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EDUCATIONAL GUIDANCE 
 
 AN EXPERIMENTAL STUDY IN THE ANALYSIS 
 
 AND PREDICTION OF ABILITY OF 
 
 HIGH SCHOOL PUPILS 
 
 BY 
 
 TRUMAN LEE KELLEY 
 
 SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 
 
 FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 
 
 IN THE FACULTY OF PHILOSOPHY 
 
 COLUMBIA UNIVERSITY 
 
 PUBLISHED BY 
 
 (Eeacfjers College, Columbia Umuergttp 
 NEW YORK CITY 
 
 1914 
 
EDUCATIONAL GUIDANCE 
 
 AN EXPERIMENTAL STUDY IN THE ANALYSIS 
 
 AND PREDICTION OF ABILITY OF 
 
 HIGH SCHOOL PUPILS 
 
 *?• 
 
 BY 
 
 TRUMAN LEE KELLEY 
 
 SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 
 
 FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 
 
 IN THE FACULTY OF PHILOSOPHY 
 
 COLUMBIA UNIVERSITY 
 
 PUBLISHED BY 
 
 fteacfjers; College, Columbia ftfmbersitp 
 NEW YORK CITY 
 
 1914 
 

 Copyright 193 5 
 
 By 
 
 TRUMAN LEE KELLEY 
 
 Gift 
 
PREFACE 
 
 The task of giving tests, establishing averages, and calculating 
 relations, which shall serve as a basis for prognosis of mental 
 ability, is, in every sense, a social undertaking, and it is only 
 because of the kindly cooperation of the principals, teachers, 
 and pupils of the two schools studied that it has been possible 
 to secure the data that supply the material for this investigation. 
 The evaluation of the data has equally been a social task and I 
 am particularly indebted to Professors E. L. Thorndike, S. S. 
 Colvin, and H. A. Ruger for assistance in grading the preferences 
 of pupils in the interest test as to vocations, sports, and enter- 
 tainments, and to Mrs. Grace Osgood and Miss Grace Kelley for 
 the unique assistance which, as librarians, they were able to 
 render in grading magazines and books. 
 
 To the ever-ready, stimulating criticisms of Professor Thorn- 
 dike, I am peculiarly indebted, for it is due to his encouragement 
 that the investigation covers the three fields of mathematics, 
 English, and history instead of one only, and that the number 
 of relations determined is as extensive as it is. The field covered 
 gives the work whatever of value it has, but the accomplishment 
 of it and its appearance in print at this time has been possible only 
 because of the devoted and untiring assistance, in grading, 
 calculating coefficients of correlation, and deriving regression 
 equations, rendered by my wife. 
 
 September, 1914. T. L. Kelley. 
 
CONTENTS 
 
 SECTION PAGE 
 
 1. Statement of the Problem 1 
 
 2. Method and Specific Object 4 
 
 3. Elementary School Grades and Their Significance as Evi- 
 
 dence of High School Efficiency 7 
 
 4. Teachers' Estimates and Their Significance 14 
 
 5. Special Tests and Their Significance 19 
 
 Algebra Test 19 
 
 Geometry Test 22 
 
 English Test 25 
 
 History Test 33 
 
 w Interest Tests 40 
 
 Grading of the interest tests 44 
 
 Two kinds of reliability coefficients 53 
 
 Grade for entire interest test 55 
 
 Combination of Grades of Various Tests for Purposes of Prog- 
 nosis 62 
 
 Mot — Combination of tests with reference to (a) algebra 
 
 and (b) geometry 63 
 
 E ot — Combination of tests with reference to English 64 
 
 Hct — Combination of tests with reference to History 64 
 
 M C i — Combination of the interest tests with reference to 
 
 mathematics 65 
 
 E i — Combination of the interest tests with reference to 
 
 English 65 
 
 H c i — Combination of the interest tests with reference to 
 
 History 66 
 
 M — Combination of M ot and M i 66 
 
 E c — Combination of E ct and E ci 67 
 
 H c — Combination of H t and H c i 67 
 
 Use of Regression Equations 67 
 
 6. Use of all Sources of Data in Estimating Probable Average 
 
 Standing 71 
 
 7. The Age of Pupils as a Factor 73 
 
 8. Comparison with Other Studies 74 
 
 9. Practical Application in High School Classification 81 
 
 10. Guidance Methods 84 
 
 11. Appendix 
 
 - Ages of Pupils 86 
 
 Assignment of Numerical Magnitudes for Literal Grades 86 
 
 Extent of error in averaging literal grades 88 
 
 Elementary School Grades 89 
 
 Teachers' Estimates and Combinations of the Same 92 
 
 Bearing of the various factors upon M, E and H 94 
 
vi Contents 
 
 SECTION PAGE 
 
 11 Appendix — Continued. 
 
 Grading of the Algebra Test 95 
 
 Derivation of formulae 96 
 
 Grading of the Geometry Test 97 
 
 Grading of the English Test 98 
 
 Grading of the History Test 99 
 
 Bearing of the Various Tests upon Mathematics 99 
 
 Bearing of the Various Tests upon English 100 
 
 Bearing of the Various Tests upon History 100 
 
 Interest Tests — Grading of Books 101 
 
 Grading of Interest Tests with Reference to (a) English, (b) 
 
 Mathematics, (c) History 101 
 
 Combination of Parts of Interest Test with Reference to (a) 
 
 Mathematics, (b) English, (c) History 103 
 
 Combination of Mathematics Tests with Reference to Mathe- 
 matics. Similar Combinations of English and History Tests 105 
 •" Combination of all Sources of Data with Reference to Average 
 
 Class Standing 106 
 
 12. Table Giving Original Data 107 
 
EDUCATIONAL GUIDANCE 
 
 SECTION 1.— STATEMENT OF THE PROBLEM 
 
 Humanity's unvoiced plea for guidance is the foundation of 
 all professions. The doctor, the lawyer, the minister find that 
 belief and obedience are more often the result of need than of 
 understanding and conviction. The modern idea of education 
 is crystallizing into an effort to guide rather than to instruct — to 
 answer to a need rather than to cater to a curriculum. The 
 growing recognition of the need for vocational and educational 
 guidance is resulting in the establishment of bureaus endeavoring 
 to give the former, and in the training of psychologists to solve 
 the problems of the latter. 
 
 The movement for vocational guidance is in its infancy, but 
 it only depends upon improved methods and more extended 
 research to give it a place with the older professions. Vocational 
 guidance has sprung up out of two needs — the need of the em- 
 ployer for efficient clerks, mechanics, and laborers and, still more 
 important, the need of the individual to utilize his talents to the 
 best advantage in order to cope with present-day industrial con- 
 ditions. 
 
 This latter demand is most pressing at the time that the 
 individual is about to leave school, and it is at this point that the 
 major efforts of vocational guidance bureaus have been expended; 
 but even a hasty consideration will show that the guidance 
 exercised is tardy. It should have been present when the school 
 training of the individual became different from that of other 
 individuals — when he began to specialize and train himself for 
 his life work. It may be stated with assurance that in all cases 
 this specialization should be well under way before the completion 
 of the formal education of the pupil. 
 
 These remarks suffice to make apparent the need for such 
 educational guidance in the high school and college, as shall 
 precede and serve as a basis for the later vocational guidance. 
 2 1 
 
2 Educational Guidance 
 
 The general method to determine the accuracy of guidance is the 
 same, whether the guidance be educational or vocational, and 
 it is one of the chief aims of this study to determine accurately 
 the reliability of the estimation of academic capacity. The data 
 necessary for accomplishing this are at hand, for high school 
 records of academic accomplishment are universally kept. Com- 
 parable vocational records are generally not available; but for 
 the determination of the reliability of an estimate of vocational 
 fitness they are essential, and whenever available the method 
 here used is applicable. 
 
 The two chief factors entering into the problem of efficient 
 guidance are, first, a correct understanding of the demands of 
 prospective tasks and, second, an accurate valuation of the ability 
 of the person in question to meet these demands. These two 
 main elements of the problem may be stated as requiring an 
 analysis of the individual to determine his characteristics, and 
 an analysis of the needs of the situation to see to what extent 
 the individual meets these needs. This is a general statement 
 of the problem applicable to all kinds of guidance. The problem 
 here undertaken is termed one in educational guidance, since the 
 data concern high school pupils and high school subjects; but 
 the method, which is that of calculating the correlation between 
 the estimate of a person's fitness for a task and his later perform- 
 ance in it, is of general validity and importance and will inevitably 
 be used extensively in vocational guidance. 
 
 As success usually depends upon several factors, partial corre- 
 lation and the regression equation method are essential in the 
 evaluation of the data. This method will be explained more 
 fully later. The writer is not aware that it has been used before 
 in a guidance problem, but its peculiar adaptability to a problem 
 of this nature insures its extended use in the future. 
 
 More specifically, the endeavor of this study is to predict with 
 a known, and as high as possible, degree of accuracy the capacity 
 of the pupil to carry a prospective high school course. In doing 
 this, an analysis of the factors which make for success in the 
 course is obtained. The essential objects of the study are thus 
 
 (1) a measurement of the characteristics of the pupil, together 
 with the determination of the extent to which these character- 
 istics correlate with scholastic ability along certain lines, and 
 
 (2) an analysis of the demands of certain high school courses. 
 
Statement of the Problem 3 
 
 To illustrate the intimacy of these two problems it may be 
 pointed out that if all the essentials of fitness needed to fulfill a 
 certain task were known, and if the abilities of the person under 
 consideration were completely known, then prediction and 
 performance would agree perfectly; and to the extent that this 
 condition is approximated, the correlation between prediction 
 and performance is increased. 
 
SECTION 2.— METHOD AND SPECIFIC OBJECT 
 
 When selective classification of a prospective high school 
 pupil is attempted, the usual question asked is, what is his general 
 mental ability, and he is classified according to the answer to 
 that question. The present study attempts to answer that 
 question by considerations based upon one of three sources of 
 data: (1) the pupil's grammar school record, (2) estimates of 
 previous teachers of the pupil, and (3) grades obtained in special 
 tests given the pupil at the very beginning of the school year. 
 Beyond this, it is imperative, in rendering the most valid decision 
 as to the pupil's capacities, that account be taken of his specific 
 interests and peculiar genius. An excellent student of mathe- 
 matics may be a very poor English scholar, and though this sit- 
 uation is not true in the majority of cases, yet the number of 
 cases in which it is true is sufficiently great that very material 
 injustice will be worked if it is not taken into consideration. 
 
 The further aim of this study is, therefore, to determine, before 
 courses in the high school are taken, what the probable ability 
 of the pupil in question will be in them. Instead of attempting 
 to cover the field of high school work exhaustively, three subjects 
 — mathematics, English and history — have been selected for 
 study. The general method of procedure with all three subjects 
 and all three sources of data is to separate the data into ele- 
 ments that are, as far as possible, independent of each other, 
 e.g., the teachers' estimates of the pupil are four in number, (1) 
 intellectual ability, (2) conscientiousness, (3) emotional interest 
 in his work, and (4) oral expression. All of these factors are 
 important for scholastic work and it would be desirable if they 
 were totally uncorrelated with each other. The first and fourth 
 and the second and third are rather closely related with each 
 other, but even so there is sufficient independence between the 
 four to make their combined significance as indicators of scho- 
 lastic success considerably greater than that of a single estimate, 
 such as that of intellectual ability. 
 
 If the grades received, or marks given, in the original data are 
 represented by Xi, X 2 , X 3 , X*, and if the grades received in the 
 high school mathematics, English and history courses six months 
 4 
 
Method and Specific Object 5 
 
 or a year after the original data are obtainable are represented 
 by X u , X E , X H , then the problem is to establish the correlation 
 between X M and the combined measures based upon X\, X 2 , Xz, 
 Xa, and similarly with X E and X H . Expressed as an equation 
 it is X M = CQ+CiXi-\-c<LXi+CzXz+CiXi. This is equivalent to say- 
 ing that a certain constant times the grade received in the first 
 trait (or test), plus a second constant times the grade received in 
 the second trait (or test), plus, etc., gives the probable grade in 
 the course about to be taken. The statistical problem involved 
 is the determination of the constants c , c h c 2 , c 3 , c 4 , so that the 
 Xm values obtained differ on the whole, and when every indivi- 
 dual is taken into account, from the actual Xm values by the 
 smallest amount possible. 1 
 
 The equation which fulfills this condition is called a regression 
 equation, and the constants d, c 2 , cz, c 4 , are called regression 
 coefficients. They are functions of the coefficients of correlation 
 between the various X's and the standard deviations of the X's. 
 The theoretical proof of the derivation of these constants may 
 be found in Yule, "Introduction to the Theory of Statistics," 
 and a considerable ( amount of the purely mathematical work 
 involved in their calculation is given in the Appendix of the 
 present work. 2 For an understanding of this investigation (ex- 
 cept the Appendix) and the use of the method, it will suffice if the 
 reader has well in mind the fact that the value X# for each 
 individual obtained by this equation is the most probable value 
 which it is possible to obtain from the data X h X 2 , Xz, X 4 3 . 
 
 This regression equation is the means of prognosis, and to use it 
 in the case of any individual it is only necessary to substitute the 
 values Xi, X 2 , Xz, X 4 , for that individual, to obtain a value X M . 
 
 In addition to knowing the value X M , it is essential to know 
 the probable error of it, or to know its standard deviation. This 
 has been calculated in all cases, that the reliability of the prog- 
 nosis may be known. This reliability depends upon two factors, 
 the reliabilities of X\, X 2 , Xz, X4, and the extent to which these 
 
 1 Or, more accurately, that the calculated X M 's differ from the actual 
 Xjf's by such amounts that the sum of the squares of the differences is a 
 minimum. 
 
 2 The writer is about to publish tables which will greatly facilitate the 
 calculation of regression equations. 
 
 3 For the mathematician the words "in case the regression is rectilinear" 
 may be added. 
 
6 Educational Guidance 
 
 X's are correlated with Xm (this latter is in part dependent upon 
 the former). The reliability of any given measure X\ is given 
 by the reliability coefficient, 1 which is simply the value of the 
 coefficient of correlation between the given set of X\s and a 
 second set similarly derived. To obtain this measure it is neces- 
 sary to have the Xi grades assigned by at least two judges, which 
 procedure has been followed throughout except where impossible 
 because of the nature of the data, or where totally unnecessary 
 because the grading was so completely denned that the judge had 
 little or no option left to him in his grading. The formula giving 
 this reliability coefficient of a grade, which is the average or sum 
 
 nr 
 
 of the gradings of n judges, is 7—7 rr~ where r is the correla- 
 
 & » j » ) 1 -(- (r*. — l)r* 
 
 tion between gradings of different judges. Most of the tests in 
 this study have been graded by two judges, so that the formula 
 
 2r 
 becomes ~ — 
 1-f-y 
 
 It is later explained at some length that the use of correlation 
 coefficients, corrected for attenuation, is not permissible in this 
 problem. The attempt here is to prophesy accomplishment by 
 measuring an existing, not an imaginary, relationship, whereas, 
 in the studies using methods for "correcting" raw coefficients 
 of correlation, the attempt is to obtain a coefficient which is an 
 estimate of an ideal relationship and which does not represent a 
 correlation between existent data. This distinction should be 
 clearly borne in mind and comparison should not be made with 
 studies using coefficients corrected for attenuation. 
 
 In addition to being the means of prognosis, the regression 
 equation serves one other important function: the regression 
 coefficient c\ gives the weight that must be attached to the 
 measure Xi, independent of and free from any relation it may have 
 with X 2 , Xz, X4. It therefore makes it possible to consider the 
 importance of each of the factors X\, X 2 , X z , X*, independent 
 of the others. Such an analysis is essential in arriving at the 
 separate factors which go to make up efficiency in any given sub- 
 ject. This latter use of the coefficients of the regression equation 
 will be more apparent when treating of teachers' estimates and 
 the special tests, than in the following section covering the use 
 of elementary school grades as indicators of high school ability. 
 
 1 See Brown, Mental Measurement, pp. 101-102. 
 
SECTION 3.— SCHOOL GRADES AND THEIR SIGNIFI- 
 CANCE AS EVIDENCE OF HIGH SCHOOL 
 EFFICIENCY 
 
 The data here treated consist of the scholastic records of 59 
 pupils whose grades were available from the fourth grade through 
 the first year of the high school. These pupils had attended the 
 same school without a break, except for minor illness in certain 
 cases, during this period. The grades of the pupils in the follow- 
 ing subjects were copied from the high school records: Fa (first- 
 year average grade), Fm (first-year mathematics-algebra), Fe 
 (first-year English), 1 7a (7th grade average grade), 7m (7th grade 
 mathematics-arithmetic), 7e (7th grade English), 7h (7th grade 
 history), 6a, 6m, 6e, 6h, 5a, 5m, 5e, 5h, 4a, 4m, 4e, 4h. 2 
 
 The coefficients of reliability of these measures are not avail- 
 able, but they are probably not less than .80 for Fa, 6a, 4a, and 
 not less than .75 for 7a and 5a. It was first determined what 
 connection there is between 7a, 6a, 5a, 4a, and Fa. In order to 
 determine this the correlation between each one of these grades 
 and all the rest is necessary. These correlations are given in 
 the following table: 
 
 Fa 7a 6a 5a 
 
 7a .719 
 
 6a .728 .730 
 
 5a .531 .425 .541 
 
 4a .624 .551 .573 .576 
 
 There are several surprising items in this table. All of the 
 correlations involving 6a and 4a are higher than would be ex- 
 pected from the balance of the data. It certainly would not be 
 expected that 6th grade marks would correlate more highly with 
 first year standing than 7th grade marks, nor that 4th grade 
 marks would correlate more highly with first year and 7th grade 
 marks than 5th grade marks. It is possible that the teachers of 
 the 6th and 4th grades were more expert in estimating the ability 
 
 1 See Appx., pp. 108-116. 
 
 2 See Appx., p. 116. 
 
8 Educational Guidance 
 
 of their pupils than were the teachers in the 7th and 5th grades. 
 However this may be, to get the most out. of these particular 
 data in their bearing upon Fa, the regression equation, based 
 upon these coefficients of correlation and the various standard 
 deviations, must be obtained. Calculation shows it to be as 
 follows: 1 C • Fa = 1.67 (7a) + 1.3 (6a) + .4 (5a) + .7 (4a). (In 
 which C is some constant.) Calculation shows the correlation 
 between the Fa's thus obtained, and the Fa's actually obtained 
 in the first year to be .789, with a probable error of .032. This 
 correlation will be designated by the symbol ?"fa (7, 6,5,4a)' This 
 is a high correlation for data so far apart in time, and the 
 division of pupils in the high school into sections according to 
 ability, upon the basis of this prognosis, would be much more 
 accurate than that which would be possible after observing the 
 progress of the pupil in the high school for half a school year; for 
 this correlation is undoubtedly higher than that between average 
 half-year term grades. Especially would this be true if succeed- 
 ing term grades were given by different instructors. 
 
 The argument that this correlation is not perfect and would 
 work injustice in certain cases is utterly impotent if the alterna- 
 tive is the present very common system of mixing the good, the 
 medium and the poor all together, thus actually doing injury 
 to all. For any high school having more than a single section 
 of each class, and where grammar grade records are available, 
 the desirability of classification upon the basis here worked out 
 will be apparent, whether considered from the standpoint of the 
 nervous strain upon the teachers of a non-homogeneous class, 
 from the standpoint of economical administration, or from the 
 standpoint of the accomplishment of the pupil. In this connec- 
 tion it should be mentioned that the accuracy of a classification 
 based upon the marks received in the 7th grade alone is not very 
 materially less than that which is based upon the marks from the 
 4th to the 7th grades, and would be of very decided value in 
 case more extended records are not available. 
 
 There is one drawback to the use of the above regression equa- 
 tion, viz: by its use that pupil, who is particularly capable in 
 some one line, is not classified more highly in that line than he is 
 in others. A more detailed estimate of ability is desirable and 
 
 x See Appx., p. 91. 
 
School Grades and High School Efficiency 9 
 
 can be obtained by calculating the regression equations to esti- 
 mate ability in the various subjects of the first-year class, instead 
 of one regression equation to estimate average high school ability. 
 The most probable grade in first-year mathematics (Fm) 
 would be determined from the grades received in the different 
 elementary school subjects for the years for which the data are 
 available, i.e., the most probable value of Fm is equal to some 
 combination of 7m (7th grade mathematics), 6m, 5m, 4m, and also 
 7e (7th grade English), 6e, 5e, 4e, and so forth for the balance 
 of the elementary school curriculum. The grades in only three 
 elementary school subjects, mathematics, English and history, 
 were taken from the school records (it is the average of these 
 three that give the grades 7a, 6a, 5a, 4a), since these subjects all 
 run through the last four years of the elementary school, and 
 since the means of the various grades for these subjects could be 
 determined with considerable accuracy, probably very much 
 greater accuracy than with such subjects as nature study, writing, 
 music, etc. Furthermore, Fm is undoubtedly more especially 
 dependent upon the grades 7m, 6m, 5m, 4m, than upon grades in 
 other subjects in the curriculum, and similarly with Fe and 7e, 
 etc. It may also be stated that for purposes of determining the 
 difference of capacity of a pupil for mathematics and his capacity 
 for English there is very little gained by involving a subject such 
 as history in the calculation. For these reasons, the bearing of 
 7m, 6m, 5m, 4m only upon Fm has been obtained, and in doing 
 this it was assumed that the importance of the various years of 
 the elementary school was the same as in the case of the average 
 first year standing and the average standings of the elementary 
 grades. The equation of relation (the term regression equation 
 is reserved for equations satisfying entirely the conditions laid 
 down for such equations) is therefore as follows: 
 
 C • Fm = 1.67(7m) + 1.3 (6m) +.4 (5m) + .7 (4m) 
 Similarly C • Fe = 1.67(7e) + 1.3(6e) + .4(5e) + .7(4e) 
 
 The correlation between the Fm's thus obtained and the actual 
 Fm's is .580 (r FM (7> 6i 5> 4m) ). For English r FE (7> 6 , 5i 4b) = .710. The 
 greater correlation in the case of English than in the case of 
 mathematics may be partly due to an intrinsic difference in the 
 laws of development of an individual with reference to these two 
 subjects, but it is, at least in part, due to the greater reliability 
 
10 Educational Guidance 
 
 of the English elementary school marks, since these measures are 
 an average of the grades given in two English courses, whereas 
 the arithmetic grades are obtained from but a single course. It 
 is evident that there is also a greater content difference in passing 
 from arithmetic to algebra than in passing from 7th grade English 
 to first-year English. From a statistical point of view it does 
 not seem likely that the difference in reliability could entirely 
 account for the difference in correlation, and the author will 
 state that the mathematical probability of the difference being 
 due to chance is small, though he cannot express this probability 
 in exact numerical terms. 
 
 It has been stated that the value of these coefficients of corre- 
 lation lies in their power to differentiate between the ability of 
 the pupil in mathematics and in English. The extent to which 
 they perform this task in differential diagnosis can be measured 
 by comparing for each individual the difference between the 
 estimated ability in mathematics and the estimated ability in 
 English with the actual difference of ability as shown by the 
 grades in the two subjects. If individual (1) is estimated to be 
 .7 sigma (standard deviation) above the average in mathematics 
 and .4 sigma above the average in English, and the actual grades 
 which he received are .9 sigma above the average in mathematics 
 and .6 sigma above the average in English, then the estimated 
 difference between the abilities in the two subjects is equal to the 
 actual difference. 
 
 The extent to which differences in estimation correspond to 
 differences in first-year grades is given by the coefficient of 
 correlation between these two differences, /*(Fm-e) (7,6, 5,4,m-e)- It 
 is evident that if this correlation equals zero, then English 
 grades in the elementary school are as good a basis for estimation 
 Of mathematics grades in the first-year class of the high school 
 as are mathematics grades in the elementary school — in other 
 words, intelligence is general, and may be directed by the in- 
 dividual with equal result in any direction. On the other hand, 
 if the correlation is perfect, 1 then mental capacity is specific and 
 specialized to exactly the same extent and in the same manner 
 
 1 For this theoretical consideration, not in the nature of a prognosis, a 
 coefficient of correlation corrected for attenuation might be desired, but the 
 data for its calculation are not available, nor is it likely that the assumptions 
 underlying its derivation (lack of correlation of errors, etc.) would be sound. 
 Such correction, if utilized, would increase the correlation found. 
 
School Grades and High School Efficiency 11 
 
 in the high school and in the elementary school when dealing with 
 the same subjects. Calculation shows that r (FM _ E) (7i 6> 5i 4> M _ B ) = .515. 
 
 The net conclusion which may be drawn from these four 
 coefficients of correlation is, that it is possible to estimate a 
 person's general ability in the first year class from the marks he 
 has received in the last four years of the elementary school with 
 an accuracy represented by a coefficient of correlation of .789; 
 and that individual idiosyncracies may be estimated, in the case 
 of mathematics and English, with an accuracy represented by a 
 coefficient of correlation of .515. 
 
 The method of doing this is the simple one of substitution in 
 a regression equation. The regression equation given above 
 proved the best for the school from which the data are obtained, 
 but it probably would not occur in the usual school that the 
 correlations of the 6th and 4th grades would be relatively as high 
 as in this particular school. Assuming that for the usual school 
 there is a progressive gain in correlation with first-year standing 
 as one proceeds from the 4th to the 7th grade, we would have 
 correlations about as follows: 1 
 
 4a 
 
 
 Fa 
 
 7a 
 
 6a 
 
 5a 
 
 7a 
 
 .67 
 
 
 
 
 6a 
 
 .58 
 
 .67 
 
 
 
 5a 
 
 .53 
 
 .58 
 
 .67 
 
 
 4a 
 
 .50 
 
 .53 
 
 .58 
 
 .67 
 
 as 
 
 0"Fi 
 
 0-7a 
 
 0-6A 
 
 0"5a 
 
 0"4a 
 
 The regression equation based upon this table is as follows: 
 Fa = .4616^ (7a) + .1458°^ (6a) + .0910^ (5a) 
 
 °"7a 0f» °"5a 
 
 + .1094^ ( 4a ) (a) 
 
 In case the o-'s are all equal this equation becomes, to a very 
 close approximation, 
 
 54.9(Fa) = 25(7 a) + 8(6a) + 5(5a) + 6(4a) (b) 
 
 Equation (a) is the equation recommended for use in the ordi- 
 
 1 See Appx., pp. 91-92. 
 
12 Educational Guidance 
 
 nary school system. The elementary student of statistics can 
 use this equation without difficulty. First calculate the standard 
 
 deviations, <?> A , cr 7A , <t 6a> ct 5a> <t^ then express (.4616—) as a 
 
 single number, and do similarly with ( .1458— ), etc. This will 
 
 \ ,(r 6A/ 
 
 result in an equation of the type (b) except that the coefficient 
 of Fa is unity. It then only remains to substitute the values 
 7a (the average grade expressed as a deviation from the mean), 
 6a, 5a, etc., for each individual considered, to obtain the probable 
 grade, expressed as a deviation from the mean, of the individual 
 in his high school work. A similar procedure may be followed 
 for each high school subject, substituting for 7a, 6a, 5a, 4a, the 
 corresponding 7th, 6th, 5th, and 4th grade marks in the subject 
 in question. The result thus obtained will give the relative dis- 
 tribution of the pupils, but in this latter case the most probable 
 mark for the first-year grade may be expected to be numerically 
 a little smaller than the grade given by substitution in the equa- 
 tion. 
 
 This amounts to saying that the weighting of the grades of the 
 various years of the elementary school is probably the same 
 whether one deals with average grades or with grades of certain 
 subjects, but that the correlation found is probably smaller in 
 the latter case than in the former. The essential problem is to 
 divide the pupils into groups according to ability, and this the 
 values obtained by substitution in the equation will do with 
 considerable accuracy. The exact degree of accuracy can be de- 
 termined at the end of the school year by calculating the coeffi- 
 cient of correlation between the prophesied grade and the grade 
 actually obtained by the pupil, due allowance being made for 
 difference in the rigidity of grading in the various sections of the 
 same course — such differences undoubtedly being present if the 
 sections have been divided upon the basis of ability. 
 
 At first glance the fact that in the equation (b) the record in 
 the 4th grade is weighted more heavily than the record obtained 
 in the 5th grade is surprising. This arises from the fact that the 
 4th grade record has a greater independence than the 5th and 6 th 
 grade records, and therefore contributes more of an independent 
 nature upon which to estimate freshman standing. This is to 
 
School Grades and High School Efficiency 13 
 
 say that from the 4th, 6th and 7th grade records a closer estimate 
 of the 5th grade record can be obtained than can be obtained of 
 the 4th grade record from the 5th, 6th and 7th grade records. The 
 relatively greater independence of the first and last terms of the 
 series is to be expected, and is a cause of their greater weighting. 
 Before leaving this subject, it is interesting to note that the 
 correlation between the average first-year standing and the 
 average marks for the 4th grade is .624. This high correlation, 
 together with the fact that those who skipped grades were graded 
 high by giving them the grades of the preceding year, 1 instead of 
 being graded low by giving them the grade of the following year, 
 on the ground that having missed a year they would be handi- 
 capped in all their succeeding work, is strong evidence that 
 natural capacity is a very much more important factor than 
 training in determining relative scholastic standing. Indeed, it 
 seems that an estimate of a pupil's ability to carry high school 
 work when the pupil is in the 4th grade may be nearly as accurate 
 as a judgment given when the pupil is in the 7th grade, for the cor- 
 relation in the former case is .62 and in the latter only .10 higher. 
 
 1 See Appx., p. 89. 
 
SECTION 4.— TEACHERS' ESTIMATES AND THEIR 
 SIGNIFICANCE 
 
 Toward the close of the first half year the teachers in School A 
 were given lists of pupils in groups 1 , 2, and 3 and asked to grade 
 the pupils according to intellectual ability (I. a.) on each list 
 1, 2, 3, etc., as far as valid judgments could be made. Then, 
 beginning with the weakest, pupils were to be graded a, b, c, etc., 
 as far as judgments could be made. Finally, the remainder of 
 the pupils known to the teacher were to be marked M, signifying 
 a medium group. The demand that ranking be from the best 
 to the poorest, without a medium group, would probably have 
 resulted in less accurate judgments throughout the entire series, 
 for it would have been beyond the power of the majority of teach- 
 ers to have made valid distinction throughout this range. As it 
 was, on the average, about 25 per cent were placed in the medium 
 group. These rankings were then expressed as deviations from a 
 mean and the results of the gradings by the various teachers 
 combined for each pupil into a single measure. 1 
 
 The same procedure was followed for the traits conscientious- 
 ness (Cons.), emotional interest in school work (Emo. i.), and oral 
 expression (Exp.). 
 
 These estimates were obtained before the time of the English 
 and history courses used in this study and before the second half 
 year of the mathematics courses used. None of the estimates 
 used were from the mathematics instructors of the pupils. A 
 further effort was made to eliminate the possibility of the esti- 
 mates of the teachers being more highly correlated than a chance 
 selection of teachers' estimates would yield, by excluding the 
 estimates of English and history teachers who later had the same 
 pupils, in courses here utilized, that they had already taught in 
 the first half year's work. This was possible in all the 460 cases, 
 except in the case of 23 estimates which it was necessary to use 
 in order to secure sufficient data. 2 The teachers' estimates are 
 
 1 See Appx., pp. 92-93. 
 
 2 See Appx. p. 93. 
 
 14 
 
Teachers' Estimates and Their Significance 15 
 
 therefore practically free from any direct bearing upon mathe- 
 matics, English and history, but there is a certain amount of 
 direct connnection with average class standing. For example, 
 the estimate of a teacher of Latin, made near the close of the first 
 half year of school, enters into the teachers' estimate grade, and 
 the grade given by this same teacher for the yearly grade in Latin 
 of the pupil enters into the average grade for the year. This lack 
 of entire independence operates to slightly raise the correlation 
 between teachers' estimates and average class standing. From 
 the data at hand this increase is estimated to be less than .03. 
 
