whole distribution is 17.048; mean for those who had extra-mural study first, 7.667; the standard devitation for the whole distribution, 13.19. Therefore p̄/σn = —.7036 1/2(1 — a) = .0964, 1/2(1 + a) = .9136, z = .1574 Therefore q̄/σe = .1633 Therefore ren = —.431 At Springfield also there is strong negative correlation between extra-mural study first, and number of residence studies completed. Springfield is intermediate between Kirksville and Warrensburg. At Springfield students of the whole universe average a little more than 4 quarters in residence; those with residence study first, average 4.5 quarters; but those with extra-mural study first, average a little less than 2 quarters. Is the condition noted in preceding tabulations peculiar to Missouri? Fortunately, these results can be checked by data from a teachers college of a neighboring state. 4. Macomb, Illinois a. Universe of extra-mural students with residence study We take, for the years 1911-1923, a sample of students at Macomb who had both residence and extra-mural study. Table XLIII contains the tabulated data. (Page 205) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 205 TABLE XLIII RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF RESIDENCE STUDIES Number of residence studies Type of student 0-2 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 22-24 24-26 26-28 28-30 30-32 32-34 34-36 36-38 38-40 40-42 42-44 44-46 46-48 48-50 Total No. students residence first 15 51 49 28 17 13 15 10 11 6 12 4 3 5 3 1 1 0 1 1 2 0 0 1 1 250 No. students extra-mural study first 14 55 20 12 12 4 1 6 3 1 1 1 1 0 0 0 1 0 0 0 0 0 0 0 0 132 Total distribution 29 106 69 40 29 17 16 16 14 7 13 5 4 5 3 1 2 0 1 1 2 0 0 1 1 382 ren = -.311 (Page 206) 206 THE RELATION OF EXTRA-MURAL STUDY TO Mean of whole distribution is 8.638; mean for those who had extra-mural study first, 5.984; standard deviation of whole distribution, 8.008. Therefore p̄/σn = —.3314 1/2(1 — a) = .3455, 1/2(1 + a) = .6545, z = .3686 Therefore q̄/σe = 1.067 Therefore ren = —.311 So again and in another state the correlation between extra-mural study first, and number of studies completed in residence is negative and has about the same strength as at Kirksville. At Macomb students of the whole universe average a little more than 2 quarters in residence; those with residence study first, average 4.5 quarters; but those with extra-mural study first, average only 1.5 quarters. 5. Conclusions (1) In four great, tax-supported, teacher producing institutions, in a universe of extra-mural students with residence study also, it was found in each instance that there is a high negative correlation between extra-mural study first, and number of residence studies completed. (2) It was found in the universe considered, that extra-mural students with residence study first, complete from 2 to 5 times as many studies in residence as do extra-mural students with extra-mural study first. Nor does the average number of residence studies completed by those with extra-mural study first, compare at all favorably with the average number of studies completed by those with residence study only. (3) It was shown earlier that very few of those, who have extra-mural study first, enroll in residence, and now it is found that those who do enroll do not continue long in residence. IV. ORDER OF ENROLMENT AND NUMBER OF EXTRA-MURAL STUDIES. 1. Statement of problem The preceding tables and discussion show that those, who enroll in extra-mural study first, and later take residence study, do not attend school in residence nearly as long as do those who enroll in residence study first, and later take extra-mural study. It is also of interest to ask how first enrolment in extra-mural study affects the number of extra-mural courses completed. This question is considered for Kirksville, Warrensburg, Springfield, and Macomb. Extra-mural students are taken for the same periods as they, were under section III of this chapter. Since, however, only extra-mural studies are considered there is no reason for excluding students who had no residence study as was done under section III. 2. Universe of extra-mural students a. Kirksville (Page 207) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 207 TABLE XLIV RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF EXTRA-MURAL STUDIES Number of extra-mural studies Type of study 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total No. students residence first 411 186 74 59 25 18 19 14 0 4 4 2 0 2 818 No. students extra-mural study first 150 52 22 10 5 0 2 1 1 0 0 0 0 244 Total distribution 561 238 96 69 30 18 21 15 1 5 4 2 0 2 1062 ren = —.166 Mean of whole distribution is 2.268; mean for those with extra-mural study first, 1.738; standard deviation for whole distribution, 1.8342. Therefore p̄/σn = —.2263 1/2(1 — a) = .2298, 1/2(1 + a) = .7702, z = .3032 Therefore q̄/σe = 1.3629 Therefore ren = —.166 b. Warrensburg TABLE XLV RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF EXTRA-MURAL STUDIES Number of extra-mural studies Type of student 1 2 3 4 5 6 7 8 9 10 11 12 Total No. students residence first 200 203 81 81 36 35 3 5 2 3 3 0 652 No. students extra-mural study first 55 147 12 36 14 10 2 5 0 1 1 3 286 Total distribution 255 350 93 117 50 45 5 10 2 4 4 3 938 ren = .026 Mean of whole distribution is 2.639; mean for those with extra-mural study first, 2.693; standard deviation for whole distribution, 1.797. (Page 208) 208 THE RELATION OF EXTRA-MURAL STUDY TO Therefore p̄/σn = .0300 1/2(1 — a) = .3055, 1/2(1 + a) = .6945, z = .3486 Therefore q̄/σe = 1.141 Therefore ren = .026 c. Springfield TABLE XLVI RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF EXTRA-MURAL STUDIES Number of extra-mural studies Type of student 1 2 3 4 5 6 7 8 Total No. students residence first 274 190 78 62 21 16 2 4 647 No. students extra-mural study first 198 21 10 6 30 0 319 Total distribution 472 271 99 72 27 19 2 4 966 ren = -.251 Mean of whole distribution is 1.961; mean for those with extra-mural study first, 1.604; standard deviation for whole distribution, 1.285. Therefore p̄/σn = —.2777 1/2(1 — a) = .3302, 1/2(1 + a) = .6698, z = .3622 Therefore q̄/σe = 1.096 Therefore ren = —.251 d. Macomb TABLE XLVII RELATION BETWEEN ORDER OF ENROLMENT AND NUMBER OF EXTRA-MURAL STUDIES Number of extra-mural studies Type of student 1 2 3 4 5 6 7 8 9 10 11 Total No. students residence first 108 72 26 18 17 5 3 0 0 1 0 250 No. students extra-mural study first 637 21 64 48 32 20 10 5 2 1 3 1034 Total distribution 745 284 90 66 49 25 13 5 2 2 3 1284 ren = —.467 Mean of whole distribution is 1.903; mean for those with residence study first, 2.888; standard deviation for whole distribution, 1.504. Therefore p̄/σn = .6549 1/2(1 — a) = .1947, 1/2(1 + a) = .8053, z = .2731 Therefore q̄/σr = 1.4027 Therefore rrn = .467, or ren = —.467 (Page 209) Residence Enrolment and Scholastic Standing 209 For Macomb, since the number of students with residence study first, is less than one-half of the total number, the correlation was found between residence study first, and the number of extra-mural studies. The computation gives rrn = .467. Hence the correlation between extra-mural study first, and the number of extra-mural studies is ren = —.467. 3. Conclusions It thus appears that the correlation between extra-mural study first, and number of extra-mural studies completed is also strongly negative in all schools studied except at Warrensburg where it has an insignificant positive correlation. These results indicate that students who begin their college work through extra-mural study are not inclined to take even as many extra-mural studies as are those who begin their college study in residence. V. ORDER OF ENROLMENT AND RESIDENCE GRADES 1. Statement of problem Finally, in a universe of extra-mural students with residence study it is important to know the effect of order of enrolment on residence grades. There were 1062 different extra-mural students at Kirksville from 1914-1922. Of those who had extra-mural study first, 65 later enrolled for residence study. For some reason 7 of these made no grades in residence. To be fair these 7 are excluded, leaving only 58 who made residence grades. To these is added a random sample of 340 students of the year 1919-1920 who had both residence and extra-mural grades. The two groups combined furnish a universe of 398 students who have had both residence and extra-mural study-58 of these had extra-mural study first, and 340 had residence study first. Is there any relation in this universe between extra-mural study first and residence grades? 2. Universe of extra-mural students with residence study TABLE XLVIII RELATION BETWEEN ORDER OF ENROLMENT AND RESIDENCE GRADES Residence grades Type of student 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 Total No. students residence first 0 3 3 21 41 54 52 40 52 40 15 11 7 1 340 No. students extra-mural study first 1 4 1 4 8 13 8 0 9 2 2 2 1 0 58 Total-distribution 1 7 4 25 49 67 60 43 61 42 17 13 8 1 398 ren = —.18 (Page 210) 210 THE RELATION OF EXTRA-MURAL STUDY TO Mean of whole distribution is 12.70; mean for those with extra-mural study first, 12.14; standard deviation for whole distribution, 1.989. Therefore p̄/σn = —.2815 1/2(1 — a)= .1457, 1/2(1 + a) = .8543, z = .2286 Therefore q̄/σe = 1.570 Therefore ren = —.18 3. Conclusions There is a significant negative correlation between extra-mural study first, and residence grades. In the universe of extra-mural students with residence study, those students who had their first connection with the college through extra-mural study do not make as high residence grades as do those who have their first connection through residence study. VI. RELATION BETWEEN EXTRA-MURAL STUDY AND THE NUMBER OF SEMESTER HOURS COMPLETED IN RESIDENCE 1. Amount of residence credit completed, when advancement, and time at which residence study began are not taken into account Comparison is made between the credits of students having residence study only and of those having both residence and extra-mural study. In Part One of this study it was shown that having extra-mural study first, does not lead to residence enrolment. In section II of