 The correlation between gradings by different teachers of the 
 same pupil for the same trait are as follows: 
 
 '(I. a. according to one teacher's estimate) •«' 
 " " " a second " 
 
 ^"(Cons. according to one teacher's estimate) •«*** 
 " " " a second " 
 
 '(Emo. i. according to one teacher's estimate) ■**■* 
 " " " a second " " 
 
 ^(Exp. according to one teacher's estimate) •^" 
 " " a second " " 
 
 On an average there were about two and one-half estimates per 
 pupil, so that the reliability coefficients of the various gradings 
 are: 
 
 Reliability coefficient of La. grading = .493 
 " Cons. " =.605 
 " Emo. i. " =.505 
 " Exp. " =.529 
 
 The conditions laid down for securing teachers' estimates were 
 simple to use, but at the same time allowed for as detailed judg- 
 ment as possible. When first-class teachers can estimate intel- 
 lectual ability with a reliability of only .29 it lessens the confidence 
 that can be placed in such estimates of ability and conclusions 
 drawn from studies depending upon them. 
 
 Teachers' estimates of pupils have the unique value of indi- 
 cating, more or less accurately, single mental traits instead of a 
 complex of traits such as are involved in the securing of a grade 
 in a subject, but it is highly desirable that these estimates be 
 made by several competent individuals, otherwise the measures 
 are very unreliable. 
 
16 Educational Guidance 
 
 The correlations between the various estimates and the 
 average grade (Av.) of each 
 
 pupil are given in the ac- Ay L a Cong Emo[ 
 
 companying table. 1 he re- 
 gression equation based 
 upon this table is: 
 
 c - Av. =8 1. a., +4 Cons., 
 
 +2 Emo. i., 
 +1 Exp. 1 
 
 the various 
 
 estimates •< 
 
 Av. 
 
 I. a. Cons. 
 
 I. a. .72 
 
 
 Cons. .62 
 
 .61 
 
 Emo. i. .58 
 
 .61 .66 
 
 Exp. .63 
 
 .82 .55 
 
 .59 
 
 The correlation between average class standing and the regres- 
 sion equation combination of the estimates of traits 
 
 r Av. (I. a., Cons., Emo. i., Exp.), = -76. 
 
 With such a high correlation, a division of pupils into classes 
 by means of teachers' estimates would be highly reliable. The 
 use of the equation to estimate probable class standing for a 
 school system with a different system of marking from that of 
 the schools here considered follows the same general lines as in 
 the case of elementary school grades. (See Appendix.) 
 
 In so far as all high school subjects are equally dependent upon 
 the traits, intellectual ability, conscientiousness, interest and 
 expression, classification according to grading in them is not 
 selective. The extent to which these factors have a common 
 importance for different subjects can be measured by calculating 
 the regression equations involving class standing in different 
 subjects and the teachers' estimates. The following equations 
 give the regression of mathematics, English, 2 and history, respect- 
 ively, upon I. a., Cons., Emo. i. and Exp. For simplicity, all 
 standard deviations are assumed equal. M t . e . stands for the most 
 probable mathematics grading, based upon teachers' estimates. 
 E t . e . and H t . e . have similar meanings. 
 
 M t . e . = . 460 1. a. + . 114 Cons. + .129 Emo. i.-. 014 Exp. 
 
 E t . e . =.336I.a. + .251 Cons. +.068 Emo. i. + . 083 Exp. 
 
 r EEt . e . = -64 
 
 H t e = .450 1, a. - .024 Cons. + .305 Emo. i. - .287 Exp. 
 
 rHH, e =.46 
 
 1 See Appx., p. 94. 
 
 2 See Appx., pp. 94-95. 
 
Teachers' Estimates and Their Significance 17 
 
 The negative significance of expression in the case of mathe- 
 matics and history is probably entirely due to the lack of inde- 
 pendence of the estimates of oral expression. This is the most 
 objective of the four traits and for that reason it might be con- 
 sidered the easiest to estimate. This view seems incorrect, for 
 oral expression is probably a trait which teachers do not think 
 much about and which they make little attempt to measure, with 
 the result that, when called upon to give an estimate of it, they 
 rely upon associated characteristics, such as intellectual ability, 
 conscientiousness and interest, traits already evaluated in their 
 minds. The result of such a procedure is to obtain measures of 
 expression which are correlated to an unwarrantable degree with 
 more fundamental traits. The tendency to rely upon secondary 
 criteria in the estimation of mental traits is a very difficult one to 
 overcome and the intercorrelations between the four traits esti- 
 mated are probably all higher than would be shown to be the case 
 with more accurate measurement of them. 
 
 The effect of unwarrantably large intercorrelations upon the 
 regression equation is to tend to give the factor which is the 
 dependent one, e. g., in this case expression, small or negative 
 weighting. The weighting which the regression equation gives 
 is the best available for the measure, but the measure is probably 
 not at all an accurate one of the trait considered. A reference 
 to the table on page 16 shows surprisingly high correlations be- 
 tween expression and the other traits. This is itself an indication 
 that the measures called "oral expression*' are dependent com- 
 plexes of other more fundamental traits. 
 
 The equations show a decided variation in importance of the 
 different traits with reference to different subjects. Intellectual 
 ability is most important in its bearing upon mathematics and 
 least important in its bearing upon English. Conscientiousness 
 is most important in its bearing upon English and least in its 
 bearing upon history. Interest is most important in its bearing 
 upon history and least upon English. Expression is the most 
 important in its bearing upon English and least in its bearing 
 upon history. 
 
 The striking importance of interest for history work, of con- 
 scientiousness for English, and of native capacity for mathe- 
 matics are points which can be utilized by the teacher giving the 
 
18 Educational Guidance 
 
 instruction as well as by the person attempting to diagnose 
 differentially the pupil's capacities. 
 
 Such estimates of teachers are not proposed as a good basis for 
 the determination of the idiosyncracies of pupils, although it is 
 possible in a small way to say what study a pupil will be most 
 efficient in, simply upon the basis of teachers' estimates of gen- 
 eral capacities. The correlation between the differences in math- 
 ematics and English grades and the differences in estimate of the 
 same is as follows: 
 
 r ( M-E)(M L e -E t . e .) = .12 x (Probable error = .05) 
 
 It is therefore apparent that the practical value of such teach- 
 ers' estimates as are here used lies, in the main, in their power 
 to measure general ability, rather than in a power to indicate 
 points of individual strength or weakness. They probably would 
 perform much the same function in connection with vocational 
 guidance. 
 
 1 Taking into account differences in standard deviations, e.g., by reducing 
 all standard deviations to unity. 
 
SECTION 5.— SPECIAL TESTS AND THEIR 
 SIGNIFICANCE 
 
 The data here concern the same groups of pupils as in the pre- 
 ceding sections dealing with teachers' estimates. Three kinds 
 of tests were given to determine ability, interest and preparation. 
 We may say that three main factors enter into the production of 
 a grade: (1) the mental capacity of the individual, (2) the prepa- 
 ration of the individual for the particular course, and (3) the 
 effort and interest of the individual in the particular subject. 
 The importance of these three factors differs materially for differ- 
 ent subjects, e. g., it requires a previous preparation in algebra 
 and analytical geometry in order to carry calculus, and it would 
 be a very peculiar genius who could read Virgil without previous 
 Latin study. In these courses the factor of preparation is of 
 prime importance. Courses in English, history, the sciences, 
 commercial branches and the like, do not so definitely demand 
 a certain accumulated store of knowledge as a foundation. The 
 relative importance of these three factors is worthy of extended 
 study and the data here given throw but little light upon the 
 question. In drawing up tests these three factors were con- 
 sidered with rather special emphasis upon the first and third. 
 The high school subjects covered are algebra, geometry, English, 
 and History, and a description of the various tests will reveal 
 the parts devised to measure each one of these factors. 
 
 (A t ) Algebra Test 
 
 The following test (called an algebra test simply because it was 
 given to classes just starting in algebra) was devised for the pur- 
 pose of measuring the ability and preparation of the pupil for 
 algebra. Following each problem are given directions for grading 
 it. 
 
 Administration of the test: The only precaution that need be 
 indicated in administering the test is that the teacher refrain 
 from explaining any of the questions verbally. Question 5, in 
 particular, loses its value if the slightest explanation is made. 
 
 19 
 
20 Educational Guidance 
 
 Algebra Test and Directions for Grading 
 For all problems: maximum grade 10, minimum grade 
 
 Name Date 
 
 1. Add: 132 2. Multiply: 
 
 580 42976 
 
 649 30851 
 
 356 
 
 774 
 263 
 925 
 191 
 417 
 828 
 
 From 10 deduct 4 for each error in addition, or in carrying forward. 
 From 10 deduct 4 for each mistake in placing partial products, 2 for each 
 mistake in partial product, and 2 for each mistake in addition. 
 
 3. Divide 457219 by 638 and carry answer to one decimal place. 
 
 From 10 deduct 2 for each failure to draw down, 3 for a mistake in decimal 
 point, 2 for each error] in subtraction, and 2 for failure to carry work to one 
 decimal place. 
 
 4. Simplify: 6f-3i-lfH-2i-lf. 
 
 From 10 deduct 2 for each mistake in simplifying a term, 3 for each error 
 
 in addition. 
 
 „. , t zt 33 13 61 . 9 7 
 
 Give a grade of 5 for answer — — — + 7 ~ 7- 
 
 5 4 40 4 4 
 
 5. Is the square constructed on a line (3 +5) eight inches long greater than, 
 equal to, or less than, the sum of the squares constructed on lines 3 inches and 5 
 inches long? Explain. 
 
 If explanation shows an understanding of the problem grade it 10. Give 
 grade of 2 for (8 X8) - (5 X3) =49. 
 
 6. What is that number such that if it is multiplied by itself and added to 
 11 the result is 27? 
 
 Give grade of 2 for answer 16. 
 
 7. A certain balloon without its basket will just lift a weight of 160 pounds. 
 What is the weight of the balloon and basket if the basket weighs 20 pounds? 
 
 Grade 10 for answer — 140, or for statement " 140 pounds less than nothing," 
 or similar statement. Grade all other answers 0. 
 
 8. Simplify: &xix| + X. 
 
 From 10 deduct 6 for incorrect inversion, or failure to make correct inver- 
 sion, 4 for each error in cancelling, and 4 for each other error. 
 
 3_3 
 
 9. Simplify: - -. 
 
 3 8 
 Give credit of 3 for correct simplification of numerator, 3 for denominator, 
 and 4 for the balance. 
 
Special Tests and Their Significance 21 
 
 10. Simplify: 
 
 Same as 9. 
 
 2 V 11 
 3 X 12 
 
 9 2 
 
 11. Find lowest common multiple and highest common factor of 42, 56, 63, 
 84. 
 
 Give credit of 2 for all factoring correct, 4 for H. C. F. if plainly labelled 
 and 4 for L. C. M. 
 
 12. January 1 of a certain year the temperature was 70 degrees, January 2 
 it was 40 degrees. What was the temperature January 3 if it was still colder 
 and the difference between the temperatures of January 3 and January 1 was 
 three times as great as the difference between the temperatures of January 2 
 and January 1? 
 
 Give credit of 2 for answers of 90°, or 20°. 
 
 13. Find a number such that if 5 is added to 3 times that number the result 
 is 38. 
 
 Grade 10 or 0. 
 
 14. One-third of a certain number added to 7 is equal to 22. What is the 
 number? 
 
 Give credit of 2 for answer of 5. 
 
 The primary purpose of problems 1, 2, 3, 4, 8, 9, 10, 11 is to 
 test the thoroughness of the preceding preparation of the pupil. 
 The remaining questions are primarily for the purpose of testing 
 his capacity to deal with algebraic material; questions 5, 6, and 
 12 testing his ability to understand the written statement of a 
 problem and to deal with negative magnitudes, and questions 6, 
 13, 14 demanding elementary algebra, or at least a process of 
 thinking which is very closely related to simple algebraic reason- 
 ing. Problem 7 may be objected to on the ground that the stu- 
 dent of physics, who has weighed gases and the like, may be 
 misled by the term "weight" when a negative magnitude is 
 demanded for a correct solution of the problem. None of the 
 subjects showed that this particular difficulty was present in their 
 minds, probably because none of them were familiar with the 
 necessary physics. 
 
 The grading is highly objective and the reliability accordingly 
 very high. To calculate the reliability, a sample was graded by 
 two judges. The correlation between the total grades for each 
 pupil as determined by the two judges, is .996, which is the 
 reliability coefficient, as most of the papers were graded by a 
 single judge. The various problems in this test are approxi- 
 
22 
 
 Educational Guidance 
 
 mately l of equal significance and the sum of the grades of all of 
 the problems is the grade for the test. To obtain a distribution 
 which would be convenient for purposes of calculation from the 
 grade thus obtained, the average grade of the group in question 
 was subtracted and the remainder divided by 5, keeping the result 
 to the nearest integer. This grade is designated by A t (algebra 
 test) and when grouped with the grades of the geometry test by 
 M t (mathematics test). 
 
 (G t ) Geometry Test 
 
 Administration of test: In giving the following test, problems 
 1 and 2 require explanation. A demonstration is given the 
 pupils of a simpler problem, to show the nature of the requirement. 
 
 Paper, about one foot square, is held against the black- 
 board with the top edge horizontal, folded once from the 
 bottom up, a second time from the right to the left and, while 
 still close to the blackboard and without rotating the paper, 
 a V-shaped notch cut into it. The pupils 
 are then asked to describe, orally, the ap- 
 pearance of the paper when unfolded and 
 after receiving a few correct answers the 
 paper, still against the blackboard, is un- 
 folded, enabling the entire class to see that 
 the unfolded paper does have the shape 
 
 The test question is then given, folding the 
 paper along a diagonal, giving it this appearance 
 a second fold leaves 
 it in this shape 
 a third 
 in this 
 
 and after notching it appears thus 
 
 The pupils are then asked to represent its appearance when 
 unfolded. 
 
 The nature of the requirement in the second question can be 
 made clear by means of two large wooden compasses, each hand 
 holding points of the different compasses, and demonstrating the 
 
 1 See Appx., pp. 95-96. 
 
Special Tests and Their Significance 
 
 23 
 
 lack of rigidity of the diamond-shaped frame thus formed. 
 Care should be taken not to indicate the position, or number, 
 of braces necessary to make the figure rigid. 
 
 Name. 
 
 Geometry Test and Directions for Grading 
 
 All problems: Maximum grade 10, minimum grade 
 
 Date 
 
 1. The accompanying diagram represents a square 
 sheet of paper which is folded three times by the 
 teacher and cut. Draw in the square, in their correct 
 position, the holes cut out. 
 
 Credit given for drawings as follows : 
 10 8 6_ 1 
 
 u 
 
 o 
 o ♦ 
 
 
 V V 
 
 V V 
 
 2. Suppose that AB, BC, CD and DA 
 are sticks of wood hinged together at 
 points A, B, C and D. How many braces 
 are needed to make the figure rigid and 
 where would you put the brace or braces? 
 
 For one brace properly placed give credit 
 of 10, improperly placed credit of 4. For 
 two braces give credit of 2. 
 
 3. John's mother forbids him to leave 
 Broadway. James' mother forbids him to 
 leave Amsterdam avenue. They are obe- 
 dient sons, but are also very fond of seeing 
 each other, so how can they meet? 
 
 Give credit 10 for answer 72nd St. Any 
 other answer 0. 
 
 4. AB is a railroad track. C is a stake 
 to which a cow is tied with a 30 ft. rope. 
 DE measures a distance of thirty feet. 
 One day the cow, while grazing at the 
 end of its rope, is struck by the train. 
 Mark the place or places in the diagram 
 at which this must have occurred 
 
 Give credit 10 for indicating two points 
 correctly, 6 one point, 6 for distance be- 
 tween the two correct points. 
 
24 
 
 Educational Guidance 
 
 5. In the accompanying figure, 
 the distance along the circle from 
 B to C equals the distance along 
 the circle from A to B. Also, the 
 straight fine BC equals the straight 
 line AB. Does the curved line 
 from A to C equal twice the curved 
 
 line from A to B? 
 
 Does the straight line AC equal 
 twice the straight fine AB? 
 
 Give credit 10 for both answers , 
 correct, 2 for one correct. / O 
 
 6. What are the areas of figures A, B, and C? A . . 
 In what respect, if any, are figures A and B alike? 
 In what respect, if any, are figures B and C alike? 
 In what respect, if any, are figures A and C alike? . 
 
 ,B. 
 
 ;C 
 
 c. 
 
 ^ 
 
 Give credit: 
 
 1 for A =9, £ = 4, C=4. 
 3 A and B both squares. 
 
 2 A and B alike in shape. 
 
 3 B and C equal in area. 
 
 1 B and C both parallelograms. 
 3 A and C both rectangles. 
 
 2 A and C not at all alike. 
 
 7. Find the value of x from the equation f = -. 
 
 b a 
 
 Find value of y from the equation - = -. 
 
 y d 
 
 Give credit: 
 
 4 for x = ^. 
 a 
 
 6 for y = 2£ 
 c 
 
 Anything else 0. 
 
 In the following question, is the third statement proved if the first two are 
 true? Write "proved" or "not proved" after it. 
 
 8. 1. Every chalet is a bungalow. 
 
 2. Jones' house is a bungalow. 
 
 3. Therefore Jones' house is a chalet 
 
 Credit 10 or 0. 
 
 Do the same for the following question: 
 
Special Tests and Their Significance 25 
 
 9. 1. Every chalet is a bungalow and every building that is not a bungalow 
 
 is not a chalet. 
 
 2. Smith's house is a bungalow. 
 
 3. Therefore Smith's house is a chalet 
 
 Credit 10 or 0. 
 
 Do the same for the following question : 
 
 10. 1. Every building that is not a Chalet is not a bungalow. 
 
 2. Brown's house is in no particular different from a bungalow. 
 
 3. Therefore Brown's house is a chalet. 
 Credit 10 or 
 
 The primary purpose of all the problems, except problem 7, is 
 to test capacity; problem 1 testing ability to image geometrical 
 forms and movement. Problems 2, 3, 4, 5, 6, are locus problems, 
 and problems demanding a common sense interpretation of 
 geometric facts. Problem 7 is a problem to test the pupil's 
 previous preparation in the line of ratio and proportion. Prob- 
 lems 8, 9 and 10 are problems in logic aimed to test the pupil's 
 ability to handle reductio ad absurdum proofs and converse 
 propositions. Problem 10 is a difficult problem and is meant to 
 tax the most able pupil. It may be said that all the tests were 
 devised with a view to securing a good distribution of marks. 
 It was desired that the most efficient pupil would just succeed, 
 or just not succeed, in making a perfect score, while at the same 
 time the tests were meant to be sufficiently easy in places to secure 
 the cooperation of the poorest pupil. The reliability coefficient 
 for this test is very high, being .994. A number of the problems 
 in this test did not prove as significant as conferences with various 
 teachers of geometry led the author to expect, 1 and the grade 
 for the entire test is taken as the sum of the marks for problems 
 1, 7, 8, 9, 10. To obtain a convenient distribution for purposes 
 of calculation, from the grade thus obtained the average of the 
 group in question was subtracted, and the remainder divided by 
 3, keeping the answer to the nearest integer. This grade is 
 designated by G t , or M t when grouped with algebra data. 
 
 (E t ) English Test 
 
 The English test which follows, together with the explanation 
 of the grading and the sample grading, will explain the purpose 
 for which it was devised. It is fundamentally an ability test 
 and seems to meet the requirements very well, as none of the 
 
 1 See Appx., p. 97. 
 
26 Educational Guidance 
 
 pupils gave evidence of familiarity with the subject matter of the 
 test. 
 
 Administration of the test: Tell the pupils that you are about to 
 read an account of an incident in the life of the founder of one of 
 the great Eastern religions and that after reading you are going 
 to ask them questions about it. Then read the following: 1 
 
 English Test 
 
 "A woman — dove-eyed, young, with tearful face 
 
 And lifted hands — saluted, bending low : 
 
 "Lord! thou art he," she said, "who yesterday 
 
 Had pity on me in the fig-grove here, 
 
 Where I lived lone and reared my child; but he 
 
 Straying amid the blossoms found a snake, 
 
 Which twined about his wrist, whilst he did laugh 
 
 And tease the quick forked tongue and open mouth 
 
 Of that cold playmate. But, alas! ere long 
 
 He turned so pale and still, I could not think 
 
 Why he should cease to play, and let my breast 
 
 Fall from his lips. And one said, 'He is sick 
 
 Of poison'; and another, 'He will die.' 
 
 But I, who could not lose my precious boy, 
 
 Prayed of them physic, which might bring the light 
 
 Back to his eyes; it was so very small 
 
 That kiss-mark of the serpent, and I think 
 
 It could not hate him, gracious as he was, 
 
 Nor hurt him in his sport. And some one said, 
 
 'There is a holy man upon the hill — 
 
 Lo! now he passeth in the yellow robe — 
 
 Ask of the Pushi if there be a cure 
 
 For that which ails thy son.' Whereon I came 
 
 Trembling to thee, whose brow is like a god's, 
 
 And wept and drew the face cloth from my babe, 
 
 Praying thee tell what simples might be good. 
 
 And thou, great sir! didst spurn me not, but gaze 
 
 With gentle eyes and touch with patient hand; 
 
 Then draw the face-cloth back, saying to me, 
 
 'Yea! little sister, there is that might heal 
 
 Thee first, and him, if thou couldst fetch the thing; 
 
 For they who seek physicians bring to them 
 
 What is ordained. Therefore, I pray thee, find 
 
 Black mustard-seed, a tola; only mark 
 
 Thou take it not from any hand or house 
 
 Where father, mother, child, or slave hath died; 
 
 It shall be well if thou canst find such seed.' 
 
 Thus didst thou speak, my Lord!" 
 
 The Master smiled 
 Exceeding tenderly. "Yea! I spake thus, 
 Dear Kisagotami! But didst thou find 
 The seed?" 
 
 "I went, Lord, clasping to my breast 
 The babe, grown colder, asking at each hut — 
 Here in the jungle and towards the town — 
 ' I pray you, give me mustard, of your grace, 
 A tola — black:' and each who had it gave, 
 
 1 Taken verbatim from Edwin Arnold, Light of Asia, p. 124-8. 
 
Special Tests and Their Significance 27 
 
 For all the poor are piteous to the poor; 
 
 But when I asked, ' In my friend's household here 
 
 Hath any peradventure ever died — 
 
 Husband or wife, or child, or slave?' they said: 
 
 'O Sister! what is this you ask? the dead 
 
 Are very many, and the living few!' 
 
 So with sad thanks I gave the mustard back, 
 
 And prayed of others; but the others said, 
 
 'Here is the seed, but we have lost our slave!' 
 
 'Here is the seed, but our good man is dead! ' 
 
 'Here is some seed, but he that sowed it died 
 
 Between the rain-time and the harvesting ! ' 
 
 Ah, sir! I could not find a single house 
 
 Where there was mustard seed and none had died ! 
 
 Therefore I left my child — who would not suck 
 
 Nor smile — beneath the wild-vines by the stream, 
 
 To seek thy face and kiss thy feet, and pray 
 
 Where I might find this seed and find no death, 
 
 If now, indeed, my baby be not dead, 
 
 As I do fear, and as they said to me." 
 
 " My sister! thou hast found," the Master said, 
 "Searching for what none finds — that bitter balm 
 I had to give thee. He thou lovedst slept 
 Dead on thy bosom yesterday: to-day 
 Thou know'st the whole wide world weeps with thy woe : 
 The grief which all hearts share grows less for one. 
 Lo! I would pour my blood if I could stay 
 Thy tears and win the secret of that curse 
 Which makes sweet love our anguish, and which drives 
 O'er flowers and pastures to the sacrifice — 
 As these dumb beasts are driven — men their lords. 
 I seek that secret: bury thou thy child!" 
 
 The questions to the pupils are as follows: 
 
 (1) State one or two things about the story which you particularly liked. 
 (6 minutes.) 
 
 (2) Write an account of the story as fully as you can remember it. (9 
 minutes.) (5 minutes for reading the passage, giving a total time of 20 
 minutes.) 
 
 The grading was upon the following four points, though the grading upon 
 Ev, E a and Ew only, are used in obtaining a single measure of the English 
 test: 
 
 Ev Valuation of the essential ideas in the poem. (Grade approximately 
 
 from to 10, with an average of 5. Further explanation follows.) 
 Ea Accuracy and extent of description. (Start with 4 and to this add £ 
 for each point correctly made and subtract 1 for each point incorrectly 
 made.) 
 Ew Written expression. (Grade from to 10, with an average of 5. Give 
 
 some slight weight to spelling.) 
 Ed Dramatization. (Grade from to 10, with an average of 5.) 
 
 pi I p I Ty 
 
 The reliability coefficient of the English test, — — ~ ' 
 
 o 
 
 or E t , equals .969, since the grades used are the sum of the grades 
 
 of two judges and the correlation, based on a sample of 36, 
 
 between the grades given by the judges is .940. 
 
28 Educational Guidance 
 
 The grading for valuation of the essential ideas of the poem was largely 
 based upon the answer to question (1). It followed closely the following 
 scheme: 
 
 Grade below: given for selecting the following as the point liked the best: 
 
 10 ±1 Love shown in the Master's way of teaching that suffering is uni- 
 versal. 
 
 8 ±1 "The grief which all hearts share grows less for one." 
 
 8 ±2 Appreciation of poetry and language used. 
 
 6 ±1 Master's statement to the mother that the whole world suffers, or the 
 idea that suffering is universal. 
 
 5 ±1 Master's statement, "I would pour my blood if I could stay thy 
 tears." 
 
 4§±1 "The poor are piteous to the poor." 
 
 4 ±1 Mother's tenderness and love for her child, or the mother's cry that 
 she cannot lose her child. 
 
 3 ±1 Mother's trust in the Master, and her courage. 
 
 1 ±1 Honesty and strength of mother in not taking forbidden seed. 
 
 The plus or minus after each grade indicates the amount that quite gen- 
 erally is to be added or subtracted, depending upon the answer to the second 
 question, as follows : 
 
 Add 1 for genuine appreciation of the Master's character, i. e., his gentle- 
 ness, compassion, humanity, and for genuine appreciation of the 
 first three points above. 
 
 Add for correct narrative. 
 
 Add — 1 for demonstrated lack of correct appreciation and for incorrect nar- 
 rative which betrays incorrect appreciation of the Master's char- 
 acter and motive. 
 
 Having grades for accuracy (Ea), valuation (Ev) and written expression 
 
 (W) ( W = ■ — - , or the average of the grades for written expression 
 
 \ 2 \ . . , 
 
 for the English and history tests / the single grade for the entire test is the 
 average of these three grades minus the mean for greater convenience after 
 multiplication by two, i. e., Et = f (E a +Ev+W— mean). 1 
 
 In the following samples, given to illustrate the method of 
 grading, the points for which credit in accuracy has been given 
 are underscored once and the incorrect points, for which credit 
 was deducted, have been underscored twice. The grading for 
 dramatization is not used in the final score for the test, but is 
 given as it may have some interest in itself and probably has a 
 specific significance in some other bearing than upon English. 
 
 1 See Appx., p. 98. 
 
Special Tests and Their Significance 
 
 29 
 
 Name (Pupil No. 187). 
 
 Date. 
 
 I. I like the story of the poem very much. I think it 
 is very pathetic and has a good point — I refer to the 
 mothers grief being lessened because she knew all others 
 had to suffer. I also like the way the author wrote the 
 poem. It is well told, and in beautiful language. 
 
 II. The mother throws herself at the feet of the 
 master and says that she come to him to now because 
 yesterday he was so kind to her and when on the 
 desert her child was playing with a snake and it bit 
 him, and she feared for his life, she went to him and asked 
 consul of him. He said that she should get mustard seed 
 from somebody, but beware not to take it from anyone 
 in whose house there has been a death. 
 
 "Yes," says the master, "and did you get the mustard 
 seed? " 
 
 "I went into 
 asked for the mustard seed 
 
 every hut," says 
 
 all gave it to me, for 
 poor, but when I asked if 
 
 she, and 
 and the good people 
 the poor give to the 
 there had been a death 
 
 in the house, they all answered, yes. So now I have 
 to you, dear master, to once more seek consul, ere 
 my baby dies, if he be not dead already. " 
 
 The consul speaks, "Yesterday when you came to 
 me, and asked my aid, your babe was already dead, 
 
 but I let you go and try to get the mustard seed, so 
 
 H, 
 
 Ew+Hv 
 
 Et = f(E a +Ev+W-mean 1 ) =1(9+9+4-19) =2.0. 
 
 Grading 
 
 Ea 
 
 4 
 
 .5 
 -1 
 .5 
 .5 
 
 .5 
 
 .5 
 .5 
 .5 
 .5 
 .5 
 .5 
 
 .5 
 
 .5 
 
 Ev 
 
 8 
 
 1 
 
 Ew 
 
 Ed 
 
 9 
 
 9 
 
 4 
 4 
 
 4 
 
 7 
 
 1 For table of means see p. 68. 
 
30 
 
 Educational Guidance 
 
 Name (Pupil No. 188). 
 
 Date. 
 
 Grading 
 
 I. I think that the lord was very good and tender 
 in telling the mother to find something that was not, 
 and telling her that that thing would cure the baby. 
 In that way she did not get a shock. 
 
 I think the mother did right by not giving the baby 
 the wrong seed, when she could not find the right seed 
 and then going to the lord again for advice. 
 
 II. When the story opens; a young mother is 
 bending low to a lord of her religeon and tells the fol- 
 lowing story: "Yesterday while my child was playing 
 in the garden and finding a snake began to play with it. 
 
 The snake bit it leaving a small mark on the child's 
 
 skin and some neighbors said that the baby was dead, 
 others that it was not dead yet but was dying of poison. 
 And others advised me to go to a certain lord who 
 lived over the hill and to ask him what to do to the 
 baby to save him and then they told me that the man 
 in a yellow robe who was walking on the road by the 
 house was the lord so I ran up to him and knelt down 
 to salute him and then I took the face cover off his face 
 and showed the lord the mark and the lord felt the baby 
 and told me to go and get some black mustard seed 
 but it must not come from a house wherein a father, 
 mother, child or 
 
 Hw 
 W 
 
 Ea 
 
 4 
 
 Ev 
 
 E w 
 
 Ed 
 
 .5 
 
 10 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 { :i 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 10.5 
 
 10 
 
 2 
 
 4 
 6 
 
 7 
 
 Et = f (10.5+10+3-19) =3.0. 
 
Special Tests and Their Significance 
 
 31 
 
 Name (Pupil No. 200). 
 
 Date. 
 
 Grading 
 
 I. It seems to me that one of the finest points in 
 this passage, is the tenderness that runs all through it. 
 It is in the mother's speach when she talks of her 
 child, and also in the answer, — full of pity and truth. 
 Another thing about it is the wording, for the passage, 
 although written in prose, sounds almost like poetry 
 or music, on account of the beautiful words used. 
 
 II. A woman, with tears in her eyes, came and 
 threw herself at the feet of the Master. She told 
 him of her child, who, while playing in the garden 
 had been stung by a serpent. In a short time he 
 grew pale and cold, and people said he would surely 
 die. But the mother, unwilling to give up hope, had 
 gone to the Master, certain that he, in his wisdom, 
 could aid her, and restore her boy to health. And 
 the Master, full of compassion, had told her to go 
 with her child, from house to house, and beg for 
 mustard seed, but from any house where man or 
 woman, slave or child had died, she should not accept 
 the seed, but go elsewhere. Carrying her child the 
 mother had begged at every door, but, although 
 glad to give her seed, in every house someone had 
 died, so the 
 
 Hw 
 W 
 
 Ea 
 
 4 
 
 Ev 
 
 Ew 
 
 Ed 
 
 .5 
 .5 
 
 9 
 
 
 
 .5 
 .5 
 .5 
 
 
 
 
 .5 
 .5 
 
 
 
 
 .5 
 .5 
 .5 
 
 1 
 
 
 
 9 
 
 10 
 
 6 
 
 9 
 7.5 
 
 6 
 
 E< = f(9 + 10 +7.5 -19) =5.0. 
 