this chapter by means of Tables XXXVII and XXXVIII it has been shown for Kirksville, Warrensburg, and Springfield that the number of residence and the number of extra-mural studies completed are independent; hence, residence credit does not increase with extra-mural credit. In section III of this chapter it has just been, shown for the three schools named above that there is strong negative correlation between having extra-mural study first and the number of residence studies completed. By reference to Tables XXI and XXII of Chapter III, Part Two, the mean of the number of residence studies completed by those having residence study only is 22.73 and the mean of the number of residence studies completed by those having both residence and extra-mural study is 24.53. In other words when 253 students with residence study only and 280 students with both residence and extra-mural study are selected at random without any reference to equal advancement and the year when in school, those students having both types of study complete on an average 1.8 studies or 4.5 semester hours more of residence credit than do those who have residence study only. Were this comparison accepted as a fair one, extra-mural study would appear to add 5 weeks to the residence attendance of each residence student who has also had extra-mural study. But evidently this comparison is unfair to those students who have had residence study only. The truth of this statement appears from two distinct (Page 211) Residence Enrolment and Scholastic Standing 211 considerations. (1) Students who have had two or more types of study are older and they are also more advanced, when both residence and extra-mural studies are counted, than are students who have residence study only; consequently, among the residence students referred to in Chapter III, Part Two, there has been no elimination in many instances because of inability to pursue college studies. But such eliminations have taken place among extra-mural students having residence study at Kirksville in as much as 77.5 per cent of all students having extra-mural study have completed one or more quarters in residence before taking extra-mural study, and 92.6 per cent of all extra-mural students who have enrolled in residence had residence study before extra-mural study.2 (2) It is also unfair to the group of students having residence study only, in making up the average of residence studies in the residence extra-mural group, to count residence studies that were completed before extra-mural study was taken, and then ascribe credit for the whole of residence attendance to extra-mural study. 2. Amount of residence credit completed, when advancement and time at which residence study began are taken into account. Comparison is made between the credits of students having residence study only and of those having both residence and extra-mural study; students in the two groups are of equal residence advancement and also are in school at the time the count of credit begins. The files of student records at Kirksville were taken alpha-betically and 247 students were found who had been in residence and had pursued their first extra-mural study in some one of the years 1917-1918, 1918-1919, 1919-1920, or 1920-1921. These students therefore had from three to six years to enter school again for residence work after having had their first extra-mural study. However, 25 of these, or 10 per cent of them, never entered again for residence study after taking up extra-mural study. To be perfectly fair to extra-mural study these 25 were excluded from this investigation and the remaining 222 students who entered again for further residence study were retained for purposes of comparison. The number of residence studies completed before the first extra-mural study was taken is noted, and constitutes the advancement of this group of students at the time the comparisons begin; and the number of residence studies completed, after these students entered again for residence study, following their first extra-mural study, represents the achievement of the residence extra-mural group of students after the influence of extra-mural study is operative upon residence attendance. Also the quarter of the year that each of these residence-extra-mural stu- 2Chapter VI, Part One, II: 3-(2), (3). (Page 212) 212 THE RELATION OF EXTRA-MURAL STUDY TO dents entered again for residence study, after having had extra-mural study for the first time, is noted. The files of student records were again examined alphabetically for students with residence study only, who were in school during the same quarters that the residence-extra-mural students were in school upon their return to residence study after first having extra-mural study, and who also were of the same advancement, in intervals of 10 hours, as were the residence-extra-mural students at the time of their return to residence study. Thus there is formed a one to one correspondence between the 222 students in each of these two groups, so that when paired one by one the pairs were in school and were of the same advancement, measured in terms of residence studies, at the time the count of residence credits began for purposes of comparison in the two groups. Table XLIX shows the number of semester hours completed in residence by these two groups of students after the time the one to one groupings were made. In this table the number of semester hours listed is the number completed in residence by each of the paired groups counting from the time residence-extra-mural students entered again for residence study immediately following their first extra-mural study. The mean of the number of hours for students having residence study only is 33.00; the mean for those having both types of study, 31.70; the mean of the whole distribution, 32.33; the standard deviation, 22.50. Therefore p̄/σn = —.0280 1/2(1 — a) = .5000, 1/2(1 + a) = .5000, z = .3990 Therefore q̄/σb = .7980 Therefore rbh = —0.35 Accordingly there is a slight negative correlation between being a student with both residence and extra-mural study and the number of semester hours completed in residence. It is also observed that students with residence study only actually complete on an average 1.3 semester hours more than do those who have had both types of study. These results show that extra-mural study does not hold students in school for residence study and thereby increase residence attendance, but that it has a slight tendency to decrease the amount of work done in residence and consequently decreases attendance slightly. This conclusion is reached in a comparison where all residence-extra-mural students who did. not return for residence study after having had their first extra-mural study, are excluded. Moreover, the residence student is not selected for purposes of comparison until the residence- extra-mural student is back in school and pursuing residence studies after having had extra-mural study for the first time. If the comparison had begun with the last quarter the extra-mural student was in residence, just before taking his first extra-mural (Page 213) Residence Enrolment and Scholastic Standing 213 TABLE XLIX RELATION BETWEEN TYPE OF STUDENT AND NUMBER OF SEMESTER HOURS COMPLETED IN RESIDENCE, WHEN PRECEDING RESIDENCE CREDITS AND TIME AT WHICH RESIDENCE STUDY BEGAN ARE THE SAME Number of semester hours Type of Student 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 80-85 85-90 90-95 95-100 100-105 105-110 110-115 Total (r) No. students residence study only 0 10 55 12 32 11 24 11 17 8 7 6 7 5 1 3 2 4 1 0 4 1 1 222 (b) No. students with both residence and extra-mural study 1 16 48 14 27 16 25 12 21 4 11 7 3 4 1 0 2 1 2 3 0 3 1 222 Total distribution 1 26 103 26 59 27 49 23 38 12 18 13 10 9 2 3 4 5 3 3 4 4 2 444 rbh = —.035 (Page 214) 214 THE RELATION OF EXTRA-MURAL STUDY TO study, then the students with residence study only would have made a still better showing than was made in the table above, for they would have had on an average about 9 months longer to be in school. There are good reasons that could be advanced for having the comparisons begin at the time suggested above, but these considerations were left out of account, and comparisons were made beginning at the time the extra-mural student was back in residence after completing his first extra-mural study. Even on this basis it is found that extra-mural study does not increase residence study, but, on the contrary, slightly decreases it. It is also found that the mean of the total number of hours completed in residence by students having residence study only is 74.05; the mean of the total number of hours completed in residence by students having both types of study is 72.59, and the mean of the number of hours completed by them in extra-mural study is 6.30. The former group had 48 graduates, the latter 52. 3. Conclusions (1) The number of residence and the number of extra-mural studies completed are independent. (2) There is high negative correlation between extra-mural study first, and the number of residence studies completed. (3) For students selected without any reference to advancement and the year when in school, those students having both residence and extra-mural study make 4.5 semester hours more of residence credit than do those having residence study only. (4) For students selected with equal advancement and in school at the time the count of credit begins, those students having both residence and extra-mural study make 1.3 semester hours less of residence credit than do those having residence study only. (5) Extra-mural study does not increase residence attendance. In fact a slight negative correlation exists between being a student with both residence and extra-mural study, and the number of semester hours completed. VII. SUMMARY AND CONCLUSIONS In answer to the questions raised at the beginning of this chapter the following facts are established and apply to a universe of extra-mural students with residence study also: (1) The number of residence, and the number of extra-mural studies are independent. (2) Those students who begin with extra-mural study, complete much less work in residence than do those who begin with residence study. They also complete much less work in residence than do those who have residence study only.3 To begin with extra-mural study is to hazard the probability of doing very much residence study. 