32 
 
 Educational Guidance 
 
 Name (Pupil No. 206). Date. 
 
 Grading 
 
 I. The story is extremely touching. The picture of 
 the the "sad tearful face" is most vivid, and the little 
 "face so pale and still " can almost be seen. We 
 certainly hope that the mother was comforted. 
 
 II. A woman once had a beautiful little child. She 
 loved him dearly. The boy would daily sleep on some 
 dry grass. One day, the mother being tired and weary, 
 fell asleep. (How) Then came a large venomous 
 snake and bit the child, so that he died. And when - 
 the mother awoke she and saw the still pale face of her 
 baby she rent her garments, whilst all the people said 
 "There is no hope." But then one man espied the 
 doctor of the village. And quickly he spoke, saying 
 "There is the doctor! go you to him, mayhap he'll 
 give your child to you again." Then on her knees, 
 saluting humbly she begged the "wise" man. "My 
 daughter, if you wouldst your child recover go you 
 from house to house and beg and say "Give me some 
 mustard seed" but if there be by any chance a dead 
 man in that house, then leave the seed, for is a child 
 or man or woman there has died, the charm is broken. 
 Go, and if thou succeedest — 
 
 H w 
 W 
 
 E t = f(3+6+5.5-19) = -3.0 
 
 liia 
 
 4 
 
 .5 
 .5 
 
 -1 
 -1 
 -1 
 
 .5 
 -1 
 
 .5 
 
 .5 
 .5 
 
 Ev 
 6 
 
 Ew 
 
 Ed 
 
 3.0 
 
 6 
 
 5 
 6 
 
 5.5 
 
 10 
 
Special Tests and Their Significance 
 
 33 
 
 Name (Pupil No. 124). 
 
 Date. 
 
 Grading 
 
 I. After the snake bit the child how very sad the 
 mother was, and she did every thing to try and save 
 him. 
 
 II. The story was about this child that was 
 bitten by a snake and he was going to die and the 
 mother tried to get some mustard seed but nobody 
 had any and the child died 
 
 Et = |(3 + l+0-15) = -7.3 
 
 Hw 
 W 
 
 Ea 
 4 
 
 .5 
 
 -1 
 
 .5 
 — 1 
 
 Ev 
 
 2 
 -1 
 
 Ew 
 
 Ed 
 
 3 
 
 1 
 
 
 
 
 
 
 3 
 
 (H t ) History Test 
 
 The history test follows much the same lines as the English 
 test. None of the pupils showed evidence of familiarity with 
 the subject matter. 
 
 Administration of the test: Draw a map of Italy and Sicily on 
 the blackboard, indicating the following provinces and cities: 
 Piedmont, Genoa, Venice, Rome, Naples, Calabria, Messina, 
 Palermo and Marsala. In addition to these places write the 
 names "Garibaldi" and "Victor Emmanuel" on the board. 
 Give orally necessary historical groundwork as follows: "Victor 
 Emmanuel was the king of Piedmont. (Point out.) He had 
 expressed his willingness to lead an insurrection to establish a 
 free and united Italy whenever the other states of Italy should 
 revolt. The Two Sicilies (point out) and the other small states 
 of Italy were governed by rulers who were opposed to a united 
 and republican Italy. 
 
 "These are all the facts that you will need to know to under- 
 stand the selection about to be read. Remember those points 
 that you like and that you consider historically important." 
 (Allow 8 minutes for the reading.) 1 
 
 History Test 
 
 "Garibaldi was the hero on the field of battle. The last of knight-errants, 
 he was the very incarnation of Romance and Revolution. Bred to the sea, 
 
 1 This selection is a modification of pp. 392-3, 402-4, Sedgwick, A Short 
 History of Italy. 
 4 
 
34 Educational Guidance 
 
 he always retained the jaunty, gallant bearing of a mariner. His countenance 
 (childlike and lio nlik e) — with its broad tranquil brow, benign eye and reso- 
 lute mouth — in youth all sparkling, gradually changed with care and dis- 
 illusion, but he still kept the seaman's mien and the seaman's lightsome eye. 
 He was the beau ideal of a romantic hero. After his unsuccessful raid into 
 Piedmont he had gone to South America, where he lived a wild life of guerilla 
 warfare, fighting like a Paladin on behalf of republican revolutionaries who 
 were struggling for their freedom. All the time he was training a band of 
 Italian adventurers, his legion, so that they should be ready when their country 
 had need of them. These men rushed to the defense of the city. Their entry 
 was most picturesque. The gaunt soldiers, wearing red shirts and pointed 
 hats topped with plumes, their legs bare, their beards full-grown, their faces 
 tanned to copper color, with their long black hair dangling unkempt, looked 
 like so many Fra Diavolos. At their head Garibaldi, in his red shirt, with 
 loose kerchief knotted round his throat, the regular beauty of his noble, 
 leonine face set off by his waving hair, mounted on a milk white horse, rode 
 like a demigod." 
 
 "A short time after what has just been read the following 
 events took place:" 
 
 "In the meantime Francis II, a weak, ignorant, bigoted lad, had mounted 
 to the throne of the 'Two Sicilies.' In April, 1860, a revolt began in Palermo, 
 and, though suppressed there, spread. Two young patriots, Crispi and Pilo, 
 went about stirring the people to action. Garibaldi was begged to put him- 
 self at the head of the proposed revolution. On the night of May 6, two 
 ships, the Lombardy and the Piedmont, secretly left Genoa, and took Garibaldi 
 and a thousand volunteers aboard. This band, known as 'the thousand,' 
 is nearly as famous and as legendary as King Arthur and his Round Table. 
 On May 11, the ships landed at Marsala. Two cruisers from Naples came up, 
 but two English men-of-war happened to be there also; and the English cap- 
 tains, under guise of friendly notifications to the Neapolitans, took some 
 action which delayed the latter long enough to let the last Garibaldians dis- 
 embark. Once on shore Garibaldi's volunteers ran to secure the telegraph 
 office. They arrived just after the operator had telegraphed that two Pied- 
 montese ships, filled with troops, had come into the harbor; a Garibaldian was 
 able to add to the message, 'I have made a mistake; they are two merchant- 
 men.' The answer came back, 'Idiot.' The volunteers marched inland. 
 A provisional government was organized; Garibaldi was made dictator, and 
 Crispi secretary of state. The cry was 'Italy and Victor Emmanuel!' Gari- 
 baldi was joined by insurgent Sicilians, and, with numbers considerably 
 increased, fought and defeated the Bourbon army. The story reads like the 
 exploits of Hector before the Greek trenches. Victory followed victory. 
 Palermo fell, Milazzo and Messina ; then he crossed the straights and invaded 
 Calabria. This marvelous triumph, for there had been thirty thousand troops 
 to oppose Garibaldi, frightened King Francis; he proclaimed a constitution, 
 but it was too late. Garibaldi swept on victorious, and the king fled from 
 Naples (Sept. 6); the next day Garibaldi marched in and assumed dictator- 
 ship of the kingdom. 
 
 "Victor Emmanuel took up the cause and, marching south, joined with 
 the forces of Garibaldi and together they decisively defeated the opposing 
 army. In February, 1861, the first Italian parliament was held and Victor 
 Emmanuel formally received the title of 'King of Italy.' Excepting Rome 
 and Venice, Italy was free and independent." 
 
 Questions as follows : 
 
 (1) What do you think was probably the next important event? (2 
 minutes.) 
 
 (2) Describe the character and appearance of Garibaldi. (4 minutes.) 
 
Special Tests and Their Significance 35 
 
 (3) Beginning with the departure of Garibaldi and his men from Genoa 
 write a detailed account of as much of the story as you have time for. (Bal- 
 ance of time — 6 minutes.) 
 
 Each paper was graded upon the following points, though the grading upon 
 Ha, only, is used as the measure of the history test. H w is used in connection 
 with the English test. 
 
 Hv Valuation — historical forecast and appreciation of the essential his- 
 torical facts. (Grade approximately from to 10, with an average 
 of 5. Further explanation follows.) 
 
 H a Accuracy and extent of description. (Start with 4 and to this add £ 
 for each point correctly made and subtract 1 for each point incor- 
 rectly made.) 
 
 Hw Written expression. (Grade from to 10, with an average of 5. Give 
 some slight weight to spelling.) 
 
 Hd Dramatization. (Grade from to 10, with an average of 5.) 
 
 The grading for valuation depended in part upon the answer to question 
 (1). The grading of this historical forecast followed closely the scheme 
 below: 
 
 Grade below: given for selecting the following as the next historical event: 
 7 del Drawing up a constitution. 
 
 6±1 Peaceful acquisition of Rome and Venice. 
 
 5±1 Conquering of Rome, or of Rome and Venice. 
 
 Garibaldi given some honor. 
 
 Establishment of a government. 
 4±1 Peace for a short time and then revolts. 
 
 Garibaldi rebels against Victor Emmanuel. 
 3±1 Failure to answer. 
 
 2=fcl Uprising and revolution by the people. 
 
 Garibaldi made king. 
 
 The plus or minus after each grade indicates the amount that quite generally 
 is to be added or subtracted, depending upon the answers to the second and 
 third questions. For the second question, 
 
 Add 1, or more, for genuine appreciation of the traits of character which 
 were essential to Garibaldi's success. 
 
 Add for correct personal description. 
 
 Add — 1 for incorrect personal description which does injustice to Gari- 
 baldi's character, and for irrelevant but correct data, e. g., trip to 
 South America. 
 
 For the third question, 
 
 Add 1 for correct references to motive and organization, e. g., "to establish 
 a free and united Italy " ; " formed a provisional government " ; " j oined 
 by insurgent Sicilians"; "proclaimed a constitution"; etc. 
 
 Add for correct narrative. 
 
 Add — 1 for incorrect narrative which violates principles involved and for 
 misunderstanding of organization, e. g., "Garibaldi sailed to Mar- 
 seilles and fought the King of France"; or for attributing incorrect 
 motives. 
 
 As already mentioned the accuracy grading H a is the measure for the 
 entire test for convenience multiplied by two, i. e., Ht = 2(H a — mean). 1 
 
 1 See Appx., p. 99. 
 
36 
 
 Educational Guidance 
 
 The reliability coefficient of H t is .956 since the grades used are 
 the sum of the grades given by two judges and the correlation 
 between the latter, based on a sample of 36, is .916. 
 
 In the following sample tests, given to illustrate the method of 
 marking, the gradings for valuation and dramatization are 
 included though they are not used in obtaining the final score 
 for the test. 
 
 Name (Pupil No. 226). 
 
 Date. 
 
 I. The next important event might have been the 
 taking of Venice and Rome by Garibaldi and Victor 
 E mm anuel, making Italy a United Kingdom. 
 
 II. Garibaldi wore a red coat, high hat with a plume 
 and boots. His character was a very strong and good 
 one. He desired to do good for his country, therefore 
 fought well and won many victories. 
 
 III. Garibaldi was a very brave soldier who was 
 sent by the King of Piedmont, Victor Emmanuel. He 
 and one thousand men started down to the southern 
 part of Italy, by water. They reached the most south- 
 ern of the two Sicilys, and conquered Palermo first. 
 A telegraph had been sent just before their arrival 
 and it said that these men were coming to conquer 
 them, but as Garibaldi reached there he said "no that 
 is not right, we are merchants," so another telegram 
 was sent. Garibaldi and his men marched on to 
 Marsala and conquered that city. He won victory . . . 
 
 Ht = 2(H a -mean) =2(1.5-6.5) = -10.0. 
 
 Grading 
 
 Ha 
 
 4 
 
 H v 
 
 Hw 
 
 Hd 
 
 .5 
 -1 
 .5 
 .5 
 
 5 
 .5 
 
 
 
 -1 
 
 .5 
 
 
 
 
 -1 
 
 
 
 
 -1 
 
 
 
 
 -.5 
 
 -.5 
 
 
 
 1.5 
 
 5 
 
 5 
 
 5 
 
Special Tests and Their Significance 
 
 37 
 
 Name (Pupil No. 225). Date . 
 
 I. The fall of Rome or Venice which would make 
 all Italy independent! 
 
 II. Garibaldi was a seamanlike, strong phisycaly 
 and mentaly with a patriotic spirit. He had a 
 handsome face, intelligent eyes. Dressed in plumed 
 cap, red shirt and loos bandana around his neck he 
 looked quite fierce. 
 
 III. It took us only a day to coast down to Palermo 
 where we disembarked as quickly as possible while 
 to English cruisers held up some of the ships of the 
 King of Sicily. We captured the town and assured 
 the King of Sicily over telegraph that no such thing 
 had happened. We had soon captured all the south- 
 ern cities and were marching north to Capture Naples 
 but the King hearing of our approach fled. King 
 Emanuel came to our help and we soon had all of the 
 states except Rome and Venice which we soon expect 
 to have. Our brave leader Garibaldi is Dictator of 
 Sicily. 
 
 Ht = 2(10-6.5)=7.0. 
 
 H a 
 
 4 
 
 H v 
 
 H w 
 
 Hd 
 
 .5 
 
 .5 
 
 .5 
 
 1.5 
 
 5 
 
 
 
 
 .5 
 .5 
 
 
 
 
 -.5 
 .5 
 
 
 
 
 1 
 
 .5 
 
 
 
 
 .5 
 
 1 
 
 
 
 10.0 
 
 6 
 
 5.5 
 
 10 
 
38 
 
 Educational Guidance 
 
 Name (Pupil No. 212). 
 
 I. The completion of the Kingdom by capturing 
 Rome (especially) and Venice; and making Emanuel's 
 claim to the throne secure. 
 
 II. Garibaldi, having been a sailor inherited their 
 jovial demeanor and carriage. He was exceedingly 
 adventurous, and, we hear of him in such countries 
 as were engaged in war. He was tanned by exposure 
 as a seaman, strong, muscular and athletic. He in- 
 herited a trait of being able to rule and govern men 
 as is shown by his checkered career. He was 
 perpetually clad in a red shirt and sometimes a 
 kerchief of the same brilliant hue, encircled his neck. 
 His hair was luxurious and abundant which set off his 
 appearance nicely. 
 
 III. In April 1860 Garibaldi left Genoa in command 
 of 1000 volunteers embarked on two Piedmontese 
 
 his men 
 Palermo 
 
 vessels. He reach Marsala and marched 
 landward to Palermo which he captured . 
 had previously revolted and his campaign was in 
 accordance to it. From Palermo he sailed to Calabria 
 which he captured. He proceeded northwards and 
 was joined by Emanuel. Together thay captured all 
 of Italy except Rome and Venice. Garibaldi assumed 
 the title of Dictator. Francis, King of the two Sicilies 
 abdicated. Carassi was made secretary. Emanuel 
 was proclaimed King and the first Parliament met 
 1861, which represented all the individual states com- 
 bined. (Deduct 1 for order of events) 
 
 Ht = 2(12-6.5) = 11. 
 
 Date 
 
 Grading 
 
 Ha Hy Hw Hd 
 
 .5 
 .5 
 
 .5 
 .5 
 .5 
 -.5 
 
 {':! 
 
 .5 
 -.5 
 .5 
 .5 
 .5 
 .5 
 .5 
 .5 
 .5 
 .5 
 
 .5 
 .5 
 .5 
 .5 
 .5 
 
 1.5 
 
 12 11.5 9 
 
Special Tests and Their Significance 
 
 39 
 
 Name (Pupil No. 234). 
 
 Date. 
 
 I. The fall of Rome was probably the next impor- 
 tant event, maybe Venice at the same time. 
 
 II. Garibaldi was a strong man. As he had been in 
 South America he was toughened to wild life. He was 
 a man who was strong as a general and could com- 
 mand troops well. 
 
 He had black wavy hair and wore a red shirt. 
 
 III. When Garibaldi left Genoa secretly he took 
 with him a thousand men. These men were like 
 King Arthur and his Knights of the Round Table. 
 When they came near Marsala two war vessels from 
 Naples followed them but at the same time t wo English 
 men-of-war were there and they delayed the men-of- 
 war from Naples. Garibaldi reached Marsala and 
 went to a telegraph office and was just too late to stop 
 a message saying that they had arrived. He had the 
 operator send the message that he mistook the vessels 
 and that they were only merchant vessels. 
 
 Ht=2(10.5-6.5)=8.0. 
 
 Ha 
 
 H v 
 
 H w 
 
 Hd 
 
 4 
 
 6 
 
 
 
 .5 
 
 
 
 
 .5 
 
 {:! 
 
 .5 
 
 1 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 10.5 
 
 7 
 
 8 
 
 3.5 
 
40 
 
 Educational Guidance 
 
 Name (Pupil No. 227). Date. 
 
 Grading 
 
 I. The two Sislies were united, no doubt. 
 
 II. Garibaldi must have been stern and had good 
 discipline to manage so many people, and train Italian 
 soldiers. (He was perfectly honest as he said he 
 would help Italy and did.) Garibaldi, was tall, 
 had dark wavy hair that fell in waves over his 
 crisp black eyebrows, his eyes stood out like black 
 diamonds in a white velvet background. Garibaldi 
 wore a flaring red shirt. 
 
 III. Garibaldi left Genoa with a crew of a thousand 
 men, sailed directly southward to Palermo ; when the 
 people there heard that vessels had landed they sent a 
 wireless of the news and also for help. Garibaldi 
 arrived just in time to add a few words to the message. 
 After he had conquored and captured Messina, and 
 the other cities he worked his way north where 
 another force joined him and together they captured 
 Naples. 
 
 Ht=2(-l-6.5) = -15. 
 
 Ha 
 
 H v 
 
 H w 
 
 H a 
 
 4 
 
 2 
 
 
 
 .5 
 
 
 
 
 -1 
 
 
 
 
 -1 
 
 
 
 
 .5 
 
 
 
 
 U 6 
 
 
 
 
 {--l 
 
 .5 
 
 
 
 
 .5 
 
 
 
 
 -1 
 
 
 
 
 .5 
 
 -1 
 
 
 
 -1 
 
 1 
 
 7.5 
 
 8.5 
 
 (Mi, Ej, Hj,) Interest Tests 
 
 In attempting to test a pupil's interest in some given high 
 school subject an error would likely be introduced if that subject 
 alone were dealt with, as the pupil would readily see the object 
 of the test and, possibly unconsciously, be influenced thereby. 
 For purposes of tapping a pupil's personal preference it is very 
 much more significant for him to say that of all vocations he 
 prefers that of teaching mathematics, than for him to reply in 
 the affirmative to the question "Would you rather teach mathe- 
 matics for a vocation than to do anything else?" This illustra- 
 tion serves to emphasize the difference in the nature of response 
 of an individual when he is indicating a spontaneous preference 
 from his response when he is accepting or rejecting a controlled 
 choice. 
 
 In order to insure such spontaneity and freedom of choice, an 
 interest test was so devised as to cover impartially all the ordi- 
 
Special Tests and Their Significance 
 
 41 
 
 nary interests of a pupil. Because this test covers so broad a field 
 it may be used equally well to measure a pupil's interest in lines 
 other than mathematics, English and history, which are the 
 lines for which its significance has been evaluated in this study. 
 When graded along the line of English, the grade of this test is 
 designated by Ej, along the line of mathematics by M;, and 
 along the line of history by H;. The grading of this test is 
 accomplished by means of tables given on succeeding pages. 
 Administration of test: The pupils were told to answer the ques- 
 tions on the sheets handed them. As much time as was needed 
 was given — most of the pupils finishing the task in 40 minutes. 
 
 Interest Tests 
 
 Name Date 
 
 1. Go through the accompanying list of magazines and put an x opposite 
 those with which you are not familiar, that is, opposite those of which you have 
 never looked through at least two numbers. 
 
 1. All Story 27. Hearst's 50. Pictorial Review 
 
 2. American Boy 28. Home Needlework 51. Popular Mechan- 
 
 3. American 29. Ill'd London News ics 
 
 4. Argosy 30. L'illustration 52. Popular Science 
 
 5. Atlantic Monthly 31. Illustrirte Zeitung Monthly 
 
 6. Black Cat 32. Industrial Eng'g 53. Printer's Ink 
 
 7. Blue Book 33. International Stu- 54. Puck 
 
 8. Bookman dio 55. Red Book 
 
 9. Cassier's 34. Ladies Home Jour- 56. Review of Reviews 
 
 10. Century nal 57. St. Nicholas 
 
 11. Collier's Weekly 35. LaFollette's 58. Saturday Evening 
 
 12. Commoner 36. Leslie's Weekly Post 
 
 13. Cosmopolitan 37. Life 59. Science 
 
 14. Country Life in 38. Lippincott's 60. Scientific American 
 
 America 39. Literary Digest 61. Scribner's 
 
 15. Craftsman 40. McClure's 62. Smart Set 
 
 16. Current Literature 41. Metropolitan 63. Strand 
 
 17. Delineator 42. Modern Priscilla 64. System 
 
 18. Electrical World 43. Moving Picture 65. Technical World 
 
 19. Etude World 66. Theatre 
 
 20. Everybody's 44. Munsey's 67. Woman's Home 
 
 21. Good Housekeep- 45. Musician Companion 
 
 ing 46. Natio'nal Geo- 68. Wilshire's 
 
 22. Graphic graphic 69. World's Work 
 
 23. Green Book 47. Outing 70. Youth's Compan- 
 
 24. Hampton's 48. Outlook ion 
 
 25. Harper's Weekly 49. Photographic 
 
 26. Harper's Monthly Times 
 
 Go through the list again, marking the five that interest you most A, B, C, 
 D and E; A for the most interesting of all, B for the next most interesting, and 
 so on. Do not spend much time in deciding exactly upon your preferences. 
 
 2. Briefly tell why you particularly enjoy reading the magazine that you 
 have marked A. 
 
 3. Name three books which you have read in the last two years that have 
 
 interested you very much. 1 
 
 2 3 
 
42 
 
 Educational Guidance 
 
 4. Suppose that you have an hour's leisure time, in what outdoor amuse- 
 ment would you prefer to spend it? 
 
 5. Suppose that you have an hour's leisure time, in what indoor amusement 
 would you prefer to spend it? 
 
 6. Of the two amusements named in your answers to questions 4 and 5 
 which do you prefer? 
 
 7. If you had the opportunity, which one of the following would you attend, 
 supposing each of them to be first class of its kind? Mark it A. 
 
 1. Moving picture entertainment. 9. Boxing contest 
 
 2. Circus 10. Band concert 
 
 3. Football game 11. Political rally 
 
 4. Baseball game 12. Light opera 
 
 5. Track meet 13. Drama 
 
 6. Musical comedy 14. Lecture, or stereopticon lecture, 
 
 7. Vaudeville performance on a subject that interests you. 
 
 8. Grand opera 
 
 8. What occupation would you prefer as a life work? 
 
 Which would you like next best? 
 
 9. In the following list of words mark with a 3 those you know the meaning 
 of perfectly and could define as a dictionary does. 
 
 If you can explain in a general way the meaning of the word and would 
 understand it when used in a sentence mark it with a 2. 
 
 If you cannot explain its meaning but are vaguely familiar with it, mark it 
 with a 1. 
 
 If the word is entirely new to you and unknown, mark it with a 0. 
 
 In doing this, go through the list four times, the first time marking the 3's, 
 the second time the 2's, the third time the l's, and the last time the 0's. 
 
 1. simile 32. physical valuation of railroads. 
 
 2. primary election 33. score (in music) 
 
 3. Mason and Dixon's line 34. commercial fertilizer 
 
 4. creed 35. Magna Charta 
 
 5. Acropolis 36. voucher 
 
 6. rip saw 37. ohm 
 
 7. hydrogen 38. string halt 
 
 8. compound interest 39. fourth dimension 
 
 9. cube root 40. piston rod 
 
 10. paradox 41. Pythagorean proposition 
 
 11. Saracens 42. single tax 
 
 12. I. W. W. 43. stamen 
 
 13. Whigs 44. hemstitch 
 
 14. theosophy 45. Spanish Armada 
 
 15. toga " 46. statute of limitations 
 
 16. block plane 47. coherer 
 
 17. NaCl 48. vertebrate 
 
 18. fissure 49. parallelogram 
 
 19. equation 50. omelette 
 
 20. guillotine 51. Reichstag 
 
 21. prose 52. Commerce Court 
 
 22. syndicalism 53. states' rights 
 
 23. H 2 54. space bar 
 
 24. transubstantiation 55. giblets 
 
 25. gladiator 56. Australian ballot 
 
 26. debit 57. mollusk 
 
 27. gravity cell 58. perspective 
 
 28. strata 59. fireless cooker 
 
 29. improper fraction 60. mortgagee 
 
 30. lever 61. referendum 
 
 31. ragtime 62. Formosa 
 
Special Tests and Their Significance 43 
 
 10. Tell what each of the following words means as well as you can. 
 
 a. simile 
 
 b. cube root 
 
 c. improper fraction 
 
 d. ragtime 
 
 e. physical valuation of railroads 
 
 f . commercial fertilizer 
 
 g. ohm 
 
 h. Pythagorean proposition 
 
 i. single tax 
 
 j. hemstitch 
 
 k. vertebrate 
 
 1. parallelogram 
 
 m. omelette 
 
 The last two questions are not solely for the purpose of testing 
 the pupil's interest, as they test his range of information as well. 
 They constitute a vocabulary test in which the words were chosen 
 because of their specific bearing upon all the usual high school 
 courses and in addition upon religion and politics, in order to 
 cover the intellectual field. 
 
 Anyone who has read the answers of a few pupils to the ques- 
 tions in this test must feel that strong individual differences are 
 shown. There is much to indicate that the data are highly signifi- 
 cant as evidence of interest, but the problem of expressing this 
 in numerical terms and with reference to specific high school 
 courses is far more elusive than simply the determination that 
 the data are significant. For purposes of evaluation, it would be 
 possible, theoretically, to have a large number of judges grade 
 each pupil's paper upon the various questions with reference to 
 the significance of each of the questions in turn as evidence of 
 interest, severally, in mathematics, English and history. Prac- 
 tically this method is valueless, as judges with sufficient leisure 
 and patience could not be found and because their work would 
 apply only to the actual papers graded and would be of no aid to 
 another party desiring to give the test. A result embodying all 
 the advantages of the former method and none of its disadvan- 
 tages, can be obtained by having a sufficient number of judges 
 grade the questions for all the probable answers. With a table 
 of such gradings for each question, it is then only a matter of a 
 single grader comparing the answers of the pupils with the grad- 
 ings of the tables. Anyone is then able to give and grade the 
 test with an accuracy which is very nearly as great as the accu- 
 racy of the original grading of the expert judges. This second 
 
44 
 
 Educational Guidance 
 
 method, which has been used, will be clearer when illustrated by- 
 reference to the specific questions. 
 
 Grading of the Interest Tests 
 
 Questions 1 and 2 — Magazines. 
 
 Each of the magazines listed was graded from zero to ten for its significance 
 as evidence of interest and information along the line of English and again 
 with reference to history, by four judges (except that only three graded fifteen 
 of the least familiar magazines), three of whom are psychologists and familiar 
 with grading of this nature, and the fourth a librarian. The average, to the 
 nearest integer, of the grades of the different judges is the grade given for each 
 magazine in the following table : 
 
 Grade 
 
 Grade 
 
 Eng. 
 1 
 2 
 5 
 1 
 10 
 1 
 
 8 
 2 
 7 
 4 
 6 
 4 
 5 
 
 5 
 9 
 3 
 3 
 3 
 5 
 4 
 4 
 
 4 
 4 
 6 
 4 
 3 
 4 
 4 
 4 
 3 
 3 
 4 
 5 
 4 
 
 Hist. 
 
 
 1 
 5 
 
 4 
 
 
 2 
 1 
 4 
 7 
 9 
 2 
 1 
 
 1 
 
 4 
 
 
 1 
 2 
 5 
 2 
 7 
 
 5 
 6 
 3 
 5 
 
 7 
 7 
 7 
 2 
 2 
 1 
 9 
 7 
 
 1. All Story 
 
 2. American Boy 
 
 3. American 
 
 4. Argosy 
 
 5. Atlantic Monthly 
 
 6. Black Cat 
 
 7. Blue Book 
 
 8. Bookman 
 
 9. Cassier's 
 
 10. Century 
 
 11. Colher's Weekly 
 
 12. Commoner 
 
 13. Cosmopolitan 
 
 14. Country Life in 
 
 America 
 
 15. Craftsman 
 
 16. Current Literature 
 
 17. Delineator 
 
 18. Electrical World 
 
 19. Etude 
 
 20. Everybody's 
 
 21. Good Housekeeping 
 
 22. Graphic 
 
 23. Green Book 
 
 24. Hampton's 
 
 25. Harper's Weekly 
 
 26. Harper's Monthly 
 
 27. Hearst's 
 
 28. Home Needlework 
 
 29. Ill'd London News 
 
 30. L'illustration 
 
 31. Illustrirte Zeitung 
 
 32. Industrial Eng'g 
 
 33. International Studio 
 
 34. Ladies' Home Journal 
 
 35. LaFollette's 
 
 36. Leslie's Weekly 
 
 Eng. 
 
 Hist. 
 
 
 
 3 
 
 1 
 
 37. 
 
 Life 
 
 5 
 
 2 
 
 38. 
 
 Lippincott's 
 
 7 
 
 7 
 
 39. 
 
 Literary Digest 
 
 5 
 
 4 
 
 40. 
 
 McClure's 
 
 1 
 
 
 
 41. 
 
 Metropolitan 
 
 3 
 
 
 
 42. 
 
 Modern Priscilla 
 
 1 
 
 
 
 43. 
 
 Moving Picture 
 World 
 
 1 
 
 1 
 
 44. 
 
 Munsey's 
 
 3 
 
 2 
 
 45. 
 
 Musician 
 
 5 
 
 9 
 
 46. 
 
 National Geographic 
 
 3 
 
 1 
 
 47. 
 
 Outing 
 
 7 
 
 8 
 
 48. 
 
 Outlook 
 
 3 
 
 2 
 
 49. 
 
 Photographic Times 
 
 2 
 
 
 
 50. 
 
 Pictorial Review 
 
 2 
 
 1 
 
 51. 
 
 Popular Mechanics 
 
 2 
 
 1 
 
 52. 
 
 Popular Science 
 Monthly 
 
 1 
 
 
 
 53. 
 
 Printer's Ink 
 
 2 
 
 1 
 
 54. 
 
 Puck 
 
 
 
 
 
 55. 
 
 Red Book 
 
 5 
 
 8 
 
 56. 
 
 Review of Reviews 
 
 6 
 
 1 
 
 57. 
 
 St. Nicholas 
 
 4 
 
 4 
 
 58. 
 
 Saturday Ev'g Post 
 
 3 
 
 2 
 
 59. 
 
 Science 
 
 3 
 
 3 
 
 60. 
 
 Scientific American 
 
 7 
 
 3 
 
 61. 
 
 Scribner's 
 
 3 
 
 
 
 62. 
 
 Smart Set 
 
 2 
 
 
 
 63. 
 
 Strand 
 
 2 
 
 1 
 
 64. 
 
 System 
 
 2 
 
 1 
 
 65. 
 
 Technical World 
 
 1 
 
 
 
 66. 
 
 Theatre 
 
 4 
 
 1 
 
 67. 
 
 Woman' s Home Com- 
 panion 
 
 3 
 
 4 
 
 68 
 
 Wilshire's 
 
 5 
 
 8 
 
 69 
 
 World's Work 
 
 5 
 
 2 
 
 70 
 
 Youth's Companion 
 
Special Tests and Their Significance 45 
 
 The correlations between the grades given by judges 1, 2, 3 and 4 are as 
 follows: 
 
 rn 
 
 .887 
 
 rn 
 
 .893 
 
 ru 
 
 .867 
 
 7*23 
 
 .788 
 
 r 24 
 
 .920 
 
 7-34 
 
 .821 
 
 Average . 863 
 
 Taking the number of judges for each magazine as three and one-half, the 
 reliability coefficient equals .956. 
 