3Part Two: Chapter II, Table XI; Chapter III, Table XXI; Chapter VI, Table XL. (Page 215) Residence Enrolment and Scholastic Standing 215 (3) Those who begin with extra-mural study, complete fewer extra-mural courses than do those who begin with residence study. (4) Those who begin with extra-mural study, make lower residence grades than do those who begin with residence study. (5) Those, who have had both residence and extra-mural study complete slightly less work in residence, than do those of equal advancement who have had residence study only. In other words, extra-mural study does not increase residence attendance. The number of residence studies is independent of the number of extra-mural studies. Residence-extra-mural students who begin with extra-mural study, complete fewer residence and fewer extra-mural studies, and also make lower residence grades than do residence-extra-mural students who begin with residence study. Moreover, extra-mural study does not increase residence attendance. These facts should be kept in mind by administrators, for they show that the residence extra-mural student who is brought in by extra-mural study, is not nearly as desirable as the one brought in by residence study; they also show that extra-mural study does not hold students in school. These remarkable results appearing collectively or separately in four great teacher producing institutions cannot be the result of chance. They offer no compensation for the insignificant influence extra-mural study has on residence enrolment. (Page 216) PART THREE CHAPTER I SUMMARY AND CONCLUSION I. METHODS OF INVESTIGATION 1. General statement In this chapter results appearing in Part One and Part Two of this study are summarized and outstanding conclusions given. The study deals with four teachers colleges of Missouri, and with one in Illinois. The State Teachers College at Kirksville receives particular attention in the study, especially in connection with grades. 2. Statistical procedure Both the theory of attributes and of variables are used extensively in this investigation. Association formulae and coefficients of association are employed frequently. The correlation coefficient and correlation ratio are employed where needed. The regression equation is used for purposes of showing relationship and extent of correlation. Pearson’s new method of determining correlation when one variable is given by alternative and the other by multiple categories is used for showing relationships and for interpreting results. His new method of correlation adapted to a variable and an attribute is also used frequently because of the nature of the material considered. Mean square contingency, coupled with methods which determine the nature of relationships, is almost indispensable in this study. Tetrachoric functions are employed occasionally to verify other and shorter methods of procedure. Weights to be attached to orders of influence and to grades are determined, and a method for dealing with orders of influence that lead to enrolment is devised.1 II. Relation of extra-mural study to residence enrolment A summary of findings now follows which shows the influence of extra-mural study in leading to residence enrolment. 1. Consensus of opinion concerning extra-mural study Reasons assigned in bulletins for offering extra-mural courses appear as follows, if listed in the order of frequency of reference: “It extends the opportunity for an education to all”; “It extends the means of education to those whose schooling has been interfered with”; and, “It improves teachers while in service”.2 If we turn to questionnaires, we find that the leading purpose as given is: “It improves teachers while in service”.3 But in replies to 1Chapter IX, Part One; Chapter I, Part Two. 2Chapter II, Part One. 3Collier's questionnaire, and Kirksville questionnaire, Chapter II, Part One. (Page 217) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 217 both of these questionnaires there appears a well defined belief that extra-mural study leads to residence enrolment. In Mr. Collier’s questionnaire, which was answered by presidents and directors of extra-mural work in teacher training institutions, more persons gave as a reason for offering extra-mural study, “It stimulates residence enrolment” than any other reason except, “It aids teachers in service”. In the Kirksville questionnaire which was answered mainly by teachers of extra-mural courses, item (c) of section (A): “Leads to residence enrolment” should probably be assigned fifth place, though it stands fourth in the total number of times it is listed. Out of 152 persons replying 72, or 47.4 per cent of all persons replying, make mention of extra-mural study leading to residence enrolment. Moreover, as previously stated, none of the headings under section (A) of the questionnaire exclude (c) and might easily imply it. Also it is evident from a study of bulletins and from observation that there is hesitancy in saying publicly: “Extra-mural study leads to residence enrolment”. However, item (a) of section (B) of the Kirksville questionnaire gives the frank view of teachers as to the influence of extra-mural study in leading to residence enrolment. Out of 149 persons replying, 51 say the influence of extra-mural study in leading to residence enrolment is pronounced; 87 say it is moderate, and only 11, that it is inconsequential. That extra-mural study leads to residence enrolment is strongly maintained in a recent bulletin by the Bureau of Education.4 So there is a well defined belief that extra-mural study leads to residence enrolment. Moreover, why should this not be a worthy reason to assign for offering extra-mural courses? This reason cannot conflict with the one so often mentioned; namely, “To improve teachers in service”. No one maintains that efficient teachers can be prepared through extra-mural study alone. Great institutions, state support, endowment, equipment, libraries, faculties, and student activities are all provided on the theory that teachers are to be educated and prepared through large cooperative and group enterprises such as can be furnished only for residence instruction. No one holds that extra-mural study is to bolster up weak, inefficient teachers who are void of desire and of ambition to make serious preparation for a life’s work through residence study. The only alternative to this undesirable condition is that extra-mural students without residence study may become residence students. By consensus of opinion expressed in the questionnaire, for a student to earn one hour of credit in extension takes a little less than twice as much of the teacher’s time as to earn one hour of credit in residence, whereas to earn one hour of credit in correspondence takes a little more than twice as much of the teacher’s time as to earn one hour of credit in residence. The view is also 4Klein, Bulletin No. 10, 1920, Bureau of Education. (Page 218) 218 THE RELATION OP EXTRA-MURAL STUDY TO expressed that 1 extension student equals about 2 residence students and 1 correspondence student equals from 2 to 3 residence students when comparison is made on basis of time required of teachers. 2. Relation between residence, correspondence, and extension enrolments In Chapter III, Part One, all students enrolled in any type of-study-for the four years 1919-1923 were considered. Enrolments in residence, correspondence, and extension study were accepted as facts without any reference to the type of study which preceded, or to the causal factors involved. From this chapter, by the use of complete and partial association formulae, the following results appear: (1) Correspondence and extension enrolments are strongly associated. This fact indicates that correspondence students are much more likely to take extension study than are students at large, and that extension students are much more likely to take correspondence study than are students at large. (2) No conclusion is reached concerning the association between residence and correspondence enrolments, and between residence and extension enrolments. In the whole universe these associations are negative, but they can be accounted for by the constitution of the universe. The association between residence and correspondence enrolments is positive in the universe of extension students, and the association between residence and extension enrolments is positive in the universe of extension students. But here also the universe of prospective students is too limited. (3) Each type of study serves as a connecting link between the two remaining types. If a student has any two types of study, the chances are largely in favor of his having the third type also. It is also clear that correspondence students, and to a less degree extension students, consist chiefly of persons who have had residence study. 