 The single grade given for these questions is the average grade for the 
 magazines after altering the grade of the magazine marked "A" (usually about 
 If points) upon the basis of the answer to question 2, and weighting maga- 
 zines A, B, C, D, and E 10, 8, 6, 4, and 2 respectively. The sample grading 
 of the entire test, given on page 56, will show the steps in detail. 
 
 The reliability coefficient for the grading of each magazine is .956, but the 
 reliability of the average of a number of such grades is higher. A factor tend- 
 ing in the other direction is the method of grading the magazine marked "A." 
 The alteration of the grade of this magazine is not arbitrary, but left to the 
 grader, and therefore its reliability is somewhat less than that of the maga- 
 zines that have been graded by three or four judges. The net result of these 
 two factors is probably to make the reliability of the grade given for the 
 question about the same as the reliability of the grading of the magazines by 
 the judges. 
 
 Question 3 — Books. 
 
 The establishment of a guide for the grading of question 3 offers greater 
 difficulties than was the case with question 1, for the reason that the number 
 of books which may be preferred is unlimited. However, quite a number of 
 books were repeatedly chosen, so that a grading for books for English and 
 history covering 300 or so of the most frequent choices does cover a very large 
 per cent of the books chosen. Furthermore, as each pupil chooses three books, 
 it is much more than likely that two of the three will be books that are graded, 
 or books by the same author as graded books, so that the grading actually is 
 quite objective. The following is such a list, and the grades given, expressed 
 as deviations from the mean, are the averages of the grades of from two to four 
 judges, about one-half being graded by three or more judges. This list of 
 about 300 titles is part of a larger list which included all the books preferred 
 by the pupils. The larger fist was given to four judges — two librarians and 
 two others familiar with such work. The directions to the judges were to grade 
 the books for English and history according to the following scheme: 
 
 Grade English History 
 
 1 The best literature. Straight histories. 
 
 2 Excellent. Books that are mainly historical. 
 
 Historical biographies, etc. 
 
 3 Good. Partly historical. Historical fiction. 
 
 4 Medium. Fiction or adventure with traces of 
 
 historical material. 
 
 5 Poor. Adventure, etc., with no claim to any 
 
 historical matter, but with lively 
 action and plot. 
 
 6 Very poor — semi-trashy. Non-historical fiction. 
 
 7 Pure trash. Books with neither plot nor historical 
 
 background, e. g., Electricity for 
 Beginners. 
 
46 
 
 Educational Guidance 
 
 The average correlation between the gradings of two judges is .882 for the 
 English grading, and .720 for the history grading. The reliability coefficient, 
 calling the number of judges 2£, is, for the English grading .947, and for the 
 history grading .861. Since all the books chosen are not in the following list, 
 and since certain of those not so listed can be graded if the grader is familiar 
 with the book or with the author, the reliability of the resulting grade of each 
 book is somewhat less than the reliability coefficient just given. 
 
 The gradings from 1 to 7 of the different judges were combined into single 
 grades, expressed as deviations from the mean, 1 and this is the grade given in 
 the following table: 
 
 Author 
 
 Scott 
 
 Eliot 
 
 Clemens 
 
 Doyle 
 
 Roosevelt 
 
 Maeterlinck 
 
 Irving 
 
 Montgomery 
 
 u 
 
 Locke 
 
 F. H. Smith 
 
 Franklin 
 
 Stanley 
 
 Haggard 
 
 Wallace 
 
 M. Warde 
 
 McCutcheon 
 
 Thompson-Seton 
 
 Wiggin 
 
 Stevenson 
 
 Vance 
 
 White 
 
 Dickens 
 
 Farnol 
 
 London 
 Kipling 
 Stockton 
 
 Garland 
 
 Dumas 
 
 n 
 
 Dickens 
 Churchill 
 L. Scott 
 Dumas 
 
 Gaskell 
 Barbour 
 
 Churchill 
 
 it 
 
 Trowbridge 
 Rostand 
 
 1 See Appx. p. 101. 
 
 Title 
 
 Abbot 
 
 Adam Bede 
 
 Adventures of Tom Sawyer 
 
 Adventures of Sherlock Holmes 
 
 African Hunt 
 
 Aglavine and Lysette 
 
 Alhambra 
 
 Ann of Avonlea 
 
 Ann of Green Gables 
 
 Aristide Pujol 
 
 Armchair at the Inn 
 
 Autobiography of Benjamin Franklin 
 
 Autobiography of Henry M. Stanley 
 
 Ayesha 
 
 Ben Hur 
 Betty Books 
 Beverly of Graustark 
 Biography of a Grizzly 
 Birds' Christmas Carol 
 Black Arrow 
 Black Bag 
 Blazed Trail 
 Bleak House 
 Broad Highway 
 
 Call of the Wild 
 
 Captains Courageous 
 
 Casting Away of Mrs. Leeks and Mrs. 
 
 Aleshine 
 Cavanaugh, Forest Ranger 
 Chevalier de Maison Rouge 
 Chicot the Jester 
 Christmas Carol 
 Coniston 
 
 Counsel for the Defense 
 Count of Monte Cristo 
 Countess de Charny 
 Cranford 
 Crimson Sweater 
 Crisis 
 Crossing 
 Cudjo's Cave 
 Cyrano de Bergerac 
 
 Grade 
 
 Eng. 
 
 Hist 
 
 1.2 
 
 1.2 
 
 2.0 
 
 -.2 
 
 .2 
 
 .0 
 
 - .2 
 
 .0 
 
 - .2 
 
 .0 
 
 .9 
 
 - .8 
 
 1.4 
 
 2.2 
 
 - .4 
 
 - .8 
 
 - .4 
 
 - .8 
 
 - .2 
 
 - .8 
 
 - .2 
 
 - .8 
 
 .2 
 
 1.5 
 
 .2 
 
 1.5 
 
 -1.2 
 
 - .8 
 
 .5 
 
 1.2 
 
 - .8 
 
 - .8 
 
 -1.7 
 
 - .4 
 
 - .2 
 
 - .4 
 
 .1 
 
 - .8 
 
 .8 
 
 - .6 
 
 -1.5 
 
 - .8 
 
 .2 
 
 .9 
 
 1.2 
 
 - .2 
 
 - .6 
 
 - .4 
 
 .4 
 
 .5 
 
 .4 
 
 - .4 
 
 .0 
 
 - .8 
 
 - .6 
 
 .4 
 
 .5 
 
 1.2 
 
 .5 
 
 .2 
 
 1.3 
 
 — .8 
 
 .1 
 
 .6 
 
 - .3 
 
 - .8 
 
 .5 
 
 .8 
 
 .5 
 
 1.2 
 
 .1 
 
 - .6 
 
 - .8 
 
 - .8 
 
 .1 
 
 1.2 
 
 .1 
 
 1.2 
 
 -1.7 
 
 - .4 
 
 1.4 
 
 .9 
 
Special Tests and Their Significance 
 
 47 
 
 Author 
 
 Title 
 
 Grade 
 
 
 
 Eng. 
 
 Hist 
 
 Eliot 
 
 Daniel Deronda 
 
 1.4 
 
 .5 
 
 Stevenson 
 
 David Balfour 
 
 .8 
 
 .5 
 
 Dickens 
 
 David Copperfield 
 
 1.1 
 
 - .4 
 
 Ferber 
 
 Dawn O'Hara 
 
 - .6 
 
 - .7 
 
 Aguilar 
 
 Days of Bruce 
 
 - .3 
 
 1.1 
 
 Cervantes 
 
 Don Quixote 
 
 1.2 
 
 .9 
 
 Dickens 
 
 Dombey and Son 
 
 1.1 
 
 - .4 
 
 Major 
 
 Dorothy Vernon of Haddon Hall 
 
 - .6 
 
 .7 
 
 Bacheller 
 
 Dri and I 
 
 .1 
 
 .9 
 
 (i 
 
 Eben Holden 
 
 - .2 
 
 - .5 
 
 Alcott 
 
 Eight Cousins 
 
 - .2 
 
 - .8 
 
 Tennyson 
 
 Enoch Arden 
 
 1.3 
 
 - .8 
 
 Longfellow 
 
 Evangeline 
 
 .4 
 
 .9 
 
 Drummond 
 
 Evolution of Man 
 
 .2 
 
 .4 
 
 Spenser 
 
 Faerie Queene 
 
 2.1 
 
 - .8 
 
 Poe 
 
 Fall of the House of Usher 
 
 1.2 
 
 - .8 
 
 Gaboriau 
 
 File Number 113 
 
 .1 
 
 .0 
 
 Fothergill 
 
 First Violin 
 
 - .4 
 
 - .8 
 
 Chaplin 
 
 Five Hundred Dollars 
 
 -1.5 
 
 - .9 
 
 Porter 
 
 Freckles 
 
 - .4 
 
 - .8 
 
 Read 
 
 Foul Play 
 
 .2 
 
 .0 
 
 Poe 
 
 Gold Bug 
 
 1.2 
 
 - .8 
 
 McCutcheon 
 
 Graustark 
 
 -1.7 
 
 - .5 
 
 Dickens 
 
 Great Expectations 
 
 1.1 
 
 - .5 
 
 Holmes 
 
 Gretchen 
 
 -2.7 
 
 - .8 
 
 Shakespere 
 
 Hamlet 
 
 2.3 
 
 .4 
 
 Dodge 
 
 Hans Brincker 
 
 - .8 
 
 - .5 
 
 Porter 
 
 Harvester 
 
 .1 
 
 .2 
 
 Thackeray 
 
 Henry Esmond 
 
 1.4 
 
 .9 
 
 Shakespere 
 
 Henry V 
 
 2.3 
 
 .9 
 
 Kelly 
 
 Her Little Young Ladyship 
 
 - .4 
 
 - .8 
 
 Redpath 
 
 History of America 
 
 .4 
 
 3.5 
 
 
 Hollow of Her Hand 
 
 -1.4 
 
 - .9 
 
 Leblau 
 
 Hollow Needle 
 
 - .2 
 
 .0 
 
 Ford 
 
 Honorable Peter Sterling 
 
 - .4 
 
 - .2 
 
 Mulford 
 
 Hopalong Cassidy 
 
 - .9 
 
 - .8 
 
 Doyle 
 
 Hound of the Baskervilles 
 
 - .2 
 
 .0 
 
 Hawthorne 
 
 House of Seven Gables 
 
 1.2 
 
 - .8 
 
 Rohlfs 
 
 House of the Whispering Pines 
 
 -1.2 
 
 .0 
 
 Clemens 
 
 Huckleberry Finn 
 
 .2 
 
 - .5 
 
 Clemens 
 
 Innocents Abroad 
 
 .2 
 
 - .8 
 
 Davis 
 
 In the Fog 
 
 - .4 
 
 .1 
 
 Crawford 
 
 In the Palace of the King 
 
 - .2 
 
 .7 
 
 Deland 
 
 Iron Woman 
 
 - .4 
 
 - .8 
 
 Scott 
 
 Ivanhoe 
 
 1.2 
 
 1.2 
 
 McCutcheon 
 
 Jane Cable 
 
 -1.7 
 
 - .8 
 
 Bronte 
 
 Jane Eyre 
 
 .8 
 
 - .8 
 
 Ford 
 
 Janice Meredith 
 
 - .4 
 
 1.2 
 
 Craik 
 
 John Halifax, Gentleman 
 
 .2 
 
 - .8 
 
 Kipling 
 
 Jungle Book 
 
 .4 
 
 - .8 
 
48 
 
 Educational Guidance 
 
 Author 
 
 Title 
 
 Grade 
 
 
 
 Eng. Hist 
 
 Scott 
 
 Kenilworth 
 
 1.2 1 
 
 2 
 
 Smith 
 
 Kennedy Square 
 
 - .4 
 
 8 
 
 Stevenson 
 
 Kidnapped 
 
 .8 
 
 5 
 
 Kipling 
 
 Kim 
 
 .4 
 
 5 
 
 Irving 
 
 Knickerbocker History of New York 
 
 .8 
 
 8 
 
 Williamson 
 
 Lady Betty Across the Water 
 
 -1.4 
 
 8 
 
 Scott 
 
 Lady of the Lake 
 
 1.2 
 
 5 
 
 Cummins 
 
 Lamplighter 
 
 - .9 - 
 
 5 
 
 Lytton 
 
 Last Days of Pompeii 
 
 .8 1 
 
 2 
 
 Cooper 
 
 Last of the Mohicans 
 
 .4 
 
 9 
 
 Reed 
 
 Lavender and Old Lace 
 
 -1.7 
 
 8 
 
 
 Letters of Abraham Lincoln 
 
 .5 2 
 
 2 
 
 Johnston 
 
 Little Colonel in Arizona 
 
 - .9 - 
 
 8 
 
 << 
 
 Little Colonel at Boarding School 
 
 - .9 
 
 8 
 
 Kipling 
 
 Light that Failed 
 
 .2 - 
 
 8 
 
 Dickens 
 
 Little Dorrit 
 
 1.1 - 
 
 4 
 
 Alcott 
 
 Little Men 
 
 .1 - 
 
 8 
 
 Barrie 
 
 Little Minister 
 
 .6 
 
 8 
 
 Fox 
 
 Little Shepherd of Kingdom Come 
 
 - .4 - 
 
 2 
 
 Alcott 
 
 Little Women 
 
 .1 
 
 8 
 
 Blackmore 
 
 Lorna Doone 
 
 .2 
 
 9 
 
 Parrish 
 
 Love under Fire 
 
 — .8 
 
 2 
 
 Rice 
 
 Lovey Mary 
 
 - .6 
 
 S 
 
 Austen 
 
 Mansfield Park 
 
 .5 
 
 8 
 
 Rinehart 
 
 Man in Lower Ten 
 
 -1.0 - 
 
 5 
 
 London 
 
 Martin Eden 
 
 .5 
 
 8 
 
 Dickens 
 
 Martin Chuzzlewit 
 
 1.1 
 
 2 
 
 Bosher 
 
 Mary Cary 
 
 - .8 - 
 
 8 
 
 Zangwill 
 
 Master 
 
 .2 - 
 
 8 
 
 Corelli 
 
 Master Christian 
 
 -1.2 - 
 
 8 
 
 Eliot 
 
 Mill on the Floss 
 
 1.4 - 
 
 8 
 
 Marryat 
 
 Mr. Midshipman Easy 
 
 -1.2 
 
 8 
 
 Hugo 
 
 Miserables, Les 
 
 1.3 1 
 
 2 
 
 Lincoln 
 
 Mr. Pratt 
 
 -1.2 - 
 
 8 
 
 Barclay 
 
 Mistress of Shenstone 
 
 — 7 — 
 
 8 
 
 Rice 
 
 Mrs. Wiggs of the Cabbage Patch 
 
 - .6 
 
 8 
 
 Abbott 
 
 Molly Make-believe 
 
 - .6 - 
 
 8 
 
 Collins 
 
 Moonstone 
 
 - .2 - 
 
 8 
 
 Norris 
 
 Mother 
 
 - .4 
 
 8 
 
 
 Mother Carey's Chickens 
 
 - .4 - 
 
 8 
 
 Spearman 
 
 Mountain Divide 
 
 - .8 
 
 6 
 
 Shakespere 
 
 Much Ado About Nothing 
 
 2.3 - 
 
 8 
 
 Verne 
 
 Mysterious Island 
 
 -1.2 - 
 
 4 
 
 Beach 
 
 Ne'er Do Well 
 
 - .9 - 
 
 4 
 
 a 
 
 Net 
 
 -1.2 
 
 8 
 
 Thackeray 
 
 Newcomes 
 
 1.4 - 
 
 6 
 
 Dickens 
 
 Nicholas Nickleby 
 
 1.1 
 
 2 
 
 Hugo 
 
 Notre Dame 
 
 1.3 
 
 5 
 
 Homer 
 
 Odyssey 
 
 2.3 
 
 9 
 
 Dickens 
 
 Old Curiosity Shop 
 
 1.1 
 
 4 
 
 Page 
 
 Old Gentleman of the Black Stock 
 
 - .2 
 
 8 
 
 Dickens 
 
 Oliver Twist 
 
 1.1 
 
 4 
 
 Burnham 
 
 Open Shutters 
 
 - .8 
 
 8 
 
Special Tests and Their Significance 
 
 49 
 
 Author 
 
 Title 
 
 Grade 
 
 
 
 Eng. 
 
 Hist. 
 
 Darwin 
 
 Origin of Species 
 
 - .6 
 
 - .4 
 
 Alcott 
 
 Our Helen 
 
 .2 
 
 - .8 
 
 Dickens 
 
 Our Mutual Friend 
 
 1.1 
 
 - .4 
 
 E. Smith 
 
 Palace Beautiful 
 
 -1.2 
 
 - .8 
 
 Cooper 
 
 Pathfinder 
 
 .2 
 
 .7 
 
 Wells 
 
 Patty's College Days 
 
 -1.2 
 
 - .8 
 
 
 Personal Memoirs of U. S. Grant 
 
 - .4 
 
 2.6 
 
 Dickens 
 
 Pickwick Papers 
 
 1.1 
 
 - .1 
 
 Cooper 
 
 Pioneers 
 
 - .2 
 
 .3 
 
 Flammarion 
 
 Popular Astronomy 
 
 - .9 
 
 -1.4 
 
 Austen 
 
 Pride and Prejudice 
 
 .4 
 
 - .8 
 
 Clemens 
 
 Prince and the Pauper 
 
 .2 
 
 - .8 
 
 Johnson 
 
 Prodigious Hickey 
 
 -1.2 
 
 - .8 
 
 Aldrich 
 
 Prudence Palfrey 
 
 .1 
 
 - .5 
 
 Harrison 
 
 Queed 
 
 .1 
 
 - .4 
 
 Scott 
 
 Quentin Durward 
 
 1.1 
 
 1.2 
 
 Sienkiewics 
 
 Quo Vadis 
 
 .4 
 
 1.2 
 
 Hornung 
 
 Raffles 
 
 -1.7 
 
 - .4 
 
 Jackson 
 
 Ramona 
 
 .4 
 
 .5 
 
 Wiggin 
 
 Rebecca of Sunnybrook Farm 
 
 - .2 
 
 - .8 
 
 Lytton 
 
 Rienzi 
 
 .8 
 
 1.2 
 
 Parkman 
 
 Robin Hood 
 
 - .8 
 
 .5 
 
 Thompson-Seton 
 
 Rolf in the Woods 
 
 - .2 
 
 - .4 
 
 Le Gallienne 
 
 Romance of Zion Chapel 
 
 .1 
 
 - .8 
 
 EHot 
 
 Romola 
 
 1.9 
 
 .9 
 
 Barclay 
 
 Rosary 
 
 -1.2 
 
 - .8 
 
 Alcott 
 
 Rose in Bloom 
 
 .1 
 
 - .8 
 
 Hope 
 
 Rupert of Hentzau 
 
 -1.0 
 
 - .4 
 
 Hawthorne 
 
 Scarlet Letter 
 
 1.1 
 
 .3 
 
 Porter 
 
 Scottish Chiefs 
 
 - .4 
 
 -1.2 
 
 London 
 
 Sea Wolf 
 
 .5 
 
 - .4 
 
 Kipling 
 
 Seven Seas 
 
 .5 
 
 - .8 
 
 Haggard 
 
 She 
 
 -1.4 
 
 - .4 
 
 Wright 
 
 Shepherd of the Hills 
 
 .1 
 
 - .8 
 
 Goldsmith 
 
 She Stoops to Conquer 
 
 1.1 
 
 - .4 
 
 Eliot 
 
 Silas Marner 
 
 1.9 
 
 - .2 
 
 Porter 
 
 Song of the Cardinal 
 
 .1 
 
 - .8 
 
 London 
 
 Son of the Sun 
 
 .5 
 
 - .8 
 
 Barr 
 
 Souls of Passage 
 
 - .9 
 
 - .8 
 
 Reed 
 
 Spinner in the Sun 
 
 -2.2 
 
 - .8 
 
 Cooper 
 
 Spy 
 
 .4 
 
 1.2 
 
 Schreiner 
 
 Story of an African Farm 
 
 - .4 
 
 - .2 
 
 Keller 
 
 Story of My Life 
 
 - .2 
 
 - .8 
 
 Johnson 
 
 gtover at Yale 
 
 - .9 
 
 - .8 
 
 King 
 
 Street Called Straight 
 
 -1.0 
 
 - .8 
 
 Vaile 
 
 Sue Orcutt 
 
 - .8 
 
 - .6 
 
 Wyss 
 
 Swiss Family Robinson 
 
 — .7 
 
 - .2 
 
 Dumas 
 
 Taking the Bastile 
 
 .5 
 
 1.2 
 
 Dickens 
 
 Tale of Two Cities 
 
 1.1 
 
 1.2 
 
 Scott 
 
 Talisman 
 
 1.1 
 
 1.2 
 
 Jacobs 
 
 Texas Blue Bonnet 
 
 -1.0 
 
 - .8 
 
 Porter 
 
 Thaddeus of Warsaw 
 
 - .3 
 
 .8 
 
50 
 
 Educational Guidance 
 
 Author 
 
 Title 
 
 Grade 
 
 
 
 Eng. 
 
 Hist 
 
 
 Thoughts of Marcus Aurelius 
 
 .7 
 
 - .1 
 
 Dumas 
 
 Three Guardsmen 
 
 .5 
 
 1.2 
 
 Jerome 
 
 Three Men in a Boat 
 
 - .4 
 
 - .8 
 
 Glyn 
 
 Three Weeks 
 
 -2.3 
 
 - .8 
 
 McCutcheon 
 
 Truxton King 
 
 -1.7 
 
 - .8 
 
 Verne 
 
 Twenty Thousand Leagues under the 
 
 
 
 
 Sea 
 
 -1.2 
 
 - •» 
 
 Stowe 
 
 Uncle Tom's Cabin 
 
 - .2 
 
 .9 
 
 Ouida 
 
 Under Two Flags 
 
 - .4 
 
 .5 
 
 Henty 
 
 Under Drake's Flag 
 
 -2.4 
 
 .9 
 
 Alcott 
 
 Under the Lilacs 
 
 .1 
 
 - .8 
 
 Thackeray 
 
 Vanity Fair 
 
 1.4 
 
 - .2 
 
 Goldsmith 
 
 Vicar of Wakefield 
 
 1.1 
 
 - .8 
 
 Wister 
 
 Virginian 
 
 - .2 
 
 - .8 
 
 Scott 
 
 Waverley 
 
 1.1 
 
 1.2 
 
 Reed 
 
 Weaver of Dreams 
 
 -1.7 
 
 - .8 
 
 Malone 
 
 West Point Yearling 
 
 - .6 
 
 - .8 
 
 Doyle 
 
 White Company 
 
 - .2 
 
 .3 
 
 London 
 
 White Fang 
 
 .4 
 
 - .8 
 
 Thompson-Seton 
 
 Wild Animals I Have Known 
 
 - .2 
 
 - .4 
 
 King 
 
 Wild Olive 
 
 - .8 
 
 - .8 
 
 Scott 
 
 Woodstock 
 
 1.1 
 
 1.2 
 
 Rohlfs 
 
 Woman in the Alcove 
 
 -1.6 
 
 .0 
 
 Hawthorne 
 
 Wonder Book 
 
 1.1 
 
 - .8 
 
 Alger 
 
 Young Adventurer 
 
 -2.2 
 
 - .8 
 
 Bennett 
 
 Your United States 
 
 - .2 
 
 .3 
 
 The grade for question 3 is the average grade for the three books, weighting 
 the first, second and third choices 3, 2, and 1 respectively. 
 
 Since this grade is an average of three grades, its reliability is greater than 
 that of a single book, and is probably close to .94 for English and .86 for history. 
 
 Questions 4, 5 and 6 — Sports. 
 
 The same general method used in establishing a guide for the grading of 
 books, has here been used in drawing up a guide for the grading of sports, 
 except that the grades were not expressed as deviations from a mean. The 
 grading was on a basis of zero to ten, and the judges consisted of three per- 
 sons experienced in such grading. The average correlation between the grad- 
 ings of the different judges, when English and history are combined into a 
 single correlation table, is .239. The reliability coefficient for the grading 
 is, therefore, .485. The grading is separate for the preferences of boys and 
 girls, as shown in the following table: 
 
Special Tests and Their Significance 
 
 51 
 
 Sports 
 
 Motoring 
 
 Baseball 
 
 Basketball 
 
 Bicycling 
 
 Cards 
 
 Domestic activities (cooking, sewing, etc.) 
 
 Drawing, painting 
 
 Fishing 
 
 Football 
 
 Hockey 
 
 Horseback riding 
 
 Pool or billiards 
 
 Musical practice 
 
 Reading 
 
 Rowing or sailing 
 
 Shop work 
 
 Skating 
 
 Swimming 
 
 Tennis 
 
 Theatre 
 
 Running games 
 
 Walking 
 
 Watching a game 
 
 Boys 
 E H M 
 
 Girls 
 
 
 E 
 
 H 
 
 M 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 2 
 
 3 
 
 2 
 
 1 
 
 3 
 
 4 
 
 3 
 
 1 
 
 1 
 
 1 
 
 i 
 
 1 
 
 2 
 
 2 
 
 2 
 
 1 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 2 
 
 9 
 
 9 
 
 2 
 
 1 
 
 1 
 
 3 
 
 1 
 
 1 
 
 3 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 5 
 
 5 
 
 
 
 1 
 
 1 
 
 1 
 
 2 
 
 2 
 
 1 
 
 The grade for the question is the average, counting the indoor choice once, 
 the outdoor choice once and the preference once. Since this grade is an 
 average of three, one of them, however, a repetition, there is a slight tendency to 
 increase the reliability of the grading over that of each sport singly. This 
 tendency is probably counterbalanced by the fact that all possible sports are 
 not included in the above list, and the grader must at times use his judgment 
 in the matter. In view of these two facts, it is likely that the reliability of 
 the grading is about .48. 
 
 Question 7 — Entertainments. 
 
 The general method used in establishing a guide for the grading of magazines 
 was followed here. Grading was upon the basis of zero to ten, and the judges 
 consisted of four persons experienced in such work. The average correlation 
 between the gradings of the judges, combining English and history into a 
 single correlation table, is .929, so that the reliability coefficient of the grading is 
 equal to .981. The grading follows: 
 
 E H 
 
 Entertainments 
 
 Moving pictures 
 
 Circus 
 
 Football game 
 
 Baseball game 
 
 Track meet 
 
 Musical comedy 
 
 Vaudeville 
 
 Grand opera 
 
 Boxing contest 
 
 Band concert 
 
 Political rally 
 
 Light opera 
 
 Drama 
 
 Lecture, or stereopticon lecture on a subject that interests you . 
 
 4 
 
 
 
 
 
 
 4 
 
 1 
 10 
 
 7 
 7 
 
 The grade given for the question is the grade of the entertainment marked 
 'A," so that the reliability coefficient of this grade is .981. 
 
52 
 
 Educational Guidance 
 
 Question 8 — Vocations. 
 
 Here again, the number of choices is unlimited, so that the method used in 
 the grading of sports is the one followed. The following list of vocations was 
 drawn up after examination of all the choices of the pupils, and was graded by 
 four judges. The average correlation between the gradings of the different 
 judges, the mathematics, English and history gradings being combined into 
 a single table, is .693, so that the reliability coefficient of the grading is .901. 
 
 Vocations 
 Actor 
 
 E 
 8 
 6 
 
 
 10 
 6 
 5 
 4 
 2 
 
 Boys 
 H 
 
 5 
 6 
 1 
 
 7 
 5 
 4 
 4 
 2 
 
 M 
 1 
 1 
 
 2 
 8 
 6 
 6 
 5 
 
 Artist 
 
 Athlete, professional 
 
 Author 
 
 Banker 
 
 Broker 
 
 Business , 
 
 Carpenter 
 
 Decorator or designer 
 
 Doctor 
 
 6 
 9 
 
 4 
 5 
 4 
 4 
 4 
 4 
 4 
 4 
 1 
 1 
 
 5 
 
 8 
 4 
 6 
 3 
 
 4 
 4 
 4 
 4 
 4 
 2 
 2 
 
 3 
 2 
 9 
 8 
 9 
 9 
 9 
 10 
 9 
 9 
 2 
 2 
 
 Journalist 
 
 Engineering 
 
 Architectural 
 
 Electrical 
 
 Civil 
 
 Marine 
 
 Mechanical 
 
 Mining 
 
 Structural 
 
 Farming 
 
 Forestry 
 
 Housekeeper 
 
 Lawyer 
 
 8 
 
 8 
 
 2 
 
 Lecturer 
 
 Librarian 
 
 
 
 
 Milliner 
 
 
 
 
 Musician 
 
 3 
 
 4 
 
 3 
 
 7 
 
 2 
 5 
 
 Member of navy 
 
 Nurse 
 
 Politician 
 
 6 
 
 9 
 
 3 
 
 Secretary 
 
 Singer 
 
 4 
 5 
 
 4 
 6 
 
 2 
 4 
 
 Charity worker 
 
 Dressmaker 
 
 Teacher 
 
 8 
 
 8 
 
 8 
 
 Domestic science 
 
 English 
 
 
 
 
 Kindergarten 
 
 
 
 
 Physical training or dancing 
 
 
 
 
 E 
 
 7 
 6 
 
 Girls 
 
 H 
 
 4 
 
 6 
 
 5 
 
 M 
 
 1 
 
 9 
 
 7 
 
 2 
 
 
 
 
 4 
 
 4 
 
 6 
 
 4 
 6 
 9 
 
 5 
 5 
 
 8 
 
 3 
 
 4 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 2 
 
 2 
 
 2 
 7 
 9 
 8 
 1 
 3 
 
 2 
 6 
 8 
 8 
 2 
 3 
 
 1 
 2 
 1 
 1 
 1 
 2 
 
 4 
 
 4 
 
 2 
 
 8 
 4 
 6 
 3 
 8 
 6 
 10 
 8 
 5 
 
 7 
 4 
 6 
 3 
 8 
 4 
 8 
 6 
 4 
 
 5 
 2 
 
 4 
 2 
 7 
 4 
 4 
 3 
 2 
 
 Question 9 — Vocabulary. 
 
 The grading of the words followed the general scheme used in grading the 
 magazines. A number of words are graded zero by all the judges for their sig- 
 nificance in one or all of the three lines, and as these do not enter into the 
 grade which the pupil received, they have been omitted in calculating the 
 reliability of the grading for mathematics, English and history, though simply 
 as a measure of the reliability of the grading this is not desirable. The inclu- 
 sion of these zero gradings would increase the reliability coefficient. The 
 reliability differs considerably for English from that for mathematics and 
 
Special Tests and Their Significance 53 
 
 history so that the coefficients are calculated separately. The average cor- 
 relation for the different judges, excluding the zeros, as stated, between the 
 gradings of the words, equals for mathematics .785; for English .542; for his- 
 tory .795, and the average for all is .707. Since three judges graded all the 
 words, the reliability coefficients for the grades of these subjects are .916 for 
 mathematics, .780 for English and .921 for history; an average of .872. 
 
 The grade the pupil receives for mathematics is the sum of the various 
 words checked, after it has been multiplied by the factor of accuracy obtained 
 in the last question; and similarly for English and history. Since this grade 
 is made up of a considerable number of grades, whose reliability is given above, 
 the reliability of the grade, before multiplication by the factor of accuracy, 
 is appreciably greater than the reliability of the grading of each of the words, 
 and is probably not less than .96 for mathematics and history, and not less than 
 .92 for English. 
 
 As given in the next section, the reliability of the factor of accuracy is 
 about .95, so that the reliability of the grade for the question is close to .91 
 for mathematics and history and in the neighborhood of .87 for English. 
 
 Question 10 — Factor of Accuracy. 
 
 To determine the accuracy of the pupil's estimate of his knowledge, he is 
 asked to define 13 of the words upon which he has previously expressed a judg- 
 ment as to his familiarity with them. His definitions of these 13 words are 
 graded 1, 2, 3, or 4. The sum of these grades gives a quantitative statement 
 of the extent of the pupil's knowledge of the 13 words. This sum, which may 
 be called the measure of the pupil's actual knowledge, divided by his claim, 
 gives the factor of accuracy sought. In adding up the marks which constitute 
 the pupil's own claim, it will be noticed that not infrequently the pupil has 
 erased or marked over his previous marking, giving himself a lower mark in the 
 second case. In all such cases the first grade put down by the pupil is the grade 
 used. A magnifying glass may be of assistance, though it is seldom needed, 
 the pupil making the correction probably not because he wishes to be dis- 
 honest, but because he realizes that he has over-estimated his knowledge and 
 wishes to be honest and straighten it out. 
 