3. Influence of extra-mural study on residence enrolment a. Order of enrolment In this investigation there is something more fundamental than the actual status of types of enrolment. When a student has been enrolled in more than one type of study, the order in which the enrolments took place becomes very important, if the influence of one type of enrolment in leading to other types of enrolment is to be determined b. Whole universe of students In this universe at Kirksville, 1919-1920, residence students are very strongly associated with first study in residence. In fact Q = .923. Consequently, among students in general, a probability, amounting almost to certainty, exists that a given residence student did not have extra-mural study first enrolment. (Page 219) Residence Enrolment and Scholastic Standing 219 c. Universe of students who had both residence and extra-mural study In this universe at Kirksville, 1919-1920, there is almost perfect association between residence enrolments and first enrolments. Q = .996. This association indicates that students who have had both residence and extra-mural enrolments almost without exception have residence enrolment first. Naturally the coefficients of association are positive and large, as explained in Chapter IV, Part One. But, if extra-mural study were functioning appreciably in bringing students into residence, the coefficients would be reduced considerably below unity in each universe. The significant fact is not that the associations are positive, but that both are almost complete. d. Universe of public school teachers of northeast Missouri The universe of teachers furnishes a good standard for comparison. In this universe there is a slight negative association between residence study at Kirksville and first enrolment in extra-mural study. Here Q = —.062, and r =—.023. When teachers at large are considered, some new and some old, some students in other colleges and some graduates of other colleges, some just graduated from high school and some who have been students at Kirksville, it is found that the student who "begins with extra-mural study at Kirksville is less likely to enroll for residence study at Kirksville than is a teacher selected at random from the universe exclusive of those who have had residence study at Kirksville. Moreover, extra-mural study is strongly associated with earlier residence enrolment in the universe of teachers. The association is expressed by Q = .809. e. Conclusions From Chapter IV, Part One, the following well established results appear: (1) Nearly all residence students have their first connection with the school through residence study. (2) The great majority of extra-mural students have residence instruction before they take up extra-mural study. This condition does not exist at Macomb, Illinois. (3) Extra-mural study does not increase residence enrolment appreciably. (4) Extra-mural students who have had no residence instruction in a school are hardly as good prospective residence students as are teachers chosen at random, who also have had no residence instruction. 4. Extra-mural students as prospective college students a. Introductory statement In Chapter V, Part One, it was found by an intensive and rather extensive study of high school graduates, that those who (Page 220) 220 The Relation of Extra-mural Study To have a college preference are much the best prospective students, that those who have no school preference come next, and that those who prefer another school come last of all. The standards set up in Chapter V, Part One, are used for purpose of comparisons in Chapter VI, Part One. Our universe has now been extended to include the extra-mural students of three teachers colleges of Missouri and one in Illinois. The schools in Missouri are Kirksville, Warrensburg, and Springfield; the one in Illinois is Macomb. b. Teachers colleges of Missouri If in Chapter VI, Part One, k stands for Kirksville; w, for Warrensburg; s, for Springfield and a, for the three schools combined, then the coefficients of association between residence study and first enrolment, in the universe of extra-mural students who have had residence study also are Qk = .983, Qw = .982, Qs = .977, and Qa = .983. In the same universe, by tetrachoric functions, the coefficient of correlation between residence study and first enrolment for the three schools combined is r = .98. This universe gets at the heart of the question. These coefficients show that the data dealt with in Missouri are homogeneous; they indicate that practically all students of teachers colleges of Missouri have their first connection with the school through residence study. Hence residence students who had their first connection with the school through extra-mural study are practically negligible. If the whole universe of extra-mural students without restriction is used the coefficients are just slightly less. It is clear that extra-mural study first, in Missouri has no appreciable effect in advancing residence enrolment. c. Macomb Teachers College The consideration of the influence of extra-mural study on residence enrolment raised some difficult questions at Macomb. These difficulties were fully considered in Chapter VI, Part One. It is evident, if extra-mural study increases residence enrolment, that the increase must come from extra-mural students who had extra-mural study first. In the Missouri schools, especially at Kirksville, the number who have extra-mural study first is small, whereas at Macomb, Illinois, the number is large. However, the per cent of those, who had their first connection with a school through extra-mural study and later entered for residence study, is as follows: 26.6 per cent at Kirksville, 22 per cent at Warrensburg, 21.6 per cent at Springfield, and 12.6 percent at Macomb. Though Macomb reaches many more new students than the Missouri schools do, a smaller per cent of those, who had extra-mural study first, comes later into residence study in Illinois than in Missouri. The same conclusion is reached by forming a fourfold table between extra-mural study in Missouri and Illinois as one variate, and residence registration and non-registration as the other (Page 221) Residence Enrolment and Scholastic Standing 221 variate. It gives Q = .323. This result shows that extra-mural study in Missouri, when compared with extra-mural study in Illinois, is strongly associated with residence registration when the universe consists of extra-mural students with extra-mural study first. But it is seen that extra-mural study in Missouri has very little influence on residence enrolment. Hence the influence in Illinois is even less, and the conditions found in Missouri extend beyond the boundaries of the state. d. Application of standards In Chapter V, Part One, a study was made of the relation between college preference and later registration of high school graduates. The standards derived for high school graduates that enrolled at Kirksville are now employed.5 When high school graduates are classified as, “Kirksville preference”, “No preference”, “Other school preference”, and “All high school graduates”, the numbers expressing the per cent of each group that later enrolled at Kirksville are, respectively: 40.1,15.7,10.9,22.2. The numbers expressing the per cent of extra-mural students with extra-mural study first, who enrolled for residence study at Kirksville, Warrensburg, Springfield, Macomb, and all four schools combined are, respectively: 26.6, 22.6, 21.6, 12.6, 17.4. The per cent of residence enrolments is highest at Kirksville and lowest at Macomb. e. Conclusions In this universe of extra-mural students, with extra-mural study first, it is found: (1) The per cent of residence enrolments for each school is much lower than the per cent of enrolments for high school graduates who prefer Kirksville. (2) The per cent of residence enrolments for all extra-mural students, in the four schools combined, is considerably less than the per cent of enrolments for all high school graduates at Kirksville. (3) The per cent of residence enrolments for all extra-mural students, in the four schools combined, is only slightly greater than the per cent of enrolments for the “No preference” group of high school graduates at Kirksville. It therefore follows that extrar-mural students with extra-mural study first, as prospective college students, are almost exactly on a par with high school graduates who have no college preference; they are not quite as good prospective students as high school graduates in general; and, when compared with high school graduates with college preference, extra-mural students 5Chapter VI, Part One, Table XXXIII. (Page 222) 222 THE RELATION OF EXTRA-MURAL STUDY TO are completely outclassed. Thus public school teachers and high school graduates furnish teachers colleges more accessible and productive universes of prospective residence students than do extra-mural students whose first connections with the school are through extra-mural study. 5. College graduates, and extra-mural study a. Common belief Doubtless, some persons think that the influence of extra-mural study on residence enrolment will be at a maximum among college graduates. If extra-mural students are ambitious, persistent, and full of initiative, as some writers of extension course bulletins seem to think, there may be ground for this belief. b. Conclusions Data are available from Kirksville, Warrensburg, Springfield, and Macomb for 970 graduates. These results follow: (1) Eleven graduates out of 970 had extra-mural study first, and nine of these eleven came into residence through extension study.6 (2) At Kirksville, Warrensburg, Springfield, and Macomb respectively, 1 out of 381, 1 out of 162, 1 out of 42, and 1 out of 16 graduates had extra-mural study first. There were only 48 graduates at Macomb. (3) For all schools combined, out of every 88 persons being graduated 1 had extra-mural study before being enrolled for residence study. (4) Out of 852 graduates in the three Missouri schools during the last 4 years, 8 persons, or 1 out of 106, had extra-mural study first, and 6 out of these 8 came into residence through extension study.7 (5) In the three Missouri schools, during the last four years 436 graduates had both residence and extra-mural study; 428 of these had residence study first, and 8 had extra-mural study first. The coefficient of association between residence study, and first enrolment, in this universe is Q = .9993. This coefficient shows that extra-mural study is a negligible factor in leading to residence enrolment among teachers college graduates of Missouri. Thus the influence of extra-mural study on residence enrolment is even less among college graduates than among students in general. 