 The reliability of this factor of accuracy is undoubtedly high, and is esti- 
 mated at .95. 
 
 Two Kinds of Reliability Coefficients 
 
 The reliability coefficients given, mean simply that the gradings of the 
 questions as determined by the grader with the help of the tables formulated 
 by the various judges, would probably correlate with the gradings determined 
 by a second grader with the help of tables drawn up by a second set of judges, 
 to the extent indicated. They do not mean that the gradings of the prefer- 
 ences of the pupils would correlate with similar gradings derived from different 
 but similar data, to the extent indicated. The extent of this latter correla- 
 tion can be determined for those questions that are not exhaustive, i. e., those 
 for which a second similar test is possible. The vocabulary and the factor 
 of accuracy questions fulfill these conditions. For the vocabulary test it 
 would only be necessary to devise a second fist of words, as similar as possible 
 to the words in this list, have their significance evaluated by the same number 
 of qualified judges as here used and have a second person grade them, using 
 the guides of the judges. The correlation between the grades of the pupils in 
 this second vocabulary test and their grades in the test here given, gives the 
 reliability coefficient of the grading as a measure of the trait in question, based 
 upon such a limited sampling as that here used. 
 
 Another method is to treat the halves of the present test as separate vocab- 
 ulary tests and calculate the correlation between them. This latter method 
 has been used for the history grading, giving a correlation of .620, derived 
 from a sample of 36 pupils. The English and mathematics data are not so 
 
54 Educational Guidance 
 
 extensive, so that the correlation in those cases would be somewhat smaller. 
 Since the correlation between the gradings of the halves of the history words 
 equals .620, the extent to which the two halves combined, or the whole test, 
 
 TIT 
 
 would correlate with a similar test, is given by the usual formula — • 
 
 l + (n — l)r 
 This value equals .765, which is the reliability coefficient of the data as a 
 measure of the pupil's vocabulary of historical words (this is, of course, before 
 multiplication by the factor of accuracy). 
 
 Dividing the words used in determining the factor of accuracy, into two 
 parts, one part consisting of words a, b, c, d, e, m and the other part of the 
 balance, and proceeding in a similar manner, it is found that the reliability of 
 the obtained factor of accuracy equals .453. The smallness of this reliability 
 coefficient shows the limitation of the vocabulary test used, while the fact that 
 the present test is significant, as will be shown later, demonstrates that a more 
 accurate determination of the factor of accuracy would result in a vocabulary 
 
 test of greater and very substantial value. Using the formula - — ; — 
 
 l-\-(n — l)r 
 the reliability of a test, based upon any given number of words, may be ob- 
 tained, and for certain numbers it is as follows: 
 
 Question similar to No. 9, except In which case the coefficient of 
 
 that number of words = reliability = 
 
 124 .867 
 
 186 .907 
 
 76 .80 
 
 Question similar to No. 10, except 
 that number of words = 
 
 26 .624 
 
 39 .713 
 
 52 .768 
 
 24 .60 
 
 37 .70 
 
 63 .80 
 
 It is apparent from these data that the determination of the factor of accu- 
 racy should be based upon about three times as many words as have been 
 used, to make its reliability about the same as the grading of the history 
 words. 
 
Special Tests and Their Significance 55 
 
 Grade for Entire Interest Test 
 
 Mathematics: 
 
 The combination of the mathematics grades for the various 
 questions into a single grade for the test, designated as M„ is 
 as follows : 
 
 M i = 2(.2M Spt8 +.05M Ent8 +.4Mv OC3 +1.0F of A+.08M wds ). 
 
 The factor 2 is introduced to secure a better distribution. 
 M Sp ts = grade of the sports for their mathematical significance, 
 and similarly for other designations. 1 
 
 English : 
 
 The single grade of the test for English is as follows : 
 
 E i = .2E 8 ptB+.05E Enta +.4EvocB-5.0Fof A+.OSEwd.+S.SEM.p, 
 + .165E Bk3 . 
 
 History : 
 
 The single grade of the test for history is as follows : 
 
 H i = .2Hspt3+.05H Ent8 +.4Hvocs-2.0F of A + .08H Wd8 +3.3H Mag8 
 + .165H Bks . 
 
 Sample grading of the interest test: 
 
 The occasions for the exercise of judgment in this test are so few that a very 
 few illustrations will suffice to make the method clear. To avoid decimals in 
 the samples that follow, 5 times the measures contributing to Mi and 10 times 
 those contributing to E> and Hi are calculated. 
 
 J See Appx., pp. 101-103. 
 
56 
 
 Educational Guidance 
 
 Name (Pupil No. 90). 
 
 Magazines Checked in Question I 
 
 Date. 
 
 X American 
 
 X Atlantic Monthly 
 
 X Blue Book 
 
 X Bookman 
 
 D Century (4) 
 
 X ColHer's Weekly 
 
 X Cosmopolitan 
 
 X Country Life in America 
 
 C Craftsman (6) 
 
 X Current Literature 
 
 X Delineator 
 
 X Electrical World 
 
 X Etude 
 
 X Everybody's 
 
 X Good Housekeeping 
 
 X Green Book 
 
 X Hampton's 
 
 X Harper's Weekly 
 
 X Harper's Monthly 
 
 X L'illustration 
 
 X International Studio 
 
 X Ladies' Home Journal 
 
 X Leslie's Weekly 
 
 X Life 
 
 X Lippincott's 
 
 X Literary Digest 
 
 X McClure's 
 
 X Metropolitan 
 
 X Modern Priscilla 
 
 X Munsey's 
 
 A National Geographic (10) 
 
 (See question 2) 
 
 X Outing 
 
 X Pictorial Review 
 
 E Popular Mechanics (2) 
 
 X Popular Science Monthly 
 
 X Puck 
 
 X Red Book 
 
 X Review of Reviews 
 
 B St. Nicholas (8) 
 
 X Saturday Evening Post 
 
 X Science 
 
 X Scientific American 
 
 X Scribner's 
 
 X Smart Set 
 
 X Strand 
 
 X Technical World 
 
 X Woman's Home Companion 
 
 X World's Work 
 
 X Youth's Companion 
 
 X Outlook 
 
 Grade op 
 
 Same for 
 
 M E H 
 
 Factor Con- 
 tributing 
 to Total 
 Grade 
 
 Frequency (75) 
 
 Average grade 
 
 33 times average grade 
 
 5 
 
 10 
 
 8 
 
 28 
 4 
 4 
 5 
 
 30 
 9 
 3 
 3 
 3 
 5 
 4 
 
 4 
 4 
 6 
 4 
 3 
 4 
 4 
 3 
 5 
 7 
 5 
 1 
 3 
 1 
 
 50 
 
 3 
 2 
 
 4 
 2 
 2 
 
 5 
 48 
 4 
 3 
 3 
 7 
 3 
 2 
 2 
 4 
 5 
 5 
 7 
 
 336 
 4.5 
 
 5 
 4 
 
 2 
 
 16 
 7 
 2 
 1 
 6 
 4 
 
 1 
 2 
 5 
 2 
 
 5 
 6 
 3 
 7 
 2 
 1 
 7 
 1 
 2 
 7 
 4 
 
 
 1 
 
 90 
 
 1 
 
 2 
 1 
 1 
 
 
 Mi Ei Hi 
 
 246 
 3.3 
 
 149 109 
 
Special Tests and Their Significance 
 
 57 
 
 Answer to question 2: 
 
 "The National Geographic Magazine is interesting because 
 it tells so many interesting things of people we know very 
 little, and of places none of us have seen.'' 
 
 No warrant is found in this answer for altering the grade 
 assigned to the National Geographic Magazine 
 
 Answer to question 3 : 
 
 1. Spenser's — Faerie Queene (3) 6.3 -2.4 
 
 2. Scott's— The Abbot (2) 2.4 2.4 
 
 3. Poe's— Fall of the House of Usher (1) 1 . 2 - . 8 
 
 Frequency . . . 
 Average grade . 
 
 (6) 
 
 1.65 times average grade 
 
 Answer to question 4: 
 
 "In a long walk through the woods.". 
 Answer to question 5 : 
 
 "Reading." 
 
 Answer to question 6 : 
 
 "Number 4" 
 
 Frequency (3) 
 
 Average grade 
 
 2 times average grade 
 
 Answer to question 7: 
 
 "A" Grand Opera 
 
 .5 times the grade 
 
 Answer to question 8 : 
 
 1st choice: "Landscape Architect (2) 
 
 2d " "Designing." 
 
 Frequency 
 
 Average grade 
 
 4 times average grade , 
 
 (3) 
 
 4 
 1.3 
 
 19 
 6.3 
 
 9.9 
 1.67 
 
 11 
 3.7 
 
 ■ .8 
 .13 
 
 11 
 
 3.7 
 
 17 
 
 5.7 
 
 25 
 
 19 
 
 23 
 
 Answer to question 9: 
 Pupil's 
 mark 
 
 Word 
 
 simile 
 
 primary election 
 
 Mason and Dixon's line . 
 
 creed 
 
 Acropolis 
 
 rip saw 
 
 hydrogen 
 
 compound interest 
 
 cube root 
 
 paradox 
 
 Saracens , 
 
 I. W. W 
 
 Whigs 
 
 theosophy 
 
 toga 
 
 block plane 
 
 NaCl 
 
 fissure 
 
 
 
 15 
 
 
 
 
 
 27 
 
 
 
 
 6 
 
 6 
 
 
 
 
 9 
 
 27 
 
 
 
 18 
 
 
 
 
 
 24 
 
 6 
 
 6 
 9 
 6 
 
 30 
 
 6 
 
 27 
 
 3 
 
 27 
 
 3 
 
 
 
58 
 
 Educational Guidance 
 
 Pupil's 
 mark 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 1 
 
 3 
 
 3 
 
 2 
 
 3 
 
 3 
 
 3 
 
 3 
 
 
 
 3 
 
 3 
 
 3 
 
 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 
 
 3 
 
 3 
 
 2 
 
 3 
 
 
 
 2 
 
 3 
 
 3 
 
 3 
 
 3 
 
 3 
 
 Word 
 
 equation 
 
 guillotine 
 
 prose 
 
 syndicalism 
 
 H 2 
 
 transubstantiation 
 
 gladiator 
 
 debit 
 
 gravity cell 
 
 strata 
 
 improper fraction 
 
 lever 
 
 ragtime 
 
 physical valuation of R.R 
 
 score (in music) 
 
 commercial fertilizer 
 
 Magna Charta 
 
 voucher 
 
 ohm 
 
 string halt 
 
 fourth dimension 
 
 piston rod 
 
 Pythagorean proposition 
 
 single tax 
 
 stamen 
 
 hemstitch 
 
 Spanish Armada 
 
 statute of limitations 
 
 coherer 
 
 vertebrate 
 
 parallelogram , 
 
 omelette 
 
 Reichstag 
 
 Commerce Court 
 
 states' rights 
 
 space bar 
 
 giblets 
 
 Australian ballot 
 
 mollusk 
 
 perspective 
 
 tireless cooker 
 
 mortgagee 
 
 referendum 
 
 Formosa 
 
 Total 
 
 F. of A. (obtained in next question) 
 
 .57Xtotal 
 
 .8 times the grade 
 
 21 
 
 9 
 15 
 
 27 
 
 15 
 
 15 
 
 6 
 6 
 
 9 
 
 15 
 
 3 
 
 9 
 
 3 
 
 3 
 12 
 
 9 
 
 6 
 
 30 
 3 
 
 21 
 
 
 18 
 
 
 6 
 
 30 
 15 
 
 18 
 
 
 18 
 24 
 
 3 
 
 3 
 
 3 
 
 6 
 
 
 3 
 15 
 12 
 
 144 
 
 96 
 
 426 
 
 82 
 
 55 
 
 243 
 
 66 44 194 
 
Special Tests and Their Significance 
 
 59 
 
 Answer to question 10: 
 
 Definitions of terms: 
 
 a. simile 
 
 b. cube root "When a number is multiplied 
 
 by itself three times." 
 
 c. improper fraction 
 
 d. rag-time — "music that is used in songs 
 
 and vaudeville." 
 
 e. physical valuation of railroads 
 
 f. commercial fertilizer — "Fertilizer that 
 
 is used in a commercial way." 
 
 ohm 
 
 g 
 
 h. Pythagorean proposition 
 
 single tax 
 
 j. hemstitch — "In sewing when threads 
 are drawn out and then 4 or more 
 
 drawn together in the centre." 
 
 k. vertebrate — "The small parts that 
 
 make up the back bone." 
 
 1. parallelogram — "A figure where oppo- 
 site sides are parallel." 
 
 m. omelette — " A dish made from eggs 
 
 Sum 27 
 
 Factor of accuracy 15,5 = . 57 
 
 27 
 
 Grade given 
 by 
 
 pupil 
 
 
 3 
 1 
 
 3 
 2 
 
 3 
 
 
 3 
 
 10X.57. 
 -50X.57. 
 -20X.57. 
 
 Mi+mean (mean in question = 16) 
 Ei+mean( " " " =15) 
 
 Hi+mean ( " " " =22) 
 
 or Mi =4 
 Ei=5 
 Hi = 10 
 
 grader 
 
 
 2 
 1 
 
 2 
 
 
 
 
 
 
 
 3 
 2.5 
 
 15.5 
 
 -29 
 
 100 
 20 
 
 197 
 
 20 
 
 -11 
 
 324 
 
 32 
 
60 
 
 Educational Guidance 
 
 In the following sample only the detailed grading is given where the judgment 
 of the grader is involved : 
 
 Name (Pupil No. 14). 
 
 Date. 
 
 Question 1. 
 
 Combination of all the magazines, except 
 
 that one marked "A." (56) 
 
 A, Life (See question 2) (10) 
 
 66 
 
 Grade of 
 
 Same for 
 
 Factor Con- 
 tributing 
 to Total 
 Grade 
 
 M 
 
 E 
 
 160 
 30 
 
 190 
 2.9 
 
 H 
 
 113 
 1.7 
 
 Average grade 
 
 33 Xaverage grade 
 
 Question 2. 
 
 "I enjoy it because it is humorous and has some very in- 
 teresting comments on the important things which are at- 
 tracting attention." 
 
 The interest here shown in current events warrants the in- 
 crease in the history grading of Life, so, for this individual, 
 the magazine is graded 3 for history instead of 1. 
 
 Questions 3-9. 
 Sum of the grades for questions 3 to 9 inclusive 
 
 Mi Ei Hi 
 
 96 
 
 59 39 
 
 56 
 
 135 
 
Special Tests and Their Significance 
 
 61 
 
 Question 10: 
 
 Terms and definitions of same 
 
 a. simile "A simile is a certain kind of a 
 
 sentence." 
 
 b. cube root — "I can't explain." 
 
 c. improper fraction — "is a fraction which 
 
 is not proper." 
 
 d. ragtime — "A form of music with no 
 
 special time." 
 
 e . physical valuation of railroads — ' 'Know 
 
 nothing about it." . 
 
 f. commercial fertilizer — "Know nothing 
 
 about it." 
 
 g. ohm — "Can't explain." 
 
 h. Pythagorean proposition 
 
 i. single tax — " A tax on your personal be- 
 longings." . 
 
 j. hemstitch — "A certain kind of stitch. 
 
 Can't explain." 
 
 k. vertebrate — "Know nothing about it." 
 1. parallelogram — ''A figure. I can't ex- 
 plain." 
 
 m. omelette — "Can't explain." 
 
 Factor of accuracy = .66 
 
 10X.66 
 
 -50X.66. . 
 
 -20X.66 
 
 Grade for 
 
 same given 
 
 by 
 
 Pupil 
 
 1 
 2 
 
 2 
 
 3 
 
 
 
 1 
 1 
 1 
 
 16 
 
 Mi+mean (mean in question = 18) = 
 Ei -[-mean (mean in question = 17) = 
 Hi -{-mean (mean in question = 26) = 
 
 or Mi= —5 
 
 Ei=-7 
 Hi = -8 
 
 Grader 
 
 1.5 
 1 
 
 1.5 
 
 1.5 
 
 
 
 
 1 
 1 
 
 10.5 
 
 -33 
 
 66 
 13 
 
 102 
 
 10 
 
 -15 
 
 176 
 
 18 
 
62 
 
 Educational Guidance 
 
 The following sample covers determination of the factor of accuracy only: 
 
 Name (Pupil No. 158). 
 
 Date 
 
 a. simile — "A comparison." 
 
 b. cube root — "A quantity multiplied by itself then into 
 
 the product produces a certain cube." 
 
 c. improper fraction — "A fraction whose numerator is 
 
 larger than its denominator." 
 
 d. ragtime 
 
 e. physical valuation of railroads — "Actual value of 
 
 material and construction." 
 
 f . commercial fertilizer 
 
 g. ohm — "A certain degree to which magnets are wound." 
 h. Pythagorean proposition — "Proposition discovered 
 
 by Pythagoras regarding squares over the sides of 
 rectangular triangle." 
 
 i. single tax — "Tax on land only." 
 
 j. hemstitch — "An open kind of stitch used in sewing." 
 
 k. vertebrate — "An animal having a skeleton." 
 
 1. parallelogram — "A figure having two pairs of parallel 
 
 sides." 
 
 m. omelette — " A preparation made with milk and eggs." 
 
 Factor of accuracy = 33/32 = 1 .03 
 
 Grade fob Same 
 Given by 
 
 Pupil 
 3 
 
 Grader 
 3 
 
 2 
 
 3 
 
 1 
 3 
 
 3 
 1 
 
 3 
 
 3 
 
 3 
 
 
 2 
 
 3 
 2 
 3 
 3 
 
 3 
 3 
 3 
 3 
 
 3 
 3 
 
 3 
 3 
 
 32 
 
 33 
 
 The grading of this interest test is not as long or difficult a 
 task as it might at first seem. It can be greatly expedited by 
 grading one question at a time after having memorized the table 
 pertaining to that question, except the table for books, which it is 
 impracticable to attempt to memorize. The use which is made 
 of the interest test grades as well as the grades of the other tests, 
 is given in the following section. 
 
 Combination of Grades of Various Tests for Purposes 
 
 of Prognosis 
 
 Taking the grading of all the tests, there are six measures for 
 each individual as follows: M t , mathematics test, which is 
 either the algebra or the geometry test; E t , English test; H t , 
 history test; Mi, Mathematics interest test; E,, English interest 
 test; and Hi, history interest test. Not only do the gradings of 
 each of these tests have significance in connection with the sub- 
 ject for which they are specifically graded, but they also have 
 some significance for other courses. In other words, the most 
 probable first-year grade in English may be said to be a function 
 
Special Tests and Their Significance 63 
 
 of M t , E t , H t , Mi, Ei, Hi. The regression equation, expressing 
 E as a function of these six variables, might be calculated, but 
 the labor would be very great, and therefore a slightly different 
 method has been used, probably with little loss in the degree of 
 correlation. The regression equation expressing E as a function 
 of M t , E t , and H t , is calculated, and this particular function is 
 called E ct (meaning the measure that represents that combina- 
 tion of the tests M t , E t and H t , which correlates the most highly 
 with English). A second regression equation expressing E as a 
 function of Mi, E 4 and Hj, is also calculated and designated as 
 E ci (meaning the measure which represents that combination of 
 the interest tests Mi, Ei and Hi, which correlates most highly 
 with English). Finally a regression equation is calculated ex- 
 pressing E as a function of E ct and E c i, and this function is 
 designated as E c (meaning the measure which represents that 
 combination of E ct and E ci which correlates the most highly 
 with English). So far as English is concerned, the entire object 
 of the tests has been the derivation of this measure, E c ; and the 
 correlation between E and E c establishes the extent to which 
 grades in the tests given serve as a basis for the prognosis of 
 ability in high school English. The same procedure is followed 
 with reference to mathematics and history, leading to measures 
 M c and H c . The following sections will be devoted to explaining 
 the derivation of M ot , E ct , H ct , M C1 , E ci , H ci , M c , E c and H c , in 
 the order named. 
 
 M ct — Combination of Tests with Reference to (a) Algebra 
 and (6) Geometry 
 
 (a) Algebra: In order that it may not be lost sight of, it is 
 repeated here that all of the measures mentioned in the last 
 section are measures that are expressed as deviations from the 
 means of the groups to which the measures belong. For one 
 duplicating this test, the means given on page 68 may be assumed, 
 or better, they may be calculated anew for the group tested. 
 
 The combination A ct , of A t , E t , H t , which correlates the 
 highest with A is as follows: 1 
 
 A ct = .6A t +.4E t +.llH t 
 
 This equation is self explanatory. To obtain A ct it is only 
 1 See Appx., p. 99. 
 
64 Educational Guidance 
 
 necessary to add .6 of A t , .4 of E t and .11 of H t , paying proper 
 attention to sign. The correlation between A and A ct equals .48. 
 The apparent weighting of the three tests, .6, .4, .11 is not the 
 exact weighting of the tests, for the standard deviations affect 
 these regression coefficients. Since the standard deviation of 
 H t is large the weighting is somewhat greater than .11. The 
 weighting seems very reasonable, bearing in mind that H t is 
 not as reliable a measure as E t as it has but a single measure 
 entering into it, whereas E t is an average of three. 
 
 (b) Geometry: The regression equation for geometry is: 
 
 G ct = .8G t +.08E t +.184H t 
 
 The correlation between G and G ct equals .43. The small 
 weighting of E t is somewhat of a surprise. It must be assumed 
 that some of the elements entering into the grading E t are more 
 directly related to algebra than to geometry. 
 
 The measures A ct and G ct are entered in the same correla- 
 tion tables and designated as M ct , for purposes of determining 
 the relative weighting of mathematics, English and history tests. 1 
 
 E ct — Combination of Tests with Reference to English 
 
 That combination of M t , E t , H t which proved the most feasible 
 is: 2 
 
 E ct =!(M t +E t +H t ). 
 
 The correlation between E and E ct equals .46. The weighting 
 here used yields a correlation practically as high as that given 
 by the regression equation but this is not an accurately deter- 
 mined regression equation and it is impossible to use it for deter- 
 mining the relative importance of the factors M t , E t and H t with 
 reference to E. It may, however, be said that they do not differ 
 greatly in their relative bearing upon E. 
 
 H ct — Combination of Tests with Reference to History 
 
 The combination for history is the same as that for English : 3 
 H rt =!(M t +E t +H t ) 
 
 1 See Appx., pp. 99, 105. 
 * See Appx., p. 100. 
 3 See Appx., p. 100. 
 
Special Tests and Their Significance 65 
 
 No accurate analysis of the importance of the factors M t , E t and 
 H t with reference to their bearing upon history is possible from 
 this datum. 
 
 M c , — Combination of the Interest Tests with Reference to 
 Mathematics 
 
 The regression equation giving that combination of Mj, Ej 
 and Hj which correlates the highest with M is: 
 
 M ci = .5M i +.65E i -.2H i 
 
 The correlation between M and M ci equals .30. The mathe- 
 matics interest test is weighted the most heavily in this equation 
 in spite of the fact that the coefficient of E L is the largest. This 
 comes about from the fact that the standard deviation of Ej is 
 considerably smaller than that of M,. The actual weighting 
 of the different elements is approximately in the ratio of 224: 
 183: — 95. The occasion of the negative weighting of the history 
 interest test may be determined from the raw data for the calcu- 
 lation of the regression equation given in the Appendix. 1 In 
 brief it is due to the low correlation between M and Hj, .15, 
 and the high correlations between M 4 and Hj, .54, and between 
 E, and Hi, .63. Why the first of these three correlations is low 
 and the second and third high is not apparent — an accurate 
 calculation of the regression equation involving the parts of the 
 interest test would reveal the cause, but it would be a very labo- 
 rious task. 
 
 E c i — Combination of the Interest Tests with Reference to English 
 
 The regression equation giving that combination of Mj, Ei, 
 and Hi which correlates the highest with E was found to have 
 only a trifling advantage over the use of E 4 alone. 2 
 Therefore the relation used is: 
 
 E ci = Ei 
 
 The correlation between E and E^ equals .46. 
 
 1 See Appx., pp. 103-104. 
 
 2 See Appx., p. 104. 
 
66 Educational Guidance 
 
 H ci — Combination of Interest Tests with Reference to History 
 
 The regression equation giving that combination of M i; Ej, 
 and Hj which correlates the highest with history is : 1 
 
 H ci =-.5M i +.38E i +.7H i 
 
 The correlation between H and H c i equals .33. The negative 
 weighting of H; in its bearing upon mathematics is comparable 
 to the negative weighting here, of Mj in its bearing upon history. 
 The data for definitely determining the cause of this latter, as 
 well as the former, are lacking. 
 
 M c — Combination of M ci and M ct with Reference to Mathematics 
 
 The regression equation giving that combination of M ci and 
 M ct which correlates the highest with mathematics is : 2 
 
 M c = .66M ci + 1.00M ct 
 
 The correlation between M and M c differs somewhat for the 
 pupils taking geometry from that for the algebra pupils. The 
 correlations are: rqQ =.44, r^ =.49. These correlations are 
 not as high as could be desired, nor as high as the correlation 
 between grammar grade mathematics and first year mathematics, 
 which is .58. However, r^ is only .09 less than ?"f m (7, 6, 5. 4 M )> 
 and when it is considered that the former is a correlation based 
 upon tests of a few hours duration while the latter is based upon 
 the work of four years, it is a very satisfactory showing and is of 
 positive value for purposes of prognosis and classification. 
 
 Lacking information as to the pupil's past performance, classi- 
 fication, at present, usually depends upon such things as the 
 pupil's, ^or teacher's, preference as to the hour when the subject 
 is to be taken, or upon the first letter of his last name, or some 
 other equally irrelevant point. It is earnestly hoped that tests 
 will be devised enabling a very accurate prognosis, but, pending 
 such tests, there is nothing to lose and everything to gain by the 
 use of the tests here given, whose significance has been accurately 
 evaluated upon the basis of the performance of some 235 pupils. 
 A summarized statement of the procedure in using the test data 
 is given on page 68. 
 
 1 See Appx., pp. 104-105. 
 
 2 See Appx., p. 105. 
 
Special Tests and Their Significance 67 
 
 E c — Combination of E ci and E ct with Reference to English 
 
 E ci and E et have equal significance in determining the most 
 probable standing in English. The regression equation is: 
 
 E c = E C i+E ct 
 
 The correlation between E and E c is equal to .55. This correla- 
 tion is higher than the correlation just above, for mathematics, 
 though considerabley less than r FE ( 7i6i5t4E ), which equals .71. 
 It is interesting to note that whether dealing with grammar 
 school grades or with special tests it is possible to give a closer 
 estimate of a pupil's performance in English than it is in mathe- 
 matics. The greater difference between the natures of algebra 
 and arithmetic, than between high school English and elementary 
 school English, is probably a contributing cause in the case of 
 these special tests as well as in the case of elementary school 
 records. 
 
 H c — Combination of H c j and H ct with Reference to History 
 
 The regression equation giving the best combination of H ci 
 and H ct with reference to history is: 
 
 H c = .4H ci +H ct 
 
 The correlation between H and H c equals .49. The apparent 
 unimportance of H ci in comparison with H ct exists only in part, 
 as the standard deviation of H ci is much larger than that of H ct . 
 The actual relative weighting of H c ; and H ct is approximately 
 in the ratio of 22:39. 
 
 Use of Regression Equations 
 
 Substitution of the test grades in the regression equations is 
 required in order to use them for purposes of estimation of prob- 
 able high school standing in the subjects, algebra, geometry, 
 English and history. After having given and graded the tests 
 for the pupil whom it is desired to examine the grades are sub- 
 stituted in the equation giving A c , for purposes of estimation of 
 his probable standing in freshman algebra, in the equation giving 
 E c , for estimation of his probable English standing, etc. The 
 necessary equations are here summarized: 
 
68 
 
 Educational Guidance 
 
 M c = A c orG c . 
 
 A c = .66M ci +M ct = .33M i +.44E i -.132H i +.6A t +.4E t +.llH t . 
 
 G c = .66M ci + M ct = .33Mi + .44 Ej - .132 Hi + .8G t + .08E t 
 + .184H t . 
 
 E c = E ci +E ct = E i +|(M t +E t +H t ). 
 
 H c = .4H ci +H ct =-.2M i +.15E i +.28H i +KM t +E t +H t ). 
 
 M ci = A ci or G ci = .5M i +.65E i -.2H i . 
 
 E ci = Ej. 
 
 H ci =-.5M i +.38E i +.7H i 
 
 M ct = A ct or Get. 
 
 A ct = .6At+.4Et+.llH t . 
 
 G ct = .8G t +.08E t +.184Ht. 
 
 Eet = KM t +E t +H t ). 
 
 H c t = E ct . 
 
 Mi = A i0 r G i = i(2M Spt3 +.5M Ent8 -f-4Mvo C8 +10F of A+.8M Wd9 
 — mean) . 
 
 Ei = .l(2E Spt8 +.5E EntB +4E V oc3-50F of A + .8E wds +33E Mag8 
 + 1 .65 E B k 3 — mean) . 
 
 H i = .l(2H Spta +.5H Ellt8 +4Hvocs-20F of A + 8E wda +33E M a g8 
 + 1.65 EBks — mean) . 
 
 M t = A t or G t . 
 
 A t = ^(Sum of grades of all the problems — mean) . 
 
 G t = |(Sum of grades of problems 1, 7, 8, 9, 10 — mean). 
 
 E t = f(E a +E v +W-mean). 
 
 H t = 2(H a — mean). 
 
 To obtain any of the last eight grades subtract the mean from 
 the pupil's gross mark and divide the remainder by the divisor 
 given in the equations and repeated in the following table of 
 means and divisors. 
 
 
 Math. 
 
 Eng. 
 
 Hist. 
 
 Math. 
 
 Eng. 
 
 Hist. 
 
 
 TESTMt 
 
 TESTEt 
 
 TESTHt 
 
 Int. Mi 
 
 Int. Ei 
 
 Int. Hi 
 
 Group and 
 Class 
 
 3 
 
 go 
 
 00 
 
 GO 
 
 m 
 
 no 
 
 m 
 
 a 
 
 £ 
 
 § 
 
 OS 
 
 t-l 
 
 00 
 
 S3 
 
 S 
 
 
 o3 
 
 GO 
 
 c3 
 
 GO 
 
 o3 
 
 GO 
 
 a 
 
 GO 
 
 03 
 
 00 
 
 03 
 
 E° 
 
 
 0> 
 
 > 
 
 <u 
 
 > 
 
 0> 
 
 !> 
 
 0J 
 
 > 
 
 <u 
 
 > 
 
 0> 
 
 > 
 
 
 § 
 
 
 
 S 
 
 P 
 
 § 
 
 Q 
 
 £ 
 
 P 
 
 2 
 
 p 
 
 2 
 
 P 
 
 1 Beginning 2d 
 
 
 
 
 
 
 
 
 
 
 
 
 
 year 
 
 Gt25 
 
 3 
 
 18.5 
 
 3/2 
 
 7 
 
 1/2 
 
 95 
 
 5 
 
 170 
 
 10 
 
 260 
 
 10 
 
 2 Mid-year 1st 
 
 
 
 
 
 
 
 
 
 
 
 
 
 year 
 
 At89 
 
 5 
 
 16 
 
 3/2 
 
 6 
 
 1/2 
 
 80 
 
 5 
 
 150 
 
 10 
 
 220 
 
 10 
 
 3 Entering 1st 
 
 
 
 
 
 
 
 
 
 
 
 
 
 year 
 
 At72 
 
 5 
 
 15 
 
 3/2 
 
 6 
 
 1/2 
 
 65 
 
 5 
 
 160 
 
 10 
 
 200 
 
 10 
 
 4 Beginning 2d 
 
 
 
 
 
 
 
 
 
 
 
 
 
 year 
 
 Gt26 
 
 3 
 
 19 
 
 3/2 
 
 5.5 
 
 1/2 
 
 100 
 
 5 
 
 190 
 
 10 
 
 280 
 
 10 
 
 5 Entering 1st 
 
 
 
 
 
 
 
 
 
 
 
 
 
 year 
 
 At88 
 
 5 
 
 17.5 
 
 3/2 
 
 6.5 
 
 1/2 
 
 70 
 
 5 
 
 170 
 
 10 
 
 240 
 
 10 
 
Special Tests and Their Significance 
 
 69 
 
 If A represents the most probable algebra grade expressed as 
 a deviation from the mean, for some given numerical system of 
 
 marking it is related to A c as follows : A = r AA — A c = .49 — — A c 
 
 c <ta c 3.736 
 
 in which A c is given for each pupil by the tests and <ta is to be 
 determined for the school in question. If the grading is on a 
 percentile scale with a passing mark of 70, c A will be in the neigh- 
 borhood of 8. The following are the standard deviations of the 
 type <r Ac . 
 
 (T Ac = 3.736; c7 G(j = 4.066; <r Ec = 5.328; er Hc = 3.622. 
 
 If G, E, and H have similar meanings to A, their values are as 
 follows : 
 
 G = .44^-G c 
 4.066 
 
 E = .55-^-E c ; H = .49-^- 
 
 5.328 
 
 3.622 
 
 The calculation may be presented as follows: 
 
 Gross Grade of 
 Pupil Group 3 
 
 Alg. test 
 Eng. test 
 Hist, test 
 Math. int. test 
 Eng. int. test 
 Hist. int. test 
 
 71 
 
 22.5 
 9 
 
 68 
 153 
 141 
 
 
 Devia- 
 
 
 Means 
 
 tions from 
 
 Mean 
 
 Divisors 
 
 72 
 
 -1 
 
 5 
 
 15 
 
 7.5 
 
 3/2 
 
 6 
 
 3 
 
 1/2 
 
 65 
 
 3 
 
 5 
 
 160 
 
 -7 
 
 10 
 
 200 
 
 -59 
 
 10 
 
 Deviations 
 4- Divisors 
 
 = At or Mt 
 
 5=Et 
 
 6 = Ht 
 
 l=Ai or Mi 
 -l=Ei 
 -6 = Hi 
 
 Substitution of these values in equations M c , E c , H c gives 
 A c = 4, E c = 3, H c = 2. If these measures are divided by their 
 respective standard deviations (o-a c = 3.736, o- Ec = 5.328, o"h c = 
 3.622), the resulting measures, 1.070, .563, .552, express the 
 predicted standing in terms of the standard deviation. 
 
 The calculation carried through is typical, being in fact that of 
 pupil No. 157, and it is to be noted that the prediction is quite 
 selective, for the estimate for algebra, 1 .070, is one-half a standard 
 deviation larger than the prediction for English. The advan- 
 tage of such a differential prognosis over one of average ability 
 only is very evident, if classification of the pupil is the aim. 
 The extent to which the method performs this differential 
 diagnosis may be measured by taking the differences between 
 measures such as 1.070 and .563 and correlating them with the 
 actual differences in grades in mathematics and English courses, 
 
70 Educational Guidance 
 
 these latter likewise expressed in units of the standard deviations. 
 This correlation may be expressed by the symbol /"(m-exm -ej 
 
 and calculation gives its value to be .31. This correlation 
 is far from negligible and indicates the selective nature of 
 ability. It may be expected that further use of the same 
 method will lead to higher correlation and to very valuable tests 
 for purposes of differential diagnosis. 
 
 The scheme just given for evaluating the record of any one 
 pupil is a rather long process. It will be found that there is a 
 very great saving in time if the work is tabulated and the steps 
 performed one at a time upon the entire number of pupils' rec- 
 ords, rather than as in the example, where the steps were per- 
 formed consecutively and in toto for one pupil before going on to 
 the next pupil. 
 
 The time of giving and evaluating the tests can be further 
 shortened by omitting those parts not used in the final result. 
 In the geometry test the following problems may be omitted: 
 2, 3, 4, 5, 6. In the English and history tests omit the grading 
 for dramatization, and in the history test omit the grading for 
 valuation. It is, however, recommended that in the interest 
 test a larger number of words be used in determining the factor 
 of accuracy. 
 
 It will at times happen that test records for a given pupil are 
 incomplete, in which case a zero may be put in for the missing 
 record, without greatly lessening the significance of the measure. 
 It would be a little more reliable to estimate closely, from the 
 data at hand, the probable value of the missing record and enter 
 it, but there is danger that the estimate will be quite inaccurate, 
 in which case it is worse than no estimate at all. The assigning 
 of a zero grade is simply assigning the mean grade. 
 
SECTION 6.— USE OF ALL SOURCES OF DATA IN 
 ESTIMATING PROBABLE AVERAGE STANDING 
 
 Of the group of pupils whose elementary school records were 
 available 33 were entering first year of high school. All of the 
 following data were available with reference to these 33: (1) 
 average first-year grade, F A ; (2) elementary school grade (7, 6, 5, 
 4a); (3) teachers' estimates, Est A ; (4) special tests M c , E c , and 
 H c . The special tests are arbitrarily combined into a single 
 
 measure by averaging, 
 
 M c +E c +H c ^ 
 
 To determine the total bearing of these four sources of data 
 upon average first-year standing the regression equation com- 
 bining them with reference to it has been calculated from the 
 data in the accompanying table. 
 
 It is to be noticed that here F a ( 7 > 6, 5, 4 A ) Est A 
 
 rF A (7,6,5,4 A ) = .83>.789 (given (7,6,5,4 A ) .83 
 on p. 8), and that r F Est = 
 
 Est A .81 .68 
 
 T A .51 .56 .54 
 
 .81 > .76 =^ A v(I.a.,Cons.,Emo.i.,Exp.). 
 
 (Given on p. 16). These differences are probably entirely 
 accounted for by fluctuations due to sampling. The smaller 
 values are the more reliable, being based upon larger populations. 
 The regression equation is l 
 
 F A = .536 (7, 6, 5, 4 A ) + .481 Est A -.043T A . 
 
 The negative regression coefficient, — .043, is probably due to 
 fluctuations in sampling. The probable error of the partial 
 correlation coefficient entering into this regression coefficient is 
 .112, so that no great significance can be attached to its negative 
 value. 
 
 ^f [(7, 6, 5, 4 ),Est t ] = -89, with a probable error of .023. 
 
 This very high correlation is of interest in showing the great 
 stability of individual character. To know that a pupil's grades 
 
 ^ee Appx., p. 106. 
 
 71 
 
72 Educational Guidance 
 
 in the first year of the high school are so largely determined by 
 what he possesses within his own personality is convincing 
 evidence of the paramount importance of nature over and above 
 nurture. With the undoubtedly varying environments under 
 which these pupils lived there would be a greater divergence 
 between estimate and accomplishment if nurture were the major 
 factor. 
 
 There is a likelihood that the correlation of .89 is higher than 
 might be ordinarily expected from similar data, for, as noted, 
 the particular sample dealt with seems to show a slightly closer 
 relation than usual. This is true to the greatest extent in the 
 case of teachers' estimates, where it is likely that the teachers 
 who made the estimates were particularly well acquainted with 
 the pupils, for these pupils had been in the elementary depart- 
 ment of the same school for the preceding four years, and their 
 capacities for accomplishment were probably very well known. 
 The lack of absolute independence between teachers' estimates 
 and average class standing, noted on page 15, is a factor to be 
 borne in mind. 
 
 In case it is essential to obtain as close an estimate as possible 
 of a pupil's ability all three sources of data could profitably be 
 used, but for ordinary needs of classification one source should 
 be adequate. The method of combining the three measures into 
 a single measure is given in the Appendix, p. 106. 
 
SECTION 7.— THE AGE OF PUPILS AS A FACTOR 
 
 The number of factors involved in this study has been so 
 great that the age factor has been omitted. 
 
 The correlation between average class standing and age, using 
 all the data, is —.31. Eliminating the bearing of innate mental 
 capacity (or mental capacity as existing at one certain age) 
 would certainly give a positive partial correlation between age 
 and standing in a given grade. Though it is a fact that the aver- 
 age twelve-year-old first-year pupil has a higher average standing 
 than the average sixteen-year-old first-year pupil, it of course is 
 not true that the average twelve-year-old is brighter than the 
 average sixteen-year-old. 
 
 The occasion of the negative total correlation, —.31, is prob- 
 ably due to the fact that dull and over-age pupils are advanced 
 more rapidly than their talents warrant, thereby always keeping 
 them in a class which taxes their capacities and in which they 
 can secure only low marks. 
 
 Since there exists this negative correlation between age and 
 average standing in a given grade, the use as a measure of in- 
 telligence, of the age at which a pupil reaches a certain grade, 
 gives to the bright pupil but part of the credit due him. The 
 bright pupil is less advanced, and the dull pupil more advanced, 
 judged by the grade attended, than talent warrants. The 
 effect of this is to make the measure "age of attaining a certain 
 grade" less reliable as a measure of ability than it otherwise would 
 be. 
 
 73 
 
SECTION 8.— COMPARISON WITH OTHER STUDIES 
 
 The most fundamental distinction between this and the great 
 majority of correlation studies is that the aim of this study is 
 prognosis and not at all to establish the existence and magnitude 
 of some theoretical relationship. This fact has already been 
 referred to but is mentioned again as some important points of 
 method depend upon it. It will be noted that, in the following 
 paragraphs, where comparison with other investigations of 
 mental relationships is impossible, it is generally due to difference 
 in method, necessitated by this difference in purpose. 
 
 A number of investigations, notably several by Spearman and 
 his pupils, have as their object the determination of the abstract 
 relationship which exists between certain tests and mental 
 capacities. The aim is to establish the relationship that exists 
 after errors of sampling, observation, and the like have been 
 eliminated. The direct conclusions from such studies are of 
 necessity theoretical, whatever may be the indirect practical 
 implications resulting therefrom. Acting upon these implica- 
 tions educational practice might be altered, but it still would 
 remain to be seen if it were bettered thereby. 
 
 This is not a criticism of theoretical investigations for, by 
 suggesting relationships and methods, they have been the fore- 
 runners of progress; but it is for the purpose of pointing out the 
 difference in object and the consequent difference in method 
 between such investigations and the present one, which has as 
 its object the utilizing of measures obtainable under ordinary 
 class-room conditions, with whatever errors may be inevitable, 
 for whatever they actually demonstrate themselves to be worth 
 as evidence of the capacity it is desired to measure. 
 
 If one set of test measures correlates with class standing to a 
 certain extent, no amount of superimposed treatment for elimi- 
 nation of observational errors, chance errors, or the like can 
 change this raw relation which exists. Correction for atten- 
 uation would lessen the accuracy and vitiate the significance of 
 the use of marks as a prognosis of other "raw" marks. Knowing 
 the correlation between tests and average standing and wishing 
 74 
 
Comparison with Other Studies 75 
 
 to estimate the latter from the former, the most reasonable 
 prediction is that given by the regression equation. This is 
 exactly what the regression equation has been devised to give, 
 and ''correction" of the correlation coefficients in any way at all 
 would lead to less accurate estimation. For this reason, none 
 of the studies, the conclusions of which are based upon "cor- 
 rected" coefficients of correlation, are comparable with this work, 
 nor should the size of the coefficients of correlation here obtained 
 be compared to "corrected" coefficients. The latter are meant 
 to be a prophecy of what would be the correlation provided errors 
 of various kinds were absent, while the former state the relation 
 between existent measures. 
 
 The results of this study, however, do shed some light, and 
 give a method of attack, upon the problem of the existence, or 
 non-existence, of a single mental function which is paramount 
 in all intellectual activities. The statement of the view of those 
 holding to the idea of a single mental function has undergone 
 much development and elaboration, until it now seems to be 
 about as follows: — that every intellectual performance depends 
 not only upon a general factor, "but also in varying degrees upon 
 a factor specific to itself and of very similar performances." 1 
 
 How the most ardent advocate of the specific nature of ability 
 can object to such a statement, is hard to see. The problem 
 is no longer a qualitative but a quantitative one. It is now 
 necessary to measure intellectual performances and ascertain 
 what part of each is a common element and what part is unique. 
 The regression equation method, involving more than two vari- 
 ables, is beautifully adapted to solving this problem, and corre- 
 lation between differences in accomplishment, or capacity, gives 
 first-hand testimony as to the uniqueness or generality of mental 
 function. 
 
 Pupils in the elementary school demonstrate a unique ability 
 along the line of mathematics or English, by getting, relative to 
 their average accomplishment, higher or lower marks in these 
 subjects. That these marks do represent a unique ability and 
 are not due to chance and the vicissitudes of teachers' gradings, 
 is evidenced by the fact that different teachers, in the high 
 
 1 See B. Hart and C. Spearman, General Ability, Its Existence and Nature, 
 British Journal of Psychology, 1912. Also C. Spearman, Theory of Two 
 Factors, Psych. Rev., Vol. 21, No. 2. 
 
76 Educational Guidance 
 
 school, recognize the same relative superiority or inferiority in 
 the one subject, or other. The correlation r(p M . E )(7 t6tSt 4 M . E ) = .52, 
 with a probable error of .065. The size of the probable error 
 precludes the possibility of the correlation being due to chance. 
 The alternative is that intellectual function is specific, unless it 
 is argued that ability to secure grades is not solely an intellec- 
 tual function. 
 
 This might be maintained, but grades have been used by 
 proponents of the general factor theory as measures of intellect; 
 and, furthermore, if so fundamental a mental characteristic as 
 the ability to earn grades is not a fit capacity for consideration 
 in connection with the general factor theory, then the theory 
 must be of very limited scope in its application, and the traits of 
 importance for scholastic and business success will lie outside 
 its realm. The same conclusion may be drawn just as con- 
 vincingly from the correlation r(M-E)(Mc-Ec) == -31, for its pro- 
 bable error is only .040. 
 
 Another requirement of method is that the means used in the 
 study shall be capable of determination at the time of prognosis. 
 Studies which have dealt with the correlation between high school 
 and university marks, or between elementary school and high 
 school marks, have, without exception so far as the author is 
 aware, selected the group upon the basis of attendance in the 
 higher school, and then calculated the means in the lower school 
 of the group thus selected. It follows that the means used for 
 the lower school data are not capable of determination until the 
 selection has occurred upon the basis of attendance in the higher 
 school. Any elimination that takes place is entirely obscured 
 by the method, and the use of the correlation found, for purposes 
 of prediction, is not sound because it is not known from what 
 mean, deviations should be measured. 
 
 However, though theoretically justified this criticism is prob- 
 ably not of very great moment when dealing with elementary 
 school and first-year high school pupils. The evidence of this 
 study is that there is not a sufficient selection of the brighter 
 pupils in passing from the elementary school to the high school 
 to necessitate changing the elementary school mean of pupils 
 who attended high school from the mean of elementary school 
 pupils in general. It is quite possible that this would not be 
 
Comparison with Other Studies 77 
 
 true in schools where there is a greater elimination than in the 
 well-to-do schools from which these data are obtained. 
 
 The study of Dearborn 1 is excellent evidence that high school 
 efficiency is highly correlated with university proficiency, but 
 the method is not a serviceable one for a quantitative prognosis 
 problem; and the high school means in his distributions are 
 means of high school pupils who later attended college and are 
 therefore the means of a selected group. 
 
 The same remark may be made in regard to the means used 
 in the study by Miles 2 and it may be a material point in this 
 case, for the amount of elimination between the elementary 
 school and the fourth year of the high school is very much more 
 extensive, and probably also selective, than between the elemen- 
 tary school and the first year of the high school. Miles finds 
 that the correlation between the average elementary school 
 grade and the average high school grade is .71. This is quite in 
 harmony with the results of the present study and it is probable 
 that Miles' data, treated by the regression equation method, 
 would yield correlations between .80 and .90. 
 
 The fact that Miles deals with the average of all high school 
 grades results in higher, or lower, correlations than would be 
 obtained in dealing with first-year high school marks only, 
 dependent upon which of the two following factors is the stronger : 
 (1) In general, as the time between testing is increased the 
 correlation decreases; and as the second, third and fourth years 
 of the high school are more and more remote from the elementary 
 school in time, it might be expected that correlation between the 
 elementary school record and the first-year record would be 
 greater than that between the elementary school record and the 
 average of the entire high school record. (2) A factor tending 
 to offset this is the fact that the reliability of an average increases 
 as the number of grades entering into it increases, and, to the 
 extent that a grade represents native ability, the greater the 
 number of grades averaged the greater the reliability of this 
 measure. It is impossible to say, a priori, which of these factors 
 is the more important, but it is the author's opinion that the 
 
 *See Dearborn, W. F., Relative Standing of Pupils in the High School and 
 in the University, Wis. Univ. Bulletin, No. 312, 1909. 
 
 2 See Miles, W. R., Comparison of Elementary and High School Grades, 
 Univ. of la. Studies in Education, Vol. 1. No. 1. 
 
78 Educational Guidance 
 
 importance of the second factor has been, quite generally, under- 
 valued, and might easily be the more important of the two. 
 
 Another class of studies has been undertaken, especially in 
 England by investigators who have found the correlations be- 
 tween various tests and intellectual ability — the latter based 
 upon teachers' and headmasters' estimates. It is pertinent to 
 ask what relation there is between intellectual ability and the 
 ability to secure grades. 
 
 The regression equation giving the bearing of teachers' esti- 
 mates of intellectual ability, conscientiousness, emotional in- 
 terest, and oral expression, upon average class standing, weights 
 these factors in the ratio of 8:4:2:1, or, combining the first and 
 last and designating it as the intellectual factor, and combining 
 the second and third and designating it as the motive factor, or 
 factor of effort, it is seen that the weighting is in the ratio of 3 :2. 
 Since effort is so important a factor in accounting for the ability 
 to secure grades, it is apparent that the correlation between tests 
 and intellectual ability will be quite different from, and probably 
 higher than, the correlation between the same tests and class 
 standing. This is a common finding and in the study by Wyatt 1 
 it is possible to estimate the extent of this difference. 
 
 Wyatt finds that the average correlation between his tests 
 and intelligence, as determined by the headmaster's estimate, 
 averaged .63, and that the correlation, for a different group, 
 between the same tests and intelligence, as judged by class stand- 
 ing, averaged .51. As the headmaster did not grade upon both 
 intellectual ability and effort it is probable certain evidence of 
 excellent effort received credit as intellectual ability. Accord- 
 ingly it may be expected that the difference in correlation be- 
 tween Wyatt's tests and real intellectual ability, from that be- 
 tween his tests and class standing, is actually greater than the 
 .12 found. 
 
 Wyatt's tests apparently were given at about the same time 
 that the marks which determined class standing were earned, so 
 that his results are not comparable with the results of this study. 
 Also the age of pupils is different, but his results suggest that 
 certain of the tests used, especially the analogy and completion 
 tests, are highly indicative of average class standing, and tests 
 
 x See Wyatt, S., Quantitative Investigation of Higher Mental Processes, 
 Brit. Jour, of Psyc, Vol. VI, Pt. 1. 
 
Comparison with Other Studies 79 
 
 of this nature are worthy of investigation for purposes of esti- 
 mating average capacity, but it is doubtful if they have par- 
 ticular value for purposes of differential prognosis. In giving 
 such tests it is not to be expected that the care with which Wyatt 
 gave them will be duplicated under ordinary class conditions. 
 
 There are at least two classes of tests which are comparable 
 with the tests here given, so far as purpose is concerned. One 
 of these is entrance examinations. They perform their task, in 
 the main, by attempting to measure acquired knowledge, whereas 
 the tests here given, in the main, attempt to measure interest 
 and capacity. Both types of examinations have a function to 
 perform and the former should be supplemental to the latter in 
 the final determination of the classification of the pupil. Acquired 
 knowledge tests, of themselves and alone, are too likely to be 
 evidence of the degree of success which has attended a cramming 
 process, and not very definitely evidence of ability, which is the 
 more important consideration. The following correlations, 
 given by Thorndike, 1 show a progressive decrease in correlation 
 between the median entrance examination grade and the average 
 grade in the different years of the college course; freshman year 
 .62, sophomore year .50, junior year .47, senior year .25. In- 
 tellectual capacity could hardly have changed much, relatively 
 from pupil to pupil, during the four years of the college course. 
 These correlations seem to indicate that the capacity measured 
 by the entrance examination was, in the main, acquired knowl- 
 edge and not intellectual ability, otherwise, why the decrease 
 from year to year? 
 
 For purposes of immediate differential diagnosis tests of ac- 
 quired knowledge undoubtedly perform an important function, 
 but for the broader problems of vocational guidance and the 
 selection of general courses of study they have very limited 
 scope. 
 
 The second class, tests of the Binet type, have classification 
 as their object, and in this respect are comparable to the tests 
 here given. Thus far, however, they have not shed much light 
 upon the points of relative strength or weakness of the individual 
 tested. If mental deficiency is not general, but selective, an 
 individual being normal in one capacity and quite defective in 
 
 »See Thorndike, E. L., in Science, N. S., Vol. XXIII, p. 839. 
 
80 Educational Guidance 
 
 a second, then a mass test of mental age gives no light upon the 
 distinctive feature which it is desirable to be acquainted with. 
 There is plenty of evidence to indicate that deficiency is selective 
 in many cases and the defect of the Binet tests on this point 
 should be remedied. However, there is sufficient correlation 
 between defects to make a Binet test of considerable value for 
 purposes of classification; just what value has never been deter- 
 mined, so far as the author is aware, in quantitative terms, i.e., 
 in terms of the correlation between capacity, as estimated from 
 the test, and capacity as determined by as complete and con- 
 clusive measurements as possible. It is essential that mental 
 age tests be tested by such methods, in order to judge which are 
 the more accurate and what their accuracy is. 
 
 The use of tests of this nature as a guide to classification may 
 be illustrated by the work of Adler, in New York School 77. 1 
 Boys in the first and fourth grades were tested with Dr. Goddard's 
 1911 revision of the Binet tests, with additions from the tests 
 of Terman, Whipple and Courtis. In both the first and fourth 
 grades the 35 pupils, out of about twice that number, who 
 tested highest, were placed in an advanced class. The results 
 were highly satisfactory. To quote the results in the case of 
 the advanced section of the fourth grade: "Twenty-two of the 
 thirty-five pupils are ready to begin the second half of the fifth 
 grade work. Thirteen of the pupils begin the regular fifth grade 
 work, though several of these will probably catch up with the 
 advanced pupils before the end of the term. One pupil, who was 
 absent because of contagion, will be retarded." The tests are 
 evidently of high significance, but the calculation of the coeffi- 
 cient of correlation between them and the accomplishment in 
 class would be of value in giving a quantitative measure to the 
 degree of accuracy of the classification. 
 
 ^ee Adler, Martha, Mental Tests as a Basis for Classification, Jour, of 
 Educ. Psych., Vol. V, No. 1. 
 
SECTION 9. — PRACTICAL APPLICATIONS IN HIGH 
 SCHOOL CLASSIFICATION 
 
 There can be little question as to which of the three sources of 
 estimate of a pupil's scholastic ability is the preferable one to 
 use, in case it is not desired or possible to use all of them. The 
 elementary school records of the pupils give the most accurate 
 estimate of average class standing, as well as of standing in 
 specific courses. A higher correlation than .80 between estima- 
 tion and actual first-year standing should not be demanded, or 
 expected, in a correlation of this nature. 
 
 There would be a great advantage in having a uniform record 
 card, for each state school system, to contain, in addition to 
 other data, the pupil's grades from year to year, together with a 
 definite statement of the significance of the grades in terms of a 
 normal distribution, or as deviations from the grade mean for the 
 local system in question, expressed as multiples of the variability 
 for that system. If these cards were freely transferred from school 
 to school, as the pupil changed, it not only would be possible to 
 classify pupils accurately each year, but it would be of incal- 
 culable value from other standpoints as well, for there is prob- 
 ably no easily obtainable data which could compare in signifi- 
 cance with such a record. 
 
 The estimates of several of the previous teachers of the pupil 
 give an excellent basis for classification, but wherever available, 
 the more valuable records in the elementary school are probably 
 also available, so that, for high school classification, they are 
 not of prime importance. 
 
 They are, however, of specific value in analyzing the elements 
 which contribute to scholastic success. In the regression equa- 
 tion based upon teachers' estimates, effort shows itself to be a 
 very important factor. There would, therefore, be many advan- 
 tages for educational, and even more particularly for vocational, 
 guidance if there were available grades representing ability and 
 effort, as well as accomplishment. 
 
 The importance of the interest and specific subject tests is not 
 6 81 
 
82 Educational Guidance 
 
 to be measured solely by the extent of their correlation with class 
 standing, as they probably are not at all measures of conscien- 
 tiousness. Conscientiousness has been shown to be second in 
 importance to intellectual ability only and to deserve a weight 
 of 4 to 12 for all other factors measured, intellectual ability, 
 emotional interest, and oral expression. A classification of 
 pupils which does not take into account conscientiousness may 
 be particularly advantageous in that it throws the indolent in 
 with conscientious pupils of equal mentality, thus acting as a 
 strong spur to the lazy while, at the same time, the group is 
 homogeneous so far as capacity is concerned and it does not 
 require a dual technique of presentation on the teacher's part 
 to answer the needs of dull and bright pupils. It may be that 
 in a small way a different technique of presentation is needed to 
 best present a subject to a lazy pupil, from that needed in pre- 
 senting it to an industrious one of the same mentality, but the 
 difference does not compare with that needed in the case of dull 
 and bright pupils. 
 
 It is also undoubtedly true that the tests here given, if given 
 in a high school with classes one year apart, would yield higher 
 correlations than here obtained. In the school from which 
 groups 1, 2, and 3 came classification is close and grades differ by 
 one-half year. In the school from which groups 4 and 5 came 
 particular attention is paid to classification, resulting in courses 
 which fit the needs of the pupil probably fully as thoroughly as 
 in the other school. In fact, in both of these schools, certain 
 classes differ from each other by not more than a quarter of a 
 year. The effect of this is to make the classes more homogeneous 
 and such homogeneity always decreases the correlation. Ref- 
 erence to the tables of means, p. 68, shows that the groups 
 differ materially in their average accomplishments in the various 
 tests. This shows that by means of these tests pupils could be 
 classified as to their most probable place in the high school much 
 more accurately than they can be classified as to their place in a 
 class. The former is not the question which it is attempted to 
 answer, but it is mentioned to show that the ability to place a 
 pupil among all pupils is considerably greater than the ability 
 to place him in a more or less homogeneous group, and as the 
 groups here considered are unusually homogeneous the signif- 
 
Practical Applications in High School Classification 83 
 
 icance of the tests is correspondingly greater than the correlation 
 coefficients indicate. 
 
 To make the classification still more reliable it is recommended 
 that in the case of a pupil whose previous record is not available 
 the tests here given be supplemented by acquired knowledge tests, 
 particularly in mathematics and foreign languages. 
 
SECTION 10— GUIDANCE METHODS 
 
 It will be found that having once initiated a guidance bureau 
 the demands upon it will be positive and innumerable — many of 
 them extravagant. In the attempt to meet these demands, and 
 to meet them on the spot and without a moment's delay, one of 
 the richest sources of information is likely to be only very parti- 
 ally utilized. Reference is made to that product accumulated 
 by every pupil — school grades. Whatever capacity it is that a 
 grade, say, in mathematics, stands for, it is measured with a 
 high degree of accuracy when the records of several years and 
 of several teachers are combined. A pupil's school record is the 
 most complete, detailed and accurate of all records, of the 
 ordinary pupil, from his entrance in school to his entrance into 
 work. Unless the significance of this record is evaluated with 
 reference to all the important studies and vocations the most 
 readily available and accurate data concerning the applicant for 
 a place in some class, or for a job, are not being utilized. The 
 evaluation of these data will require much statistical work, but its 
 use after evaluation is simple. 
 
 Teachers' estimates of a pupil are second in importance only 
 to grades. It requires, however, the estimates of several teachers 
 to secure an accurate rating, and, under present conditions, it 
 frequently is not possible to secure the estimate of more than 
 one and, in cases where either the pupil or the principal changes 
 location, even this is lacking. If each teacher were to place on 
 record, at the end of every course, an estimate of several of the 
 qualities, important for success, of each of his pupils, these data 
 would be of inestimable value to the guidance expert. In this 
 case, as that of school grades, a uniform record card, carrying a 
 standardized grading, is essential for the best results. 
 
 The use of special tests in vocational guidance is unlimited. 
 There could well be certain specialized tests for each important 
 vocation, but first of all there might be devised a general test, 
 somewhat along the line of the interest test in this study, which 
 would have significance in all vocations and which could be 
 evaluated with reference to any one desired. This general test 
 84 
 
Guidance Methods 85 
 
 could test interest and general mental capacity, while it could 
 be left to the specialized tests to measure specific capacity and the 
 necessary acquired knowledge. 
 
 In so far as guidance becomes a science and not an intuition, 
 in so far as its method and conclusions are capable of definition 
 and free use by different individuals and are not simply inner 
 convictions of the expert making them, the problem of relation- 
 ship, expressed in quantitative terms, between the capacity of 
 the applicant and the demands of the position will become more 
 and more insistent for solution. A guidance bureau should be 
 like a type distributing machine, which will take a hopperful of 
 type, of all the letters of the alphabet, and place each in its partic- 
 ular niche, in the one place of all places where it fits. That a 
 fitting distribution of human talent is a task of unmeasured 
 intricacy is apparent, but the peculiar service thereby rendered 
 to groping humanity makes the solution worthy the greatest 
 effort. 
 
 In broad outline, as already pointed out, the problem of vo- 
 cational guidance consists of measuring the demands of the 
 possible vocations, and of the capacities of the applicant and then 
 fitting the applicant into that place which best suits his talents 
 and his ambitions. In detailed procedure, the regression equa- 
 tion method is a powerful instrument, for it enables any number 
 of factors to be combined with the highest significance with 
 reference to the vocation in question. When a large number of 
 factors, none of them of predominant importance, contribute to 
 a total result, the human intellect, unaided, cannot compass 
 their total significance and it is only by mathematical means 
 that they can be summed and interpreted. 
 
SECTION 11.— APPENDIX 
 
 Ages of Pupils 
 
 This study covers four different groups of pupils: (1) 59 pupils starting the 
 second year of the high school of School A; (2) 42 starting the second term of 
 the first year of the same school; (3) 81 starting the first term of the first year 
 of the same school; (4) 26 pupils starting the second year of the high school of 
 School B, and (5) 25 pupils starting the first year of the high school of School 
 
 B. Ages are expressed in years and tenths of a year from birth up to January 
 1, 1913. Since the algebra and geometry tests were given during the last of 
 September and the first of October, 1913, and the English, history and interest 
 tests were given in January, 1913, the average ages at the times of the tests 
 may be obtained from the given means by subtracting .30 of a year in the cases 
 of the algebra and geometry tests and by adding .05 of a year in the cases of 
 the other tests. The mean ages of the different groups January 1, 1913, is as 
 follows : 
 
 Group 1 16.1 years. 
 
 Group 2 14.6 " 
 
 Group 3 13.7 " 
 
 Group 4 15.7 " 
 
 Group 5 14.4 " 
 
 The Assignment of Numerical Magnitudes for Literal 
 
 Grades 
 
 In both schools a literal grading system is in use. In School A letters A, B , 
 
 C, D and E are used. The mark E is used very infrequently — some teachers 
 not using it at all. In averaging the grades for two or more terms it was 
 assumed that the difference in ability represented by grades of A and B was 
 equal to the difference in ability represented by grades of B and C, etc. That 
 little error resulted from this assumption will be shown in the next section of 
 this appendix. In averaging the grades of four terms the following differences 
 in ability may occur: 
 
 A _A +A+A+A _ A+A+A+B 
 
 A , A 2 - , 
 
 _, A+A+B + B A+A+A+C _ x , A+B+B + B 
 
 a+= = , ±52 + = = etc, 
 
 4 4 4 
 
 B= B+B+B+B ^ A+B+B+C _ ctc 
 
 4 4 
 
 And so on for other combinations. The literal grades thus obtained were then 
 transformed into numerical grades, assuming a normal distribution of talent. 
 This is very readily done by noting the percentage frequencies of the different 
 
Appendix 
 
 87 
 
 grades and using such a table for transformation as that given by Thorndike 
 in his " Mental and Social Measurements," pp. 221-225, second edition. Upon 
 this basis literal grades were assigned numerical values as follows : 
 
 Courses in which Tests Were Given at Beginning of Term 
 
 
 
 
 
 
 
 
 
 
 Hist. 
 