6. Views of student as to influences that led to residence enrolment a. Nature of replies The views of 2272 students were secured as to leading influences, aside from accessibility and economic reasons, that induced 6Table XLII, Chapter VIII, Part Two. 7Table XLIII, Chapter VIII, Part Two. (Page 223) Residence Enrolment and Scholastic Standing 223 them to enroll in a teachers college. At Kirksville the views of students were obtained during the spring quarter which is typical of the enrolment for the three quarters of the regular school year. Also the views of students were obtained at Kirksville, Warrensburg, and Cape Girardeau for the summer-quarter of 1923. As students who have had extra-mural study are congregated in the summer quarter, the samples of replies received are decidedly favorable to extra-mural study.8 b. Conclusions By the special methods devised for dealing with the data of Chapter IX, Part One, it is found that, when all schools are considered, extra-mural study ranks next to lowest in the ten well defined influences listed as leading to residence enrolment; but, when the spring quarter at Kirksville is taken as representative of the three quarters of the regular school year at the four schools considered, then extra-mural study stands lowest of the ten enumerated influences leading to residence enrolment. In brief, the results deduced are: (1) Consensus of opinion, expressed mainly by summer term students in three teachers colleges of Missouri, places “Newspapers and advertising" lowest with a strength of 2.8 per cent, “Extra-mural study” next lowest with a strength of 3.2 per cent, and “Teachers in home schools” highest with a strength of 19.6 per cent. (2) Consensus of opinion, expressed by spring term students at Kirksville, places “Extra-mural study” lowest with a strength of .9 of 1 per cent, “Newspapers and advertising” next, lowest with a strength of 3.1 per cent, and “Teachers in home schools” tied with “Parents and relatives” for highest place, each with a strength of 18.9 per cent. Since the expressed views of students in a universe especially favorable to extra-mural study coincide quite definitely with the findings noted in this study, the conclusion is reached that extra¬mural study exercises a very minor influence on residence enrolment. However, this conclusion is at wide variance with the consensus of opinion expressed by teachers of extra-mural courses.9 It is also in direct contradiction to the views expressed in a bulletin by Arthur J. Klein.10 7. Relation between types of study and order of enrolment a. Relations involved In Chapter VII there is found the relation between residence, correspondence, and extension study in connection with order of enrolment, when students have had at least one type of extra-mural study, and residence study also. Data from Kirksville, 8Table LV, Chapter IX, Part One. 9Table II-(a), Chapter II, Part One. 10U. S. Bureau of Education Bulletin, 1920, No. 10, p. 28. (Page 224) 224 THE RELATION OF EXTRA-MURAL STUDY TO Warrensburg, and Springfield treated by the mean square contingency method, and by Pearson’s new method of correlation show very definite relations between type of study, and order of enrolment. b. Conclusions (1) It has been shown for each of the three Missouri schools separately, and for all combined that there is strong positive correlation between type of study, and order of enrolment as we pass from correspondence through extension to residence study, while at the same time we pass from third enrolment to first along the enrolment variate. (2) It appears from the standpoint of order of enrolment that extension study is much more closely related to residence study than is correspondence study. This fact suggests that type of study represents contact with teacher, and that different degrees of this contact, in diminishing strength, are represented by residence, extension, and correspondence; and that order of enrolment represents established relationship with a school, and that different degrees of this relationship in diminishing strength are represented by first, secondhand third enrolments. (3) The close relationship between residence and extension study noted in (1) and (2) also holds for the universe of college graduates and appears repeatedly under varying conditions in this study. It suggests that extension study probably has greater influence on residence enrolment than has correspondence study. This view is borne out in a study of college graduates.11 The relationship noted doubtless has an important lesson for organizers and administrators of extra-mural courses. It indicates that, if extra-mural courses are to be offered, it would be well to devote more time to extension courses, and less to correspondence courses. III. RELATION OF EXTRA-MURAL STUDY TO SCHOLASTIC STANDING 1. Consensus of opinion concerning extra-mural study Reference is made to the Kirksville questionnaire in Chapter II, Part One. From (b) in section (B), it is seen that the consensus of opinion is that residence and extra-mural grades of students in general are about the same (with the weight of opinion slightly inclined to the view that extra-mural grades are higher). In (c) the view is expressed, that residence grades of persons having both residence and extra-mural credits are higher than the grades of those having residence study only. In (d) the view is expressed that extra-mural students have ability superior to that of students who have, had residence study only. In (e) the consensus of opinion is emphatic in the view that extra-mural study is inferior to residence study from the standpoint of helpfulness to the student. The consensus of opinion of extra-mural students 11Present Chapter, II: 5-(1), (4). (Page 225) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 225 who answered the last question supports with less unanimity the view expressed by teachers. Mr. Klein says, “students in residence who have taken work by correspondence ordinarily rank in the upper fourth of their classes.”12 Mr. Klein also says that “the average of preparation of earnestness and of intellectual capacity of correspondence students, when compared with [sic] the average college student in residence, is far higher.” Later these opinions are checked against facts. 2. Grades in different types of study a. Extent of inquiry A careful and detailed study was made of grades in the Teachers College at Kirksville. To some extent the data at Kirksville were supplemented by data from Macomb, Illinois. As far as comparisons were made only minor differences in results appeared. b. Conclusions By reference to Chapter I, Part Two, and in particular to Table VII, it is found that these results follow for Kirksville: (1) Students who have had both residence and extension study, or residence and correspondence study make higher grades in residence than do students with residence study only, higher grades in extension than do students with extension study only, and higher grades in correspondence than do students with correspondence study only. This result conforms with the consensus of opinion expressed in (c) of section (B) of the questionnaire. (2) When grades in the three types of study are compared, they are in every instance lowest in residence study, medium in extension study, and highest in correspondence study. This relation is true whether we compare grades of students in general, grades of students with only one type of study, or grades of students with both residence and extension study, both residence and correspondence study, or both extension and correspondence study. The results appearing here go far beyond the meager difference intimated by consensus of opinion in (b) section (B) of the questionnaire. (3) Variability is least among residence grades, medium among extension grades, and greatest among correspondence grades. This result is also true in every type of comparison mentioned in (2) above. At Macomb variability is less among extension grades than among residence grades. (4) Residence grades are better criteria of either correspondence or extension grades than correspondence or extension grades are of residence grades; and extension grades are better criteria of residence grades than are correspondence grades. These deductions follow from the coefficients of correlation and regression. 12U. S. Bureau of Education Bulletin, 1920, No. 10, p. 28. (Page 226) 226 THE RELATION OF EXTRA-MURAL STUDY TO (5) Extension and residence study appear to be more closely related than do correspondence and residence study. This relation is evident when we consider central tendencies, measures of dispersion, and coefficients of correlation and regression. (6) Students who have had both residence and extra-mural study make slightly higher residence grades and grades of somewhat less variability than do students of equal advancement, with residence study only. There is a small but significant correlation between being a student with both residence and extra-mural study, and residence grades. Mr. Klein is correct in his assumption that residence grades of persons having extra-mural study are higher than grades of classmates not having had extra-mural study. However, at Kirksville, the extra-mural students would fall far short of being in the upper fourth of the class. 3. Relation of grades to age, and advancement a. Purpose in view In Chapter II, Part Two, of this study grades and other attributes are compared. Attempt is made to discover factors that affect grades, and to measure the extent of the relationship. b. Conclusions (1) Age and advancement are both significantly correlated with grades, whether residence, extension, or correspondence. (2) For both age and advancement this correlation is greatest for residence grades, medium for extension grades, and lowest for correspondence grades. (3) For both age and advancement the correlation with residence grades in general is greatest when the students have also had some form of extra-mural study. (4) Students having residence study and some form of extra-mural study are older and more advanced than students having residence study only. Doubtless, (4) is mainly responsible for the relation observed in (3). It is also found that for students with residence study only, the correlation between age and grades increases from group to group as the age of the group increases.13 Since extra-mural students with residence study are older and more advanced than students with residence study only, and since both age and advancement are correlated with grades, it is clear why students with residence study only, make lower grades than are made in residence by students who have had both residence and extra-mural study. But age and advancement do not explain why the same students make lowest grades in residence, medium in extension, and highest in correspondence courses. 