 Hist. 
 
 Hist. 
 
 
 Alg. 
 
 Alg. 
 
 Geo. 
 
 Geo. 
 
 Eng. 
 
 Eng. 
 
 Eng. 
 
 Eng. 
 
 3rd & 
 4th 
 Yr. 
 
 2nd 
 Yr. 
 
 |Yr. 
 
 1st. 
 Yr. 
 i Yr. 
 
 
 1 yr. 
 
 1 Yr. 
 
 1 Yr. 
 
 1 Yr. 
 
 §Yr. 
 
 i Yr. 
 
 1 Yr. 
 
 i Yr. 
 
 
 
 
 
 
 
 
 
 
 \ Yr. 
 
 
 
 Groups 
 
 2 and 3 
 
 5 
 
 1 
 
 4 
 
 1 
 
 2 
 
 3 
 
 4 and 5 
 
 1 
 
 1 
 
 2 
 
 A + 
 
 
 
 2.44 
 
 
 1.99 
 
 
 
 
 
 
 
 AJ + 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 2.34 
 
 
 1.42 
 
 
 1.49 
 
 2.70 
 
 1.81 
 
 
 2.23 
 
 1.23 
 
 1.96 
 
 A|- 
 
 1.69 
 
 
 .99 
 
 
 
 
 
 
 
 
 
 B + 
 
 1.29 
 
 
 .88 
 
 1.56 
 
 1.27 
 
 1.65 
 
 1.13 
 
 1.49 
 
 
 .55 
 
 1.14 
 
 B* + 
 
 1.05 
 
 1.92 
 
 .77 
 
 
 
 
 
 
 
 
 
 B 
 
 .80 
 
 .96 
 
 .51 
 
 1.28 
 
 .55 
 
 .78 
 
 .68 
 
 .67 
 
 1.29 
 
 .29 
 
 .67 
 
 Bk- 
 
 .57 
 
 .44 
 
 .23 
 
 .92 
 
 
 
 
 
 
 
 
 c+ 
 
 .38 
 
 .06 
 
 .08 
 
 .58 
 
 .07 
 
 .15 
 
 .21 
 
 - .05 
 
 .77 
 
 - .05 
 
 .28 
 
 CJ+ 
 
 .17 
 
 - .24 
 
 - .08 
 
 .15 
 
 
 
 
 
 
 
 
 c 
 
 - .01 
 
 - .58 
 
 - .20 
 
 - .36 
 
 - .48 
 
 - .28 
 
 - .39 
 
 - .70 
 
 .32 
 
 - .60 
 
 - .20 
 
 CJ- 
 
 - .24 
 
 -1.20 
 
 - .31 
 
 - .71 
 
 
 
 
 -1.35 
 
 
 
 
 D + 
 
 - .47 
 
 -2.10 
 
 - .53 
 
 -1.00 
 
 - .95 
 
 - .73 
 
 -1.13 
 
 -1.99 
 
 - .32 
 
 -1.32 
 
 - .74 
 
 D* + 
 
 - .64 
 
 
 - .81 
 
 -1.42 
 
 
 
 
 
 
 
 
 D 
 
 - .77 
 
 
 -1.09 
 
 -2.16 
 
 -1.46 
 
 -1.11 
 
 -1.99 
 
 
 - .88 
 
 -2.16 
 
 -1.33 
 
 m- 
 
 
 
 -1.49 
 
 
 
 
 
 
 
 
 
 D- 
 
 -1.03 
 
 
 -1.89 
 
 
 -1.85 
 
 -1.34 
 
 
 
 -1.17 
 
 
 
 E + 
 
 -1.54 
 
 
 -2.44 
 
 
 -2.10 
 
 -1.65 
 
 
 
 
 
 -1.86 
 
 E§ + 
 
 
 
 
 
 
 
 
 
 
 
 
 E 
 
 -2.34 
 
 
 
 
 -2.70 
 
 -2.28 
 
 
 
 -1.49 
 
 
 -2.62 
 
 E- 
 
 
 
 
 
 
 
 
 
 -2.23 
 
 
 
 The same kind of transformation tables were obtained in 18 other courses 
 in order to obtain numerical measures for the literal grades received in the 
 first year of the high school by the 59 pupils whose records were available 
 down to the third grade. The populations upon which the transformations 
 were based averaged 40.4 pupils per course. 
 
 The grades of A+ and A|+ require explanation. In mathematics and 
 English special classes were formed for the particularly bright pupils. The 
 grading of pupils in these classes was more severe than the ordinary grading. 
 It was the opinion of the teachers concerned that grades would be comparable 
 with the rest of the grades of the school if the grades received in the special 
 mathematics classes were raised one point, i.e., call C's, B's and B's, A's, etc., 
 and if the grades received in the special English classes were raised one-half of 
 a point. This was accordingly done, and accounts for the grades A+ and 
 
 The grade D — is an average of such grades as the following : first term D, 
 second term E, third term E, fourth term D. This is a passing grade for the 
 year. The grade E+ is an average of the same grades, except that the final 
 term is an E, constituting a failure for the year. It is reasonable to assume 
 that slightly greater proficiency is shown in the former case than in the latter. 
 
 A further simple transformation was made in order to obtain measures that 
 were convenient to work with. The numerical measures obtained by use of 
 the preceding transformation tables were each divided by .2 and the results 
 kept to the nearest integer. The range thus obtained has about 26 divisions 
 
88 
 
 Educational Guidance 
 
 in it and the standard deviation is about 5. This distribution is very conven- 
 ient for purposes of calculation and the effect of the grouping is so slight that 
 no correction in the value of the coefficients of correlation need be made on 
 account of it. The distributions thus obtained have means at zero, to a very 
 close approximation, and no correction to the coefficients of correlation is 
 necessary to correct for arbitrary means. 
 
 To test the extent of the error due to the averaging of literal grades, the 
 following facts are to be considered : 
 
 Extent of Error in Averaging Literal Grades 
 
 t im. i j u A plus B _, B plus C „ 
 
 In averagmg literal grades such as — =B + ; — - = C+, etc. 
 
 Zi Zi 
 
 no error is introduced because the only assumption involved is that A>B + 
 >B, etc., which is the basic assumption underlying the transformation of 
 literal grades into numerical grades. Some 92 per cent of the averaging was 
 
 of this nature. It is only when it is stated that 
 
 AplusC_BplusB 
 
 =B that 
 
 2 2 
 
 there is danger of error from this source. Simplifying we find that this equation 
 is true only in case A— B=B— C. The following data show to how close an 
 extent this assumption is true and it should be remembered that it applies to 
 only about 8 per cent of the averaging done. 
 
 
 Algebra-Groups 
 
 English-Groups 
 
 History-Group 1. 
 
 Geometrt-Group 
 
 
 2 and 3. Average 
 
 1,2 and 3. Average 
 
 Average op Two 
 
 1. Average op 
 
 
 of Two Quarters 
 Corresponding 
 
 op Two Quarters 
 
 Quarters 
 
 Two Quarters 
 
 
 Corresponding 
 
 Corresponding 
 
 Corresponding 
 
 
 grade: 
 
 grade: 
 
 grade: 
 
 grade: 
 
 A 
 
 1.41 
 
 1.80 
 
 1.57 
 
 2.03 
 
 
 A-B = .86 
 
 A-B=1.04 
 
 A-B=1.05 
 
 A-B=1.22 
 
 B 
 
 .55 
 
 .76 
 
 .52 
 
 .81 
 
 
 B-C = .71 
 
 B-C=1.00 
 
 B-C= .80 
 
 B-C= .91 
 
 C 
 
 - .16 
 
 - .24 
 
 - .28 
 
 - .10 
 
 
 C-D = .86 
 
 C-D=1.10 
 
 C-D= .99 
 
 C-D= .89 
 
 D 
 
 -1.02 
 
 -1.34 
 
 -1.27 
 
 - .99 
 
 
 D-E = .93 
 
 D-E=1.27 
 
 D-E=1.06 
 
 D-E=1.04 
 
 E 
 
 -1.95 
 
 E-F = .88 
 
 -2.61 
 
 -2.33 
 
 -2.03 
 
 F 
 
 -2.83 
 
 
 
 
 From the above table : 
 
 
 If A-B = l, 
 
 If B-C = l, 
 
 If C-D = l, 
 
 If D-E = l, 
 
 
 thenB-C = 
 
 thenC-D = 
 
 thenD-E = 
 
 thenE-F = 
 
 Alg 
 
 .83 
 
 1.21 
 
 1.08 
 
 .91 
 
 Eng 
 
 .96 
 
 1.10 
 
 1.15 
 
 
 Hist 
 
 .76 
 
 1.24 
 
 1.07 
 
 
 Geom 
 
 .75 
 
 .98 
 
 1.17 
 
 
 Av 
 
 .83 
 
 1.13 
 
 1.12 
 
 
 Average of all = 1.02 
 
Appendix 
 
 89 
 
 From similar tables for groups 4 and 5 : 
 
 Alg. . 
 Eng.. 
 Geom 
 Av... 
 
 If A-B = l, 
 
 thenB-C = 
 
 .842 
 
 .914 
 
 1.070 
 
 .942 
 
 If B-C = l, 
 
 thenC-C- = 
 
 .679 
 
 1.018 
 
 .855 
 
 .851 
 
 If C-C-=l, 
 then C D = 
 
 .99 
 
 .93 
 
 .96 
 
 Average of all = .918 
 
 Similar data from the elementary school group show a still closer approach 
 to equality. 
 
 It is therefore plain that no appreciable error has been introduced by such 
 averaging. 
 
 Elementary School Grades 
 
 In the elementary school the system of grading for certain years was different 
 from that for other years. In a few of the grades the literal system A, B, C, D, 
 E, F, was used, but in the major number of grades considered the marks given 
 were 1, 2, 3, — 1 being the highest grade used. By assuming a normal distribu- 
 tion, and expressing both the values 1, 2, 3 and A, B, C, D, E, F in terms of 
 deviations from the means, the values may be compared with each other. The 
 following relation exists: 
 
 
 
 
 Average 
 
 
 
 
 Weighted 
 
 English 
 
 Arithmetic 
 
 History 
 
 Relation 
 (Used in all trans- 
 formations.) 
 
 A to F 1 to 3 
 
 
 
 
 A= 1.2(7 = 1.0 
 
 A= 1.8(7 = .9 
 
 A= 1.7(7 = .9 
 
 A= .9 
 
 B= .2(7 = 1.6 
 
 B= .8(7 = 1.6 
 
 B= .5a = 1.8 
 
 B = 1.6 
 
 C=- .6o- = 2.1 
 
 C= .0(7 = 2.1 
 
 C=- .5(7 = 2.2 
 
 C = 2.1 
 
 D=-1.3a = 2.5 
 
 D=- .8(7 = 2.6 
 
 D=-1.4c7 = 2.8 
 
 D = 2.6 
 
 E=-1.7<r = 2.7 
 
 E=-l. 6(7 = 3.1 
 
 E=-2.2(7 = 3.3 
 
 E = 3.0 
 
 F=-2. 4(7 = 3.1 
 
 F=-2.4<r = 3.6 
 
 
 F = 3.4 
 
 With this transformation table literal grades were expressed in units that 
 are comparable with the numerical grading 1, 2, 3. The final grade given each 
 year, for each pupil, in English is the sum of the grades given for the four 
 terms of the school year in two English courses, e.g. "Reading and Literature" 
 and "Composition." Thus the poorest grade possible is 24 and the best 8. 
 The grades given in arithmetic and history are the sum of the grades for the 
 four terms for these subjects, therefore the lowest grade possible is 12 and the 
 highest 4 in each of them. 
 
 A few of the 59 pupils in this group skipped a year. In such a case the grade 
 of the year before was entered for the year skipped. This, of course, would be 
 a high grade and representative of the ability of the pupil. 
 
90 Educational Guidance 
 
 In expressing the grades of these 59 pupils as deviations from the means, the 
 means of the grades in question were obtained. Random samplings of about 
 40 from each of the grades for the various years were the basis for the calcula- 
 tion of the means. The reason for this is apparent. Since this is a prognosis 
 problem, the prognosis must be based upon the rankings of the individuals 
 in the groups in which they are found. 
 
 Several investigations have shown that there is a selective process operating 
 to eliminate backward pupils from the grammar grades. Under these condi- 
 tions, the 7th grade average of those who attend the high school would be 
 slightly greater than the average of all 7th grade pupils, still more greatly 
 above the average of all 6th grade pupils, etc. The difference would be most 
 pronounced when dealing with the average grade of these pupils in the 4th 
 grade. Calculation shows that this particular group of 59 pupils is .224 sigma 
 above the average of first year pupils in general. Calculation also shows that 
 they are .367 sigma above the average of 4th grade pupils. There is thus only 
 the small difference of .143 sigma which can be attributed to selective elimina- 
 tion of the weaker pupils. Taking all the elementary grades together, as 
 combined by the regression equation, it is found that there is not even a 
 difference of .143 sigma. In fact, these pupils who, as first year pupils, are 
 .224 sigma above the average of such pupils are, as elementary pupils, only 
 .186 sigma above the average of 7th to 4th grade pupils when grades are 
 weighted according to the regression equation. If any conclusion is justified 
 from this small population, it is that in this particular school there is no 
 selective elimination of the duller pupils. 
 
 In calculating the correlation between first year standing and the combined 
 7th to 4th grade standing, no correction is made due to the means of the popula- 
 tion of 59 being different from the means of the entire body of first-year high 
 school pupils, or the entire body of 7th to 4th grade pupils. Due to the nature 
 of the problem no correction to the first-year high school mean is permissible 
 as the object of the study is to prognosticate divergence from this mean. A 
 correction to the mean of the combined elementary grades might be applied 
 but its magnitude would be .224 sigma —.186 sigma = .038 sigma, which is 
 negligible. Even the correction to the 4th grade alone, .224 sigma —.367 
 sigma = —.143 sigma, is inconsequential. 
 
 The calculation of the regression equation giving the regression of the first- 
 year high school grades upon a combination of 7th to 4th grade marks is based 
 upon the following data: 
 
 Fa 7 a 6 a 5 a 4 a 
 
 7 A .719 
 
 6* .728 .730 
 
 .531 .425 .541 
 
 4 A .624 .551 .573 .576 
 
 a's 3.796 4.167 4.891 5.308 5.912 
 
 2.250 2.250 2.250 % 2.250 ,. v 
 
 Fa= - 3640 i^is (7i)+ ' 3113 i5H (6A)+ - 1352 iS5 (8A)+ - 2419 iSs (4a) 
 
 Fa«.3082 (7a)+.2407 (6a)+.0746 (5a)+.1291 (4a) 
 
Appendix 
 
 91 
 
 or approximately 1.803 (F A ) = §[1-667 (7 A ) +1.3 (6 A ) + .4 (5 A ) +.7 (4 A )J. This 
 combination of elementary school records is designated as (7, 6, 5, 4 A ), and the 
 correlation, ?T A (7, 6, 5, 4 A ) = -789. 
 
 The same equation is used to obtain measures in elementary school mathe- 
 matics and English, except that division by three is omitted, giving the follow- 
 ing: 
 
 (7, 6, 5, 4 M ) = 1.667 (7 M )+1.3 (6 m )+.4 (5 M )+.7 (4 m ) 
 (7, 6, 5, 4 E ) = 1.667 (7 E )+1.3 (6 E )+.4 (5 E ) + .7 (4 E ) 
 
 Calculation gives: 
 
 nF M (7, 6, 5, 4 M ) = -580 and ?T E (7. 6, 5, 4 E ) = -710 
 
 No history was taken during the first high school year so there are no history 
 correlations. 
 
 It may be noticed by reference to the preceding table that nF A 7 A and 7"F A 5 A 
 are less than would be expected from the other correlation coefficients. This 
 may be due to the teachers of these particular 7th and 5th grades being less 
 expert in estimating the ability of pupils than the 6th and 4th grade teachers. 
 Whatever the cause, probably a better regression equation for general pur- 
 poses can be obtained than the one given above. The accompanying curve 
 
 r Between Grade 
 
 in a Given Year 
 
 and Grade One 
 
 Yr. Before 
 
 r Between Grade 
 
 in a Given Year 
 
 and Grade Two 
 
 Yrs. Before 
 
 r Between Grade 
 
 in a Given Year 
 
 and Grade Three 
 
 Yrs. Before 
 
 r Between Grade 
 
 in a Given Year 
 
 and Grade Four 
 
 Yrs. Before 
 
 Av. of 4 coef's. = 
 .6415 
 
 Av. 
 
 of 3 coef's. = 
 .5753 
 
 Av. of 2 coef's. 
 .541 
 
 1 coef. =.624 
 
 ■ 6415- 
 
 was drawn with this end in view. A smooth curve, not rectilinear, is drawn 
 near the points representing the ordinates for the various abscissae. The 
 intersections of the curve with the ordinates give the values of the correlation 
 coefficients in the succeeding table. 
 
 The falling off in correlation from year to year is thought to be reasonable 
 and calculation will show that the sum of the deviations of the actual coefficients 
 of correlation from the points where the curve crosses the ordinates at the 
 various abscissae very nearly equals zero, so that the curve is not entirely 
 arbitrary. 
 
92 
 
 Educational Guidance 
 
 
 Yk. in 
 
 1 Yk. Be- 
 
 2 Ybs. Be- 
 
 3 Yrs. Be- 
 
 4 Yrs. Be- 
 
 
 Question 
 
 
 fore 
 1 
 
 fore 
 2 
 
 fore 
 3 
 
 fore 
 4 
 
 1 
 
 2 
 3 
 4 
 
 .67 
 .58 
 .53 
 .50 
 
 .67 
 .58 
 .53 
 
 .67 
 .58 
 
 .67 
 
 
 <r's 
 
 00 
 
 fi 
 
 f2 
 
 0"3 
 
 OK 
 
 The following regression equation is derived from the table: 
 X, 
 
 4616 - Xi + . 1458 - Xs + . 0910 - X, + . 1098 - X4 
 
 In case the standard deviations are all equal, this equation becomes, to a very 
 close approximation: 54.9 X = 25Xi+8X 2 +5X3 +6X4. 
 
 Teachers' Estimates and Combinations of the Same 
 
 Having the estimates of several teachers of the mental traits of each pupil, 
 it is necessary to combine these estimates into single measures of the trait in 
 question for the pupil in question. Each teacher reported on about 25 pupils, 
 and it is assumed that the talent follows a normal distribution. The rankings 
 of the teachers were then expressed as deviations from their respective means, 
 using the same method as used in transforming literal into numerical grades. 
 The number of gradings obtained for each pupil ranges from two to seven. 
 It will be seen from the following table that the correlation between these 
 estimates is low: 
 
 (i. a. —first judge) (i.a.— second judge) — • ±«v»"* 
 
 (cons. " 
 
 ) (cons. " 
 
 ) = .38±.022 
 
 (emo. int. " 
 
 ) (emo. int. " 
 
 } = .31 ±.024 
 
 r (exp. 
 
 ) (exp. 
 
 } =.29±.024 
 
 Because of this, it is impossible to average these grades and have them even 
 approximately comparable, for the standard deviation of the measures which 
 are the averages of the grades of two judges is materially greater than the 
 standard deviation of the measures which are the averages of the grades of a 
 greater number of judges. The extent of this difference can be readily esti- 
 mated, for if Xi, X%, • • • X n are measures of the same trait, and if r is equal 
 to the correlation between such measures, and if sigma X l = sigma Xt 
 = • • ' sigma X n , then we have: 
 
 'X1+X2 
 
 * + 2X 1 X 2 + X£) 
 
 = / sCXx+Xa) 2 = /z(Xr 
 
 2 
 
Appendix 
 
 93 
 
 Similarly, 
 
 Finally, 
 
 °"Xi+X2+X 
 
 ^Xi+ZH X 
 
 
 +2r 
 
 + (n-l)r 
 
 In order to make the standard deviations of measures which are averages of 
 varying numbers of estimates comparable, it is only necessary to divide the 
 measures by their respective sigmas, i.e., if but a single measure divide by sigma 
 
 X -\-X 
 Xi, if an average of two measures divide by sigma — ~ — , etc. The follow- 
 ing table gives the desired divisors for the various cases: 1 
 
 No. of grades 
 
 I. a. 
 
 Cons. 
 
 Emo. i. 
 
 Exp. 
 
 averaged 
 
 Intellectual 
 
 Conscientious- 
 
 Emotional 
 
 Expression 
 
 
 ability 
 
 ness 
 
 interest 
 
 
 1 
 
 .92 
 
 .92 
 
 .92 
 
 .95 
 
 2 
 
 .74 
 
 .79 
 
 .74 
 
 .76 
 
 3 
 
 .66 
 
 .73 
 
 .66 
 
 .68 
 
 4 
 
 .63 
 
 .69 
 
 .63 
 
 .65 
 
 5 
 
 .61 
 
 .67 
 
 .61 
 
 .63 
 
 6 
 
 .59 
 
 .66 
 
 .59 
 
 .61 
 
 7 
 
 .58 
 
 .65 
 
 .58 
 
 .60 
 
 The mean number of grades averaged to obtain each individual's measure is 
 about two and one-half, therefore the reliability coefficients have approxi- 
 mately the following values: 
 
 r (i.a. measures as derived) (i. a. meas. similarly derived) = -493 
 »"(cons. " " ) (cons. " " " )=-605 
 
 r (emo. i. " " ) (emo. i. " " " )=.505 
 
 r (exp. " " ) (exp. " " " )=.529 
 
 In 23 cases of group 2, teachers' estimates were not available, except teachers 
 of English and history who later had the same pupils in test courses, which were 
 continuation courses of the first half year's work under the same teacher. 
 The estimates of such teachers were not used when it could be avoided, i.e., in 
 all cases except these 23. The following correlations justify excluding such 
 estimates: 
 
 r G(i. a.— estimate of geometry teachers) = -^ I P°P- = ^ ' 
 r G(i.a.- " " other " ) = -44 \ group 1 
 
 r E(i. a.— 
 r E(i.a.— 
 
 English 
 other 
 
 } = .54/pop. = 33 
 -> = .36 I group 2 
 
 1 This method of averaging varying numbers of correlated measures was 
 used frequently in other portions of this study, e.g., m averaging grades of 
 pupils for some given term or year where the number of studies varied 
 appreciably. 
 
94 Educational Guidance 
 
 The estimates of "other" teachers may be considered as accurate as those of 
 the geometry or English teachers, so that the excess of .57 over .44, and of .54 
 over .36 is, in a sense, a measure of the extent to which a teacher's estimate is 
 based upon the unique ability shown in the subject he teaches. 
 
 The combination of the measures, based upon teachers' estimates, into a 
 single final measure or estimate of scholastic ability is accomplished by the 
 usual regression equation, as follows: 
 
 Av. I. a. Cons. Emo. i. Exp. 
 I. a. .72 
 Cons. .62 .61 
 
 Emo. i. .58 .61 .66 
 
 Exp. .63 .82 .55 .59 
 
 ff'a 4.048 5.193 5.166 5.138 5.190 
 
 Av. = . 3584 |^J (I. a .) + . 2456 1^ (Cons.) + . 1161 f^g (Emo. i.) 
 ^.oyl o.ooO o.547 
 
 + Q471 2J530 (E ) 
 
 2.905 
 
 or Av.= .364(1. a.) + .183 (Cons.) + .086 (Emo. i.) + .043 (Exp.) 
 
 or, approximately, 1.1 (Av.) = . 4 (I. a.) + . 2 (Cons.) + . 1 (Emo. i.) +.05 (Exp.) 
 
 — which is a very simple equation to use. 
 
 r (Av.) (I. a., Cons., Emo. i., Exp.) = ■ 7551 - 
 
 Bearing of the Various Factors, I. a., Cons., Emo. ?"., and Exp., upon M, E> 
 
 and H. 
 
 From the accompanying data: 
 M,e. = -460^Ll.a. + .114-^L M I& Cons . Emo . L Exp . 
 
 'I. a. "Cona. 
 
 La. .591 
 
 Cons.+.129-^**-Emo.i. Cons. .467 .61 
 
 a Vmn . Emo. i. .472 .61 .66 
 
 Exp. .496 .82 .55 .59 
 
 -014-^Exp. a ' S °M °La. °Cons. °Emo.i. ^Exp. 
 
 ^Exp. 
 r MM t = - 61 (Population = 178). 
 
 From the accompanying data: 
 
 E te =.336— S- I. a. +.251- 
 *• e - o-j (r CoilB E I. a. Cons. Emo. i. Exp. 
 
 * ' I. a. .598 
 
 Cons. +.068 1- Emo. i. gons. .546 .61 
 
 ov. i Emo. i.. 487 .61 .66 
 
 Exp. .536 .82 .55 .59 
 
 + 083-^- Exp a ' B °E °"l.a. ^Cons. ^Emo.i. ""Exp. 
 
 ^Exp. 
 r E E = . 64 (Population = 179) 
 
Appendix 95 
 
 From the accompanying data: 
 
 H t e = .450-^1. a.-. 024— 1_ tt T ^ t? ■ t? 
 
 *• e - <r T a* H I- &• Cons. Emo. i. Exp. 
 
 Ia - ^ La. .381 
 
 Cons. + .305 -^5- Emo. i. gonj- . -gj .61 
 
 ov, Emo. l. .390 .61 .66 
 
 h " ao - 1 - Exp. .245 .82 .55 .59 
 
 -.287-°^ Exp. a ' a * R ^I.a. ^Cons. °Emo.i. ^Exp. 
 
 °Exp. 
 r HH = . 46 (Population = 68) 
 
 Grading op thb Algebra Test 
 
 Having the gradings for the various problems in the algebra test, it is 
 impossible to say, a priori, with any assurance, which are the most significant 
 and which are the least so. The common procedure in a case like this is to call 
 them all of equal importance and add or average. Whether such a procedure 
 results in getting out of the data all that is in them or not, is a fit subject for in- 
 vestigation. The question is simply this — does the magnitude (grade of prob. 
 1 + grade of prob. 2 • • • + grade of prob. 14) correllate as highly with the 
 algebra grade received at the end of the school year, as the magnitude (Ci X grade 
 of prob. l+C 2 Xgrade of prob. 2+ • • • Cu Xgrade of prob. 14) where Ci, C% • • • 
 Cu have the best values possible. Of course the second magnitude would result 
 in the higher correlation, or, what amounts to the same thing, the stand- 
 ard deviation of the residuals in the second case is smaller than the standard 
 deviation of the residuals in the former case. Using the notation given by 
 Yule, this is to say that 
 
 °A. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14 < °A. 1+2+3+4+5+6+7+8+9+10+11+12+13+14 
 
 (A = grade in algebra course, 1 = grade of first problem, etc.) It is manifestly 
 impractical to attempt to calculate c A i 2 3 4 5 6 7 8 9 10 n 12 13 14 but an 
 approximation to this may be obtained if the problems 1, 2, • • • 14 that have 
 about the same standard deviations, and that are correlated to about the same 
 extent with A, and are correlated with each other to approximately an equal 
 extent, are grouped, thus reducing the variables to such a number that the 
 calculation is feasible. In attempting to fulfill these conditions, problems 1-4, 
 8-11, were grouped, as were also problems 6, 13, 14, giving groups A', B', C", 
 respectively. The question then is to determine <r A &> & qi and a A a>±.w+q'. 
 Formulae giving these expressions (derived in the next section) are as follows: 
 
 ^2 ff 2 f 1 * r \ A'- 2 ^ r AA' r AB' r A'B'-^AA' r2 B'C + 2 ^ r AA' r AB' r A'C' r B'C' ~] 
 
 °A.A>B>C> A^" l-* AV +2T A , B r A . & r vc , J 
 
 \ &r AA * A ,) 2 "I 
 
 2o- 2 A , + 2Xr A , B ,a A ,<r B ,J 
 
 'A. A+B'+C 
 
 ,= <T, 
 
96 
 
 Educational Guidance 
 
 The various coefficients of correlation and standard deviations required; are 
 given in the following table: 
 
 C" 
 
 7.0 
 
 A' 
 B' 
 
 C 
 
 c's Estimated 
 
 A 
 .39 
 .41 
 .39 
 
 A' 
 
 .17 
 .41 
 10.3 
 
 5' 
 
 .42 
 7.0 
 
 From which 
 
 
 2 2 
 0" A. A'B'C = .705 <T A' 
 
 (7 2 A. A'+B'+C = . 711 «r 2 A . 
 
 
 These coefficients were calculated by the per cent of unlike signs method 
 and only approximate to Pearson coefficients of correlation, which are necessary 
 from the theoretical standpoint, but it is thought that they satisfactorily serve 
 the purpose of this preliminary investigation. 
 
 The difference between the standard deviations given above is so small 
 that the advantage of the regression method over the simple average or sum 
 method is plainly too slight to justify the added work, and the measure for the 
 algebra test is taken simply as the sum of the grades in the test, after subtract- 
 ing the mean and dividing, for convenience, by 5. 
 
 That is, 
 
 At = 
 
 A'+B'+C'-mem 
 
 Here, as in the case with all measures used in regression equations, At is a 
 deviation from the mean. 
 
 Derivation of Formulae 
 
 o\.2=<Th(l-r 2 u) 
 <Th.n=<r 2 i(l-r\2)a-r 2 u.2) 
 
 8 i3 — 2r u ri3r 23 
 J 
 
 
 — 2'Sr 12 r ls r 2 3 | 
 
 Formula for 2 variables. 
 
 L-Sr 2 23 
 <r J i.2t4=<r 2 i(l-r 2 12 )(l-r 2 1 3.2)(l-r 2 1 4. !! 3) 
 
 1 — ^13.2 — r 2 34.2»" 2 14.2+2 r U .< i r U . i r8i.2 
 
 Formula for 3 variables. 
 
 -oMl-^Ml- 
 
 ,[" Sr 2 i 2 -2Sr 12 i 
 "^L 1 " 1 
 
 1 — r 2 34.2 
 
 — 2 Sr 12 ri3r 2 3— Sr 2 i 2 r 2 34+2 2ri 2 ri 3 r 24 r 3 4 
 
 ■2r 2 23 +2 7-23^34 
 
 Formula for 
 4 variables. 
 
Appendix 97 
 
 where 2ri 2 r 13 r- 23 = runarss+^rii^+ruru^ Zr 2 i 2 = r\ 2 +r 2 n +r 2 u 
 Sr 2 12 r 2 34 = r 2 i 2 r 2 34 +r\ 3 r 2 24 +rh &\ 3 
 Sri 2 ri3r 2 4r34 = ri 2 ri3r 2 4r34+ri 2 r 1 4r 23 r34+ri3ri4r 2 3r 2 4 
 Sr 2 23 =r 2 23 +r 2 2 4+r 2 3 4 
 
 (ri 2 o-i(r 2 +r 13 (riO- 3 ) 2 
 
 <r 2 i. 2+3 =<r 2 i(l- ^1.2+3) = ^! 
 
 = ««* 
 
 Similarly, 
 
 C 2 l-2+3+^=0' 2 i 
 
 o" 2 i (a 2 2 + ah +2r 2 30- 2 o- 3 ) 
 _ (ri 2 g- 2 +r 13 g- 3 ) 2 ~| 
 ah +ah +2r 23 0- 2 0" 3 J 
 
 ] 
 
 (ri 2 <T 2 +ri30-3+ri 4 o- 4 ) 2 
 
 = a\ 
 
 1- 
 
 (rh+<rh+<rh +2(r 2 sa 1 a 3 +r 24 o- 2 (T4 +^40-304) J 
 
 (2r 12 o- 2 ) 2 
 So- 2 2+2Sr 2 3<r 2 (r 3 
 
 It may be easily shown that this last formula is general and holds good for any 
 number of variables. 
 