4. Relation of health to number of studies, grades, and type of study a. Source of material This topic is considered in Chapter III, Part Two. Accurate 13Table XX, Chapter II, Part Two. (Page 227) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 227 records of health examinations given at Kirksville make this phase of inquiry well worth while. b. Conclusions (1) Health and number of residence studies are positively correlated. Therefore students in good health attend school longer and complete more studies in residence than do those in poor health. (2) Health and number of extra-mural studies are negatively correlated. Therefore students in poor health complete more hours of credit in extra-mural study than do those in good health. (3) Health and grades are significantly correlated in both residence and extra-mural study. So health affects achievement un the college just as certainly as it does in the elementary school. These results support conclusions reached by Dr. Jasper N. Mallory in his dissertation on THE RELATION OF SOME PHYSICAL DEFECTS TO ACHIEVEMENT IN THE ELEMENTARY SCHOOL. (4) Students with residence study only are more sensitive to health influence in respect to advancement and grades than are students with both residence and extra-mural study. (5) There is a slight tendency on the part of students in poor health to earn credit through extra-mural study. 5. Relation of mental ability to age, advancement, grades, and type of study a. Tests used This topic is considered in Chapter IV, Part Two. Otis Tests of Mental Ability were given to 605 college students at Kirksville. b. Conclusions The following deductions are made: (1) Mental ability and age are independent. This fact speaks well for the Otis Tests. (2) Mental ability and advancement are significantly correlated. This fact is shown both by central tendencies and by coefficients of correlation. (3) Mental ability and residence grades are strongly correlated, and the correlation increases sharply as we pass from the residence-extra-mural group, through the group with residence study only, to the entering freshman group. Accordingly the correlation increases as age or maturity decreases. Why there should be so much stronger correlation between mental ability and residence grades for the young and less advanced students than for the older and more advanced students is a question of considerable moment, and is worthy of consideration in a separate study. (4) Mental ability and type of study, as represented by those with both residence and extra-mural study, and by those with residence study only, are independent, as nearly as can be (Page 228) 228 THE RELATION OF EXTRA-MURAL STUDY TO judged. This result contradicts the view expressed by consensus of opinion in (d) section (B) of the Kirksville questionnaire, and also the assumption made by Mr. Klein when he says, “the intellectual capacity of correspondence students, when compared with the average college student in residence, is far higher.” Tests show that residence students, and extra-mural students of approximately the same advancement have the same mental ability. 6. Factors that account for high grades a. Causal factors In Chapter V, Part Two, of this study further consideration is given to the relation between grades and types of study. Through partial correlations it is shown that age and grades, with advancement out, and advancement and grades, with age out, are still significantly correlated. b. Conclusions (1) Age and advancement are chiefly responsible for the fact that students with both residence and extra-mural study make considerably higher grades than do students with residence study only, though the two groups have the same mental ability and the residence group is favored by somewhat better health. (2) Age and advancement may account in part for the fact that extra-mural grades are higher than residence grades, but not entirely, since extra-mural grades are higher than residence grades for the same students. (3) Age is chiefly responsible for the fact that graduates with both residence and extra-mural study make somewhat higher residence grades than graduates with residence study only. (4) There seems to be an art of making grades. The fact that mental ability and grades have so much higher correlation in the entering freshman group and in the group having residence study only, than in the group having both residence and extra-mural study, seemingly indicates that those having both types of study are receiving grades beyond that warranted by their mental ability. Is it possible that the teacher accepts maturity of manners and appearance as an index of knowledge and understanding, and for this reason records higher grades for the mature and self-assertive students, than for the youthful and less assertive ones? 7. Relations involving number of studies, order of enrolment, and grades a. Sphere of study extended These questions were considered in Chapter VI, Part Two, of this study. It was previously found that extra-mural enrolments coming first do not exert any appreciable influence upon later residence enrolment. It is now asked whether those students who have extra-mural study first, and residence study later, do not show more perseverance than other students and in consequence, (Page 229) RESIDENCE ENROLMENT, AND SCHOLASTIC STANDING 229 complete more studies in residence and in extra-mural work and make higher residence grades than other students do; and whether those students who have had both residence and extra-mural study do not complete more studies in residence than do those who have had residence study only. To answer these questions data from Kirksville, Warrensburg, Springfield, and Macomb are utilized. The conclusions reached are the same in all four schools. b. Conclusions In answer to the questions raised the following facts appear concerning extra-mural students with residence study also: (1) The number of extra-mural and residence studies are independent. (2) Those who begin with extra-mural study complete much less work in residence than do those who begin with residence study. They also complete much less work in residence than do students who have had residence study only. To begin with extra-mural study is to hazard the probability of doing very much residence study. (3) Those who begin with extra-mural study complete fewer extra-mural courses than do those who begin with residence study. (4) Those who begin with extra-mural study make lower residence grades than do those who begin with residence study. Data from Kirksville only were available in obtaining this result and the one which follows. (5) Those who have had both residence and extra-mural study complete slightly less work in residence than do those of equal advancement who have had residence study only; hence, extra-mural study does not increase residence attendance. IV. BRIEF SUMMARY OF FINDINGS 1. Relation of extra-mural study to residence enrolment (1) Extra-mural study does not appreciably affect residence enrolment.14 (a) The student who begins with extra-mural study at Kirksville is less likely to enroll for residence study at Kirksville than is a teacher selected at random from the universe of teachers exclusive of those with residence study at Kirksville.15 (b) In the universe of extra-mural students, with extra-mural study first, in the four schools studied:16 (a1) The per cent of residence enrolments for each school is much lower than the per cent of enrolments for high school graduates who prefer Kirksville. 14Present Chapter, II: 3-e, 4-d, 5, 6; Chapters IV, V, VI, VIII, and IX, Part One. 15Chapter IV, Part One. 16Chapter VI, Part One. (Page 230) 230 THE RELATION OF EXTRA-MURAL STUDY TO (b1) The percent of residence enrolments for all extra-mural students, in the four schools combined, is considerably less than the per cent of enrolments for all high school graduates at Kirksville. (c2) The per cent of residence enrolments for all extra-mural students, in the four schools, is only slightly greater than the per cent of enrolments for the “No preference” group of high school graduates at Kirksville. (c) Out of 970 college graduates in the four schools studied 11 had extra-mural study first.17 (d) Out of ten well defined influences leading to residence enrolment, consensus of opinion of spring term students and of summer term students respectively, places extra-mural study lowest and next to lowest.18 (2) There is close relationship between type of study and order of enrolment. Extension study is more closely related to residence study than is correspondence study.19 (3) The great majority of extra-mural students in the teachers colleges of Missouri have residence study before extra-mural study. This condition does not hold at Macomb, Illinois, where nearly all extra-mural study is extension study. In Missouri extension students begin with extra-mural study much oftener than correspondence students do.20 (4) Nearly all residence students have their first connection with the school through residence study.20 (5) The consensus of opinion based on time required of teacher is that 1 extension student equals about 2 residence students, and 1 correspondence student equals from 2 to 3 residence students.21 2. Relation of extra-mural study to scholastic standing a. Grades in different types of study22 (1) Students who have had both residence and extension study, or residence and correspondence study make higher grades in residence than do students with residence study only, higher grades in extension than do students with extension study only, and higher grades in correspondence than do students with correspondence study only. (2) When grades in the three types of study are compared, they are in every instance lowest in residence study, medium in extension study, and highest in correspondence study. (3) Variability is least among residence grades, medium 17Chapter VIII, Part One. 18Chapter IX, Part One. 19Present Chapter, II: (7-b)-(l), (2), (3); Chapter VII, Part One. 20Present Chapter, II: 3-e; Chapter IV, Part One. 21Present Chapter, JI: 1; Chapter II, Part One. 22Present Chapter, III: 2; Chapter I, Part Two. (Page 231) Residence Enrolment and Scholastic Standing 231 among extension grades, and greatest among correspondence grades. (4) Residence grades are better criteria of either correspondence or extension grades than correspondence or extension grades are of residence grades; and extension grades are better criteria of residence grades than are correspondence grades. (5) Extension and residence study appear to be more closely related than correspondence and residence study. (6) Students with both residence and extra-mural study make slightly higher grades and grades of somewhat less variability than do students of equal advancement, with residence study only. b. Relation of grades to age, and advancement23 (1) Age and advancement are both significantly correlated with grades, whether residence, correspondence, or extension. (2) For both age and advancement this correlation is greatest for residence grades, medium for extension grades, and lowest for correspondence grades. (3) For both age and advancement the correlation with residence grades in general is greatest when the students have had some form of extra-mural study also. (4) Students having residence study and some form of extra-mural study are older and more advanced than students having residence study only. c. Relation of health to number of studies, grades, and type of study24 (1) Health and number of residence studies are positively correlated. (2) Health and number of extra-mural studies are negatively correlated. (3) Health and grades are significantly correlated in both residence and extra-mural study. (4) Students with residence study only, are more sensitive to health influence than are students with both residence and extra-mural study. (5) There is a slight tendency on the part of students in poor health to earn credit through extra-mural study. d. Relation of mental ability to age, advancement, grades, and type of study25 (1) Mental ability and age are independent. (2) Mental ability and advancement are significantly correlated. (3) Mental ability and residence, grades are strongly correlated, and the correlation increases sharply as we pass from 23Present Chapter, III: 3; Chapter II, Part Two. 24Present Chapter, III: 4; Chapter III, Part Two. 25Present Chapter, III: 5; Chapter IV, Part Two. (Page 232) 232 THE RELATION OF EXTRA-MURAL STUDY TO the residence-extra-mural group, through the group with residence study only, to the entering freshman group. (4) Mental ability and type of study, as represented by those with both residence and extra-mural study, and those with residence, study only, are independent. e. Factors that account for high grades26 (1) Age and advancement are chiefly responsible for the fact that students with both residence and extra-mural study make higher grades than do students with residence study only. (2) Age and advancement may account in part for the fact that extra-mural grades are higher than residence grades, but not entirely, since extra-mural grades are higher than residence grades for the same students. (3) Age is chiefly responsible for the fact that, graduates with both residence and extra-mural study make somewhat higher residence grades than do graduates with residence study only. (4) There are indications of an art in making grades that gives rank beyond that warranted by mental ability. f. Relations involving number of studies, order of enrolment, and grades27 In the universe of extra-mural students with residence study: (1) The number of residence and the number of extra-mural studies are independent. (2) Those who begin with extra-mural study complete much less work in residence than do those who begin with residence study. They also complete much less work in residence than do students with residence study only. (3) Those who begin with extra-mural study complete fewer extra-mural courses than do those who begin with residence study. (4) Those who begin with extra-mural study make lower residence grades than do those who begin with residence study. (5) Those who have had both residence and extra-mural study complete slightly less work in residence than do those of equal advancement who have had residence study only. 3. General observations Students who have their first connection with a college through extra-mural study are not likely to enroll for residence study. Public school teachers and high school graduates of northeast Missouri, both taken at large, constitute better prospective student universes than do students who begin with extra-mural study. There is but little doubt if a fraction of the time and energy spent in extra-mural instruction were spent in becoming better acquainted with public school teachers, and high school graduates, and in earnest endeavor to act as supervisors and helping teachers in elementary schools and in teacher training high schools, that residence enrolment, advancement of educa- 26Present Chapter, III: 6; Chapter V, Part Two. 27Present Chapter, III: 7; Chapter VI, Part Two. (Page 233) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 233 tional standards, and improvement of the personnel of the teaching profession would be measurably advanced. It is also significant that, by every comparison, extension study is more closely related to residence study than is correspondence study, and that it has somewhat more influence on residence enrolment than has correspondence study. The administrator should not lose sight of the fact that temporary expedients and diversions from regular school work do not influence residence enrolment to any considerable extent, but that it is the reputation and high standing of the school that attract and hold students; and that day by day it is good teaching, research, writing, and productive scholarship linked with human sympathy and understanding that count in building a school to meet the growing needs and demands of the people of the whole state for more and better teachers. Thus step by step the conclusion is reached that extra-mural study does not lead to residence enrolment. Students who begin college careers through extra-mural study are unfortunate; they appear to be lacking in initiative, perseverance, and ambition, and they fail to secure adequate preparation for the teaching profession. It seems that the great ado about “ taking the school to the student who cannot go to the school” might with much more truth and point be put “taking the school to those who have not the will power and energy to go to the school.” Extra-mural students are graded too high in extra-mural courses and, probably, in residence courses; and in the universe of extra-mural students those who begin with extra-mural study complete less work both in residence and in extra-mural courses, and also make lower residence grades than those who begin their college careers with residence study. Greater care is needed in the administration of correspondence, and extension grades. A full time extra-mural faculty appears to help in this respect. When such a faculty is not provided, doubtless frequent conferences of teachers offering extra-mural courses under the guidance of an extra-mural director would be helpful. Students in poor health do less work in residence, and more work in extra-mural courses than is done by students in good health. But as health increases the number of residence studies increases, and scholarship, as represented by grades, advances. To neglect health of students is to encourage extra-mural study at the expense of residence study. It is therefore essential that teachers colleges safeguard and improve the health of students. V. THE PROBLEM FOR THE ADMINISTRATOR 1. Meeting the public need Without doubt competition for numbers has had great weight in decisions to establish extra-mural departments in teacher training institutions. But faculties and administrators of such institutions, at least in Missouri and Illinois, can dismiss from their minds, once and for all, the fanciful belief that extra-mural study (Page 234) 234 THE RELATION OF EXTRA-MURAL STUDY TO augments residence enrolment. Acceptance of this fact leaves them free to determine policies and attitudes towards extra-mural departments and extra-mural study strictly on the basis of meeting the public need through adequate teacher training. At the present time tax-supported institutions are handi-capped by the inadequacy of appropriations to care for students in residence. Besides the mounting cost of extra-mural instruction, what additional burdens shall these schools bear in extra-mural instruction, which is so prodigal of the teacher’s time and energy. It is for the administrator to decide whether energy, time, and money when spent in extra-mural instruction meet more definitely the public need than when spent in residence instruction. If they do then extra-mural instruction is justified. 2. Decision for or against extra-mural study In deciding this question it should be borne in mind that extra-mural instruction is not increasing either residence enrolment or attendance; in fact, there are some indications that it may even retard them slightly. It is the reputation, and high standing of a school that appeal to prospective students of teachers colleges today. The reputation for scholarship, and research, and teaching skill cannot come from a residence faculty bearing in general an additional extra-mural load. Many residence instructors are not fitted for extra-mural instruction, and the work becomes drudgery and depletes their energies. An extra-mural department with a separate faculty would preserve the energy and driving power of the residence faculty. The need among faculty members today is leisure to further professional interests and study. The administrator who will furnish to faculty members according to their several abilities, opportunity for writing, for research, and for teaching skill, and then hold them accountable for results, will have to provide increased college facilities to accommodate the students who will come. Teachers and students alike agree that extra-mural instruction is inferior to residence instruction.28 It is only in residence that teachers can secure adequate preparation. To be sure this preparation may be supplemented to some extent by credits earned in extra-mural courses. But what is to be said concerning the large number of students, particularly in Illinois, who complete extra-mural courses and never come to school for residence instruction? There is a probability of bolstering up weak and inefficient teachers, and encouraging them to remain in the teaching profession after they have outlived their usefulness. This danger is surely present when “county superintendents accredit extra-mural courses for the renewal of certificates” and “boards of education in leading cities give credit for extra-mural work in the grading of teachers and (in the adjusting of) their salaries.”29 28Chapter II, Part Two. 29Bulletin, Macomb Teachers College, March, 1921, p.35 (Page 235) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 235 Moreover, the effect of extra-mural study on the class room work of teachers in service has not been adequately determined. In light of the foregoing considerations the administrator of teacher training institutions must decide for or against extra-mural instruction. 3. Growth of extension study However, with administrators the reasons for offering extra-mural instruction as given in Chapter II, Part One, may outweigh the disadvantages and handicaps to which reference has been made. It is certain that the increase in tax supported teacher training schools offering extra-mural courses has been rapid. In 1918 there were 57, and in 1922, 74 such schools. But in this same time schools offering correspondence courses increased from 40 to 52 whereas schools offering extension courses increased from 32 to 60.30 Thus class extension instruction is the form of extra-mural instruction most often used in normal schools and teachers colleges, and the schools offering such courses nearly doubled in four years’ time. This tendency is in line with the findings of this study which indicates in many ways that extension study is more closely related to residence study than is correspondence study. Macomb, Illinois, has accepted this view and an extension department of instruction has been formed where nearly all of the teaching is done by the director and his associates. The extension classes are organized in centers and, with skillful teachers in charge, these centers may come to be utilized by “helping teachers” for supervising instruction, especially in the interest of beginning teachers. The future of extra-mural study appears to lie in this direction, and the policies of Macomb both as to type of instruction and function of faculties are worthy of consideration. 4. Proposed plan of organization for extra-mural study in Missouri The teachers colleges of Missouri have been offering extra-mural courses both correspondence and extension for several years. The University of Missouri offers correspondence but not extension courses for credit. At the present time the teachers colleges have approximately 3200 correspondence and extension students, and the University has about 700 correspondence students.31 If it is desirable to continue such courses, it appears 30Collier, The Administration of Extension Courses in State Normal Schools, p. 8. 31Since this dissertation was completed the University of Missouri has inaugurated a plan of extension study that utilizes the services of teachers throughout the state. Such teachers become members of the faculty of the University, are to have the A. M. degree or its equivalent, and are to receive compensation for their services. The regulation provides that credit is not to be granted for extension study until an equal amount of credit has been completed in residence. In this ruling there appears to be recognition of the fact that extension study alone is not sufficient inducement to bring students into residence. The University of Missouri Bulletin, Volume 25, Number 12, Extension Series, No. 37, 1924-1925, Pages 3-4. (Page 236) 236 THE RELATION OF EXTRA-MURAL STUDY TO that some plan of cooperation between the six state institutions engaged in teacher training is desirable. The writer believes that extra-mural instruction for teachers in the state of Missouri should be under the direction of a single cooperating extra-mural faculty composed of two divisions—the correspondence course division, and the extension course division. The correspondence course division should be located at the University of Missouri with a director in charge, and the extension course division should be divided into five groups with a director in charge of each. One group of this division should be at each of the five state teachers colleges. The director and faculty of the correspondence division, and the director and faculty of each group of the extension course division should be nominated by the president of the school they represent, and be members of the faculty of that school, and all salaries and expenses for carrying on the work should be borne by the school represented, and in turn all fees derived should go to the school performing the service. The director of the university division should be chairman of the whole extra-mural faculty, and he and the five directors of the extension groups in each teachers college, should constitute the cabinet of the extra-mural department. This cabinet should work out extra-mural curricula, make recommendations to presidents and faculties, determine fees, and prescribe rules and regulations for carrying on the work of the department. The chairman of the department should be empowered to call meetings for studying the work and problems of extra-mural instruction. This plan calls for a division of labor in schools, and in faculties, and provides for specialization of effort, and coordination of function. It would be economical, and would conserve the strength and resiliency of residence faculties for teaching and research. The extension groups in some centers at least could organize and plan their work in such a way as to approximate the function of helping teacher. Through supervision and helping teacher service, extension directors and their associates would be brought into close relationship with young teachers, and with seniors in teacher training high schools, and through this contact instruction would be improved and considerable impetus given to residence enrolment. Some such plan as this, that will avoid duplication, that will relieve residence faculty members of a load that, is impairing their efficiency, and that will discover promising young teachers and high school graduates and induce them to enroll for residence instruction, should be adopted by the teacher producing institutions of Missouri. If this proposed plan is not regarded favorably, the teachers colleges could at least improve conditions by turning over all correspondence work to the University, and then devoting their surplus energies through extension departments to the task of furnishing, extension instruction for the teachers of their respective districts. (Page 237) RESIDENCE ENROLMENT AND SCHOLASTIC STANDING 237 Facts relative to extra-mural instruction do not warrant rivalries in building up competing organizations with overlapping functions. At the present time the teachers colleges of the state have large extra-mural enrolments which could be easily doubled. Unfortunately, however, extra-mural instruction is not leading to the coveted goal of residence study; and unless this goal is attained all efforts expended in extra-mural instruction are futile, for it is only through residence study in college or university that adequate preparation can be made for the teaching profession. Consequently, as long as extra-mural study fails to induce students to come to college for residence study, so long must its value as a teacher training agency be open to question. VI. FURTHER STUDIES SUGGESTED The writer suggests: (1) That this same study be made for endowed teachers colleges, and endowed universities with departments of education. (2) That this same study be made for colleges and universities without any regard to teacher training. (3) That a study be made to determine whether there is an art of making grades. (4) That a study be made to show the effect of extra-mural study on the class room work of public school teachers in service. (5) That a study be made to evaluate extra-mural in-struction in terms of residence instruction. Questions concerning the value, and influence of extra-mural study have usually been answered empirically. The writer hopes that this study may suggest method of procedure, and stimulate scientific inquiry into a field of investigation that has as yet been scarcely touched. (Page 238) BIBLIOGRAPHY Biometrika, Volume II Biometrika, Volume VII Biometrika, Volume IX Bittner, W. S., The University Extension Movement; United States Bureau of Education Bulletin, No. 84, 1919 Bulletins, correspondence and extension, of forty-seven leading teachers colleges and normal schools Bulletin, Kirksville State Teachers College, June, 1919 Bulletin, Kirksville State Teachers College, June, 1920 Bulletin, Kirksville State Teachers College, June, 1921 Bulletin, Kirksville State Teachers College, June, 1922 Bulletin, Macomb Teachers College, March, 1921 Bulletin, University of Missouri, Volume 25, No. 12, Extension Series, No. 37, 1924-1925 Collier, Clarence B., The Administration of Extension Courses in State Normal Schools Klein, Arthur J., Correspondence Study in Universities and Colleges; United States Bureau of Education Bulletin, No. 10, 1920 Mallory, Jasper N., A Study of the Relation of Some Physical Defects to Achievement in the Elementary School Quarterly, Macomb Teachers College, March, 1921 Report, State Superintendent of Public Schools of Missouri, 1921 Rugg, Harold O., Statistical Methods Applied to Education West, Cari J., Introduction to Mathematical Statistics Yule, G. Udny, An Introduction to the Theory of Statistics (Page 239) (Back Cover)