 It was attempted to derive a formula for <x x 2345 , but paper and patience 
 were exhausted before it was accomplished. The law governing the coefficents 
 of the terms of the formula for a l 234 is not sufficiently clear to enable the 
 author to state a general formula applicable to residuals of higher order. 
 
 Grading of Geometry Test 
 
 The plan adopted in connection with the algebra test is used in combining 
 the parts of the geometry test. The following table of coefficients of correla- 
 tion (calculated by per cent of unlike signs method) supplies the necessary 
 data: 
 
 G' H' 
 
 
 
 G 
 
 E' 
 
 p> 
 
 E' 
 
 
 .25 
 
 
 
 F' 
 
 
 -.06 
 
 .13 
 
 
 G' 
 
 
 .22 
 
 .19 
 
 .06 
 
 H' 
 
 
 .40 
 
 .13 
 
 .09 
 
 Estimated 
 
 <r's 
 
 
 3.3 
 
 7.4 
 
 .45 
 4.0 9.0 
 
 ^' = problem 1; /?" = problems 2, 4, 5, 6; (r' = problem 7; #' = problems 8, 9, 10. 
 Problem 3 turned out to be too easy for the group in question, some 98 per cent 
 making a perfect score, so its grading is not used. The surprise in this table is 
 the small negative correlation between G and F'. Because of this small 
 correlation F' is also discarded. For the balance of the data the advantage of 
 the regression method over the average method is negligible, as the following 
 standard deviations show: 
 
 °" 2 G. EV'W =-800o- 2 G <x G E , G , E , =.894o- G 
 
 °" 2 G. E'+G'+H' = •817(T 2 G . a G. E'+G'+H' = - 904 (rG 
 
 °G. E'+F'+G'+H' = • 925 °G 
 
 Accordignly the sole measure of the geometry test is taken as the average of 
 
 „E'+G'+H' -mean. 
 E', <?', H'; =i.e. G t 
 
98 Educational Guidance 
 
 Grading of the English Test 
 
 The following gradings of the English and history tests may be of particular 
 significance as evidence of ability in English: E a (accuracy of description in 
 the English test), E v (valuation of important factors in the English test), 
 W (written expression in both English and history tests), D (dramatization in 
 both English and history tests). 
 
 The correlations between dramatization and English and history were cal- 
 culated by the percentage of unlike signs method, to determine with which of 
 these subjects dramatization is most closely associated, with the result that 
 r ED = .40 (later calculation gave Pearson coefficient of correlation to equal .182) 
 and r HD = .09. The correlations between English and the other elements, men- 
 tioned above, are as follows: r EE =.64, r EE =.59, r EW = .56, when calculated 
 
 by the unlike signs method. (Later calculations show that these are somewhat 
 larger than the Pearson method would give.) Furthermore, the correlation 
 between written expression and dramatization is .61 (by the unlike signs 
 method). The grading for dramatization is seen to be more closely related 
 to English than history, but because of its high correlation with written expres- 
 sion it contributes little that is unique, even with reference to English and is, 
 accordingly, not evaluated with respect to either English or history. 
 
 Another factor in connection with dramatization is the question of whether 
 its relation to English or history is linear. In grading the papers, the author 
 was quite impressed with the feeling that high grades in dramatization were 
 more likely to accompany good or poor grades in English than medium grades. 
 The author was totally unaware of the English grades of the pupils at the time 
 of the grading for dramatization, so there was no reliable foundation for the 
 belief . After the grades were available this question was tested by inspection 
 of the regression line in the correlation table for English and dramatization 
 and by calculation of the correlation ratio. The regression fine was irregular, 
 but did show some evidence of such non-rectilinearity. The value of the 
 correlation ratio between English and dramatization is .241. (Compare with 
 r ED = .182.) The excess of .241 over .182 is not sufficient to warrant the 
 assertion that the regression is not rectilinear, according to the criterion estab- 
 lished by Blakeman, 1 but the chances are in favor of its being non-rectilinear, 
 so the question is still an open one. 
 
 To return to the determination of the method of combining the parts of the 
 English test: the following table of coefficients of correlation (unlike signs 
 method) gives the necessary data: 
 
 W 
 
 °" Z E. E a E v W =0-Z E.569 
 °" 2 E. E a +E v +W = °" 2 E.571 
 
 1.65 
 
 The advantage of the regression equation method is so small as not to justify 
 the added labor necessitated by its use, and the simple average, for convenience 
 multiplied by 2, of E a , E v and W, is taken as the measure in the English test. 
 That is, E t = f(E a +E v +W-mean). 
 
 1 See J. Blakeman, Biometrika Vol. 4, pp. 349-50, for criterion of recti- 
 linearity: Here the function of 77 and r in question = 1.69, which is less than 
 2.5 the required value if non-rectilinearity is to be definitely established. 
 
 
 E 
 
 E a 
 
 Ev 
 
 Ea 
 
 .84 
 
 
 
 Ev 
 
 .59 
 
 .86 
 
 
 W 
 
 .56 
 
 .75 
 
 .64 
 
 Estimated cr's 
 
 
 2.5 
 
 2.2 
 
Appendix 99 
 
 Grading of History Test 
 
 The population in the case of history is small and therefore Pearson coeffi- 
 cients of correlation were calculated for the preliminary investigation, instead 
 of the less accurate coefficients calculated by the percentage of unlike signs 
 method. The data are as follows: 
 
 <r 2 H.H a H v =-898<r* H H H a H, 
 
 ^H.H a+ H =-906^ H . 
 
 
 H 
 
 H a 
 
 H a 
 
 .31 
 
 
 Hv 
 
 .23 
 
 .62 
 
 er'a 
 
 
 2.40 
 
 * 2 H. H, =.904(7*,!. ff>8 24Q - 169 
 
 r HH =V.096 = .310, and similarly we may say that the total correlation 
 
 between history and the c ombi ned measures H a , H v is given by the following 
 expressions: r H , H , H ^ = V. 094 = .307 and r H(H H n=V.102 = .319, where the 
 
 notation r H , H H ■. is understood to mean the correlation between history and 
 
 H a and H v when combined into a single measure by the regression equation. 
 The above results show that the average, or sum, H a +H v , will give a lower 
 correlation than H a alone, and that the regression equation yields but .009 
 higher correlation. For these reasons the sole measure of the history test is 
 taken to be H a , for convenience multiplied by two. That is, Ht = 2 (H a — mean) . 
 
 Bearing of the Various Tests Upon Mathematics 
 
 (a) Algebra. 
 
 To evaluate the significance of the algebra, English and history tests in 
 their bearing upon algebra, the regression equation between these tests and 
 algebra grades may be calculated. The following table gives the required data: 
 
 A A test E test H test 
 <r 2 A.A t E t H t =-728(7> A At .47 
 
 „i _ 77A^-2 Et .37 .37 
 
 <r A.A t +E t +H t --'' b(7 A Ht .27 .27 .40 
 
 a's 4.977 3.856 3.286 5.460 
 
 There is here a material advantage to be gained by the use of the regression 
 method, and it has accordingly been calculated: 
 
 Act = 1.316 (A) = .6 (A t ) +.4 (E t ) +.11 (Ht) 
 
 (b) Geometry. 
 
 A procedure, similar to the above for algebra, gives the following results: 
 
 G Gt Et Ht 
 
 a* =.820(7 2 P Gt .42 
 
 G.G t E t H t G Et ^ ^ 
 
 a G. G t +E t +H t -» 5t)tr G Ht .21 .20 .40 
 
 <7's 5.010 3.751 3.042 5.176 
 
 Gct = 1.53(G) = .8(Gt) + .08(Et) + .183(Ht)orGct=.8[(Gt) + .l(Et) + .23(Ht)] 
 
 The constant 1.53 has been so chosen that the standard deviation of G c t is 
 very nearly equal to the standard deviation of A c t. This is needed, for later A c t 
 and Get measures are used in the same calculation and called M c t measures. 
 
100 Educational Guidance 
 
 Bearing of the Various Tests Upon English 
 
 In the following tables which give the data for the calculation of the regres- 
 sion equations for English with the (1) algebra, English and history tests, 
 and (2) geometry, English and history tests, the probable errors of the calcula- 
 tion involving the algebra and geometry tests are given: 
 
 Since the following coefficients 
 of correlation ± their respective E At Et Ht 
 
 pi obable errors overlap, At . 35 ± . 05 
 
 r WA andr Pr ; Et .44 .37±.05 
 
 ^ , EGt . Ht .40 .27±.06 .40 
 
 r B t A t and r E t G t ' o-'s 3 . 917± . 239 3 . 274 5 . 440 
 
 and since the standard devia- _ _ 
 
 tionsof At and Gt ± their prob- & *** *** Ht 
 
 able errors overlap, At and Gt Gt .31 ±.07 
 
 may be combined into a single Et .44 .42 ±.07 
 
 mathematics group, Mt, without Ht .40 .20 ±.08 .40 
 
 materially affecting the regres- <r's 3.860±.29S 3.274 5.440 
 
 sion equation. 
 
 The regression equation has, accordingly, been calculated from the follow- 
 ing table, in which the coefficients of correlation involving the algebra test 
 and geometry test are weighted averages of the coefficients for the algebra and 
 geometry tests separately: 
 
 From this table are obtained E Mt Et Ht 
 
 the following standard devia- j^ q^ 
 
 tions: Et' ^44 .38 
 
 <r 2 E. MJ3JL =-722o- 2 E Ht .40 .25 .40 
 
 ,2 - 72Q/T" <r's 5.254 3.896 3.274 5.440 
 
 a E. M t +E t +H t _ • /zy a E 
 
 There is so little difference between these standard deviations that the 
 
 M t +Et+Ht 
 simpler method is used, i.e. E = « designated by E c t- 
 
 Bearing op the Various Tests Upon History 
 
 By parity of reasoning, the same English combination measure, E c t, is used 
 to correlate with history. The data bearing upon the problem are as follows : 
 
 H Mt Et Ht 
 
 ***** -•»»•* £' ;£ , 38 
 
 <r2 H.M t +E t +H t = - 793o ' 2 H Ht .31 .25 .40 
 
 o-'s 5.156 3.890 3.136 4.796 
 
 From which it may be deduced 1 that r HH =.455. (This value is used in the 
 
 calculation Appx. p. 105, but care should be exercised in using values obtained 
 in this way as it should be noticed that errors are cumulative and an error 
 introduced here by throwing away .001's, or for other reasons, may affect a 
 subsequent correlation considerably.) 
 
 1 Same method used as in paragraph upon Grading of History Test, Appx. 
 p. 99. 
 
Appendix 
 
 101 
 
 Interest Tests — Grading op Books 
 
 In expressing the grades of the books 1, 2,. . . .7 for English, as deviations 
 from the mean, a normal distribution was assumed for the grades given by each 
 of the judges — this method seemed to be necessary as the means for the different 
 judges varied appreciably — and use was made of the same kind of a transforma- 
 tion as in expressing literal grades in numerical terms.' 
 
 In the case of the history grading, it does not seem reasonable to assume a 
 
 normal distribution, as a straight history is surely a greater distance above the 
 
 mean, as evidence of interest in history, than is a book like "Kite Flying for 
 
 Boys" below the mean. No simple method is at hand to tell the nature of the 
 
 distribution of the books with reference to their historical significance, but the 
 
 assumption of a skewed distribution of some sort is surely more reasonable 
 
 than the assumption of a normal distribution. A distribution skewed .75 was 
 
 , 3 (Av.-Median) ! 
 assumed, skewness being measured by the formula With 
 
 a distribution so skewed, grades 1, 2. . . .7 were expressed as deviations from 
 the mean in the same manner as was done for the grading of books for English, 
 and for literal grades, under the assumption of a normal distribution. 
 
 It may be mentioned that the calculation of the reliability coefficient for the 
 grading of books foi history was done before the above-mentioned transforma- 
 tion was made, so that a small inaccuracy is present. Calculation of this 
 coefficient after the transformation would raise its value a little above the 
 obtained value, .720. 
 
 In grading sports, entertainments, words and magazines, it is not necessary 
 to resort to a transformation, for even though the means should be quite differ- 
 ent for different judges, a simple average may be taken, for the standard devia- 
 tions of the grading of the different judges were found to be very nearly equal, 
 and every judge graded every item except in the case of magazines, where the 
 means, as well as the standard deviations, were nearly equal. This does not 
 introduce the error that would have resulted from such a procedure in the case 
 of books, where the books that were graded by only two judges were not, in 
 many cases, graded by the same two. 
 
 Grading of the Interest Tests with Reference to (a) English, (b) 
 Mathematics and (c) History 
 
 The data in the following table serve as a basis for combining the various 
 parts of the interest test into a single measure to correlate with English. 
 
 Bks. 
 
 Sports 
 
 Entertainments 
 
 Vocations 
 
 Factor of accuracy 
 
 Words 
 
 Magazines 
 
 Books 
 
 <r's 1.965 3.512 2.059 4.286 4.161 2.232 2.428 
 
 E 
 
 Spts. 
 
 Ents. 
 
 Vocs. 
 
 F.ofA. 
 
 Wds. 
 
 Mags. 
 
 .20 
 
 
 
 
 
 
 
 .14 
 
 .5 
 
 
 
 
 
 
 .24 
 
 .3 
 
 .1 
 
 
 
 
 
 .04 
 
 2 
 
 .1 
 
 .1 
 
 
 
 
 .26 
 
 .3 
 
 .0 
 
 .1 
 
 .7 
 
 
 
 .37 
 
 .4 
 
 .3 
 
 .4 
 
 .2 
 
 .2 
 
 
 .13 
 
 .3 
 
 .0 
 
 .2 
 
 .0 
 
 .3 
 
 .3 
 
 
 1.965 
 
 3.512 
 
 2.059 
 
 4.286 
 
 4.161 
 
 2.232 
 
 1 The actual distribution used is that represented in Thorndike, Mental 
 and Social Measurements, Ed. 2, p. 74, but any reasonable distribution with a 
 skewness of .75 would yield comparable results. 
 
102 Educational Guidance 
 
 The coefficients of correlation in this table which involve English were calcu- 
 lated by the Pearson formula, and the balance by the percentage of unlike 
 signs method. 
 
 The standard deviations given in this table are not the standard deviations 
 of the original measures. Certain of the measures were grouped for con- 
 venience in handling: The following relations hold between the above stand- 
 ard deviations and the standard deviations of the original measures: 
 
 1 . 965 = Standard deviation of original grading of sports. 
 
 3.512 = 
 2.059 = 
 4.286 = 20 
 4.161= .2 
 2.232 = 3.3 
 2.428 = 3.3 
 
 entertainments. 
 
 vocations. 
 
 factor of accuracy. 
 
 words. 
 
 magazines. 
 
 books. 
 
 The labor involved makes it plainly out of the question to calculate a regular 
 regression equation, so that a rough approximation only has been attempted. 
 Since the grading of the magazines correlates the most highly with English, 
 the effect of that one factor is taken into account by calculating partial coeffi- 
 cients of correlation of the type r E Spts . Mags , r E Ents . Mags , etc. AU such par- 
 tial coefficients of correlation are given in the accompanying table except 
 r E F of A • Mags* ^ e ^ ac ^ 0T of accuracy is very highly correlated with the 
 grading of the words, and is therefore evaluated in connection with it. 
 
 r EFofA-Wds=--206 rEgpts . Mag3 =.061 
 
 ^EWaVFofA- -325 ^E Ents • Mags =• ° 33 
 
 Probably the average of r E Wds . Mags *E Voca . Magg = . 108 
 
 and rE Wds • F of A gives a better weight r E Wds • Mags = • 2 ^ 4 
 
 than either alone. r EBks • Mags = -021 
 
 This gives .265 as the weighting for Wds. and proportionately —.168 for 
 Fof A. 
 
 The weight assigned to magazines is the average of the following partial 
 coefficients of correlation: 
 
 r E Mags • Spts = • 331 
 r E Mags- Ents = • 348 
 r E Mags -Vocs = - 308 
 r E Mags • Wds = ■ 33 6 
 r E Mags • Bks = • 350 
 
 average = . 338 
 
 Having weighted Mags .338, proportionate weightings for other variables are 
 as follows: 
 
 '—— = —— , X = weighting for Spts. = . 062 
 .661 .Uol 
 
 Similarly " "Ents. = .032 
 
 " " "Voce. = .119 
 
 "Bks. =.020 
 
Appendix 103 
 
 Since Spts. and Ents. are highly correlated, the weights assigned to them above 
 are somewhat too high. A small amount is arbitrarily deducted from the 
 above weights. The final weights assigned are as follows: 
 
 
 W'ts 
 
 Spts 
 
 .058 
 
 Ents 
 
 .026 
 
 Vocs 
 
 .119 
 
 Fof A 
 
 -.168 
 
 Wds 
 
 .265 
 
 Mags 
 
 .338 
 
 Bks 
 
 .020 
 
 These weights, divided by the respective standard deviations, give the multi- 
 pliers of the various measures used to obtain a single interest and information 
 test grade. The single grade for the interest and information test in its bear- 
 ing on English (Ei) is accordingly given by the following equation: (In the 
 following equation the letter E indicates that the grade assigned is in relation 
 to English.) 
 
 . 1515 Ei = . 0295 (Espts) + . 0074(EEnte) + . 0578 (Evocs) - . 0392(F of A) 
 + . 0637 (Ewds) + . 1515 (EMags) + . 0082 (EBks) 
 
 ( . 1515 is taken for convenience, to make the coefficient of EMags equal to 
 unity.) 
 
 .• . Ei = . 195 (Espts) + . 048(EEnt 3 ) + . 382(Evocs) . 259 - (F of A) + . 420(Ewds) 
 +1.00 (EMags) + .054 (EBks), or, for practical purposes, 
 
 Ei = . 2 (ESpts) + . 0§ (EEnte) + . 4](EVocs) - . 2* (F of A) + . 4 (Ewds) +1.0 (EMags) 
 + .0| (E B ks) 
 
 The same relative weighting is assumed in obtaining a single measure of the 
 interest and information test to correlate with history (H) and with mathe- 
 matics (M), except that the F of A is weighted differently, since r n F of A = ®^ 
 and 7" MFof A = .173. The following weighting is used. 
 
 Hi = . 2 (Hspts) + . 0| (HEnts) + . 4 (Hvocs) - . 1 (F of A) + . 4 (Hwds) 
 
 + 1.0(HMags) + .0MHBks) 
 
 Mi = 2[.2(Mspts) + .OMMEnte) + .4(Mvocs) + .0|(Fof A) + .4(Mwds)] 
 
 The factor 2 in this last equation is simply for the purpose of obtaining a 
 more convenient distribution — by maintaining distributions with 20 or more 
 divisions it is not necessary to correct for grouping or for arbitrary means. 
 
 Combination of Parts op Interest Test Mi, Ei, Hi, with Reference 
 to (a) Mathematics, (b) English, (c) History 
 
 (a) Mathematics. 
 
 Although the interest test has been graded specifically with reference to 
 mathematics, it may be that the gradings with reference to English and history 
 give some fight upon the most probable mathematical standing of the pupil. 
 

 M 
 
 Mi 
 
 Ei 
 
 Mi 
 
 .24 
 
 
 
 Ei 
 
 .20 
 
 .21 
 
 
 Hi 
 
 .15 
 
 .54 
 
 .63 
 
 o-'s 
 
 4.93 
 
 4.64 
 
 3.13 
 
 104 Educational Guidance 
 
 The calculation of the regression equation involving M, M;, Ei, and Hj will 
 decide the question. The data for this calculation follow: 
 
 From this <r» M-MiBiH ;=.911ff» M , m Mi Ei Hi 
 
 from which it may be deduced that 
 
 r M(M i E i H i ) = • 29S 
 This correlation is considerablv above 
 the correlation for r MM ., which equals °" s 4 - 9d 4 - b4 313 b12 
 
 . 24, and by inspection of the table, it is apparent that it is considerably above 
 r M(M-+E-+H-)> ^ or ^ e l ar S e standard deviation for history (6.12), operates, when 
 taking an average or sum, to weight the history grading the highest, so the 
 regression equation method is plainly the method needed. Calculation gives 
 the following: 
 
 4.701 4.701 4.701 
 
 M = - 2238 3^5 Mi+-1826 — Ei -.095 — Hi 
 
 = .2822 Mi +.3669 Ej-. 1120 Hi 
 
 Multiplying by the convenient factor, .5646, and designating the result by M c i 
 (combination of the parts of the interest test with reference to mathematics) 
 gives the following: 
 
 Mci = . 500 Mi + . 650 Ei - . 199 Hi, or for practical purposes, M c i = . 5 Mi 
 + .65 Ei-.2 Hi. 
 
 (b) English. 
 
 Similar data with reference to English are: 
 From this E Mi Ei Hi 
 
 * 2 E.M lEi Hr- 783(r2 E ^i 
 
 from which it may be deduced that g. 
 
 r E(M i E 1 H i )=.464, o-'s 5.23 4.64 3.13 6.12 
 
 but as rgg. = . 46 there is practically no object in using the longer method. 
 Ej is therefore taken as the sole measure of the interest test in its bearing upon 
 English, and for such use will be designated E ci . 
 
 (c) History. 
 
 The data referring to history are as follows: 
 
 From this H Mi Ei Hi 
 
 ^.MjEiHr- 875 ^ g 1 
 
 from which it may be deduced that jji 
 
 r H(M i E i H i ; = .353 o-'s 5.10 4.64 3.13 6.12 
 
 It is evident that r H(M +E+H) ^ appreciably lower than this, for the rather 
 
 large standard deviation for Mi (4.64) would operate to weight Mi quite 
 heavily. The correlation .353 is sufficiently higher than the correlation r ^ . 
 
 (.30), to make the regression equation desirable. By calculation, 
 
 4.891 4.891 4.891 
 
 H== - 1597 3T77^ Mi+0767 i^ Ei+ - 2319 3^bI Hi 
 = - . 2070 Mi+ . 1585 Ei+ . 2910 Hi 
 
 E 
 
 Mi Ei 
 
 .15 
 
 
 .46 
 
 .21 
 
 .32 
 
 .54 .63 
 
 5.23 
 
 4.64 3.13 
 
 H 
 
 Mi 
 
 Ei 
 
 .02 
 
 
 
 .27 
 
 .21 
 
 
 .30 
 
 .54 
 
 .63 
 
 10 
 
 4.64 
 
 3.13 
 
Appendix 105 
 
 To obtain a convenient distribution and a simpler equation to work with, 
 this equation has been multiplied by 2.406. The result is designated by H c i. 
 H c i = -.498 Mi-h381 Ei+.700 Hi, or for all practical purposes, H c i= -.5 Mi 
 
 + .38Ei + .7Hi. 
 
 Combination of the Mathematics Tests, M c t and M c i, with Reference 
 to Mathematics. Similar Combinations of English and History 
 
 Tests 
 
 (a) Mathematics. 
 
 On page 99 of the Appendix, mathematics, English and history tests, Mt, Et, 
 Ht, were combined into a single grading, M c t, which gives the total bearing of 
 these tests upon mathematics. On page 104 of the Appendix, the gradings of 
 the mathematics, English and history interest tests, Mi, Ei, Hi, are combined 
 into a single grade, M c i, which gives the total bearing of the three interest 
 tests upon mathematics. It now remains to combine M c t and M c i into the 
 single measure which correlates the highest with M . This single measure will 
 be designated by M c , and is given by the following regression equation, which is 
 based upon the accompanying data: 
 
 4 ko 4 co M Mci Met 
 
 M -. 1606 -^ Mci +.4198-^— Met M c i .30 
 
 1.719 2.95b jyj 4 g gg 
 
 Multiplying by the convenient factor ff ,^ 5 23 186 3 48 
 
 1 . 556 gives : 
 
 M c = . 658 Mci + 1 . 00 Met, or, for practical purposes, 
 
 M c =.66 Mci+Mct. 
 
 This relative weighting is used whether it is desired to combine the grades 
 of the tests with reference to algebra or geometry. If the derivation of regres- 
 sion equations, for algebra and geometry had been undertaken separately, the 
 difference from the above weighting would have been slight and the increased 
 correlation due to the more exact weighting would have been inappreciable. 
 The terms A c and G c will be used instead of M c , when it is desired to speak 
 of the algebra combination, and the geometry combination, rather than the 
 mathematics combination. 
 
 (b) English. 
 
 Data for English, similar to the above for mathematics, are given in the 
 accompanying table: 
 
 E Eci Ect 
 Eci .46 
 
 Ect .46 .34 
 
 <r'a 5.23 3.21 3.23 
 
 Since r^ . =r EE , and <r E . is very nearly equal to <r E , a straight average or 
 
 sum of the two measures is the desired combination, i.e., Ec=E c i+E c t. 
 
 (c) History. 
 
 The data for history are given in the accompanying table: 
 
 Calculation gives : H Hci Hot 
 
 4.446 4.446 H c i .33 
 
 H= ' 2154 4l20 Cl+ 2~813 ct Hot .45 .33 
 
 = . 2168 H c i+. 5979 Hct <*» 5.10 4.80 3.23 
 
106 Educational Guidance 
 
 Multiplying by the convenient factor, 1.673, and designating the result by 
 H c , gives: 
 H c = .1814 Hci+1-00 H c t, or, approximately, H =.2H c i+H c t. 
 
 Combination of Elementary School Standing, Teachers' Estimates 
 and Test Standing with Reference to Average Class Standing 
 
 The estimation of average class F A 7,6,5,4 A Est A T A 
 
 standing based upon all three 7,6 5 4 A .83 
 
 sources of data is by means of the EstA 81 68 
 following regression equation, based 
 
 upon the accompanying data: TA 51 .56 .54 
 
 .4458 °V .4458 °X 
 
 Fa= - 6422 -«Zn^ " < 7 ' 6 > 5 > 4 A ) + .5983 A Est A 
 
 . 5340^(7, 6, 5, 4 A ) . 5666<7 Est 
 
 .4458 ff p _ 
 
 -.0771 -i T A. 
 
 .7973CTT 
 
 The equation is left in this form for reference to it. The values of the various 
 standard deviations are: 
 
 <r F =3.662; o- (7654 ^4.665; o- Egt =6.660; <r T =3.845. 
 
SECTION 12 
 
 GRADE AND TEST DATA 
 
108 
 
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 + + ++ 4- ++ + + 
 
 QOttWQQQffl pqo«Oo<iJmWQ«QmHOpqoO 
 
 + + ++ + + + 
 
 OOOOQQ O PQQQOOQPQOOfflQOHW QQ 
 
112 
 
 Educational Guidance 
 
 t-^0"HTi(Cieoe*oo»o© , >#to©»«a50o©'*»i50t»©t»<»Tf<<N!-i>Qt»F-iio 
 
 !._. »oiiiM<-ic«-*©co©>fl©«D(NiO!oeiiTji>aio»oc<5© (fiicoooiN?o©>oa» 
 
 ■H I I -H I -< I I I I I I I r« I «j« III 
 
 I_ NO«10MOOrt^H^N-*rtlOHMHlONNU! rH N 00 CO (M rH i-l rH 
 
 •a i i i i i i i i i i i ii i i i i i i 
 
 Wt_ 'Wat tO-*rHrH<00«0'»jieoe>«-»JiN©CO'<j4<NCON«D'rl<co© rH CO © CO "5 i-l «S *• 
 
 ■V- -M i I I I I I I II 
 
 13 
 
 si 
 © 
 
 !MTj*©Tjlt>.ts.^C0e0C0CO'*^lrtiH©IN(M<MtHMOS"5©i-<iaiN®(NCO 
 IT I I I II I I I I I I I l H 
 
 CN 0* -rH rH rH 5© rH t» CO © rH TH rH ©■* i-H © »« r^ IN IN t^. "S 00 rH N CO rH fr» © 
 
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 a I I rt I th IT I I I I I l rt I I IT I I I 
 
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 '«0 ft 
 
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 + 
 
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 QPQ 
 
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 + 
 
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 •TOO ++ + + + + + + 
 
 • s ooft«oo«iom ooo oomooo mopomomft 
 
 + +++ + + + + + + +++ +++ 
 
 •sug pmomQO<jo<!ooomooooo-<ftmoQOOQO<ooo 
 
 ++ +++++ + +++ + ++ +4- 
 
 ■siv— *jm oQHmom-<ooiQftmmomQmo^QomwftftommftOft 
 
 •jiJ pn S — - H 
 
 +++ + +++ +++ +++ 
 
 'a OmQWQQ«!0«s!000«1QOQQQ-<ftOQQQOOQ«iftOO 
 
 +++ I + + +4- + + I +1 + 
 
 •3iv— 'H Q«w<ipmmm<!QQOOomwwQ<i!wooowpom<!omQ 
 
 IMCO'r)(ira!Ot»00<3JOrHC<ICO'*'0'Ot»0005©rH(NM'^>n«Dt-OOOI>0'-H<N 
 OOOOOOOOHHHHHHHHHHnN«NN«OIN«INtOMCO 
 
Appendix 113 
 
 cocococoocococ^r^coiNcococ<icocococococo:ocoi-icococo"OcoM^^coNcoMcocOT)<coMcOT*ro 
 
 tO©»i-l^©COrtOCOOOWCOrH>OCONCOCO©NCOtOI^T^^I>rHCO'-iN-'#T-<c\|OOtO-<J<00 OOMIOhNho^N 
 
 -j* ii 171 ^f 1 11 11 i~ i H ^ 1 1 1 mi 1 i-j 1 
 
 III II I III I III II III I III 
 
 M'"J<t>-N<OM'.'5eOr-liM I -lTjliNOe<l'<JlTtliM-*-*'*CONr-l«0-HC<5C005'-lP5INTj<i-lTjH05'-lO>-i CXI<NCiC<ICNlt~iO>-(t» 
 
 II I II I II I I I « I I I I I I I I I I II 
 
 N HOONn<*T|l«NnH!DNlO|Nl»<DiOHNOON(B Tj«OlOtO<N .-I CO lO 00 tJI 00 CM r* O CM 00 CM O "5 tJ< N ■* 
 
 H III III H Mill I ' ' [T i > 7 
 
 CO © to UO CO <N i-i ■* CM CO *J< CM i-l CM CM ■* © CM CM CO O) i-H CO W NHNNO O >-H iH .H .-H CM CO ■* CO ■* t1< <N O «-< t- COCO 
 I I I I I II I II I I I I I I I II 
 
 COCMCOWU50SC<l'«»<'<l<CMNCOl<tO© !^(MrJiO-*'-lCO<NOtOCM>OtO'<l<^<tDCOi-lcOCSlCOCOi-llO^H^-liOINi-nnOi-l>-i'-l 
 
 I I I I I I I II I I I I I I I II I 7 - 1 
 
 N OO00O-*NC0t-N00'>t05CM00«0<NOCMOC0«D^OC0O'H«Dr-.C0O'<J<C0OOC000'<J<t»ot0(D'*tDO»h.O00 
 
 l rt I rt II II II If III Mil 
 
 O OOWOOt-NT*©OOCMOOCMC»©eM©tO©(NCMO^eM--l<N.-eM©CMCMa>^t^©©^00>OtOOtOt^tO-<i<t".''$<Tj<TjttO 
 
 II I I H III II 1-j* I I I'l I I I II I I I 
 
 ~ I v ii i i ii i •? i i i -"? ii ii ^ i 
 
 •* ^^»<D(N(NNtOfflNOOOiliONHOOC10lOOH'*NOtOMOI»ONOOOOO<000©^lOOOtD'fNNN 
 
 II I ^V I I I I II I V II I I I I I th 
 
 + + ++ ++ + +++ + + + ++ 
 
 < » O P Pq OOOWOOO OPOffl O O QO OOQO 0<!OOfflOO QO 
 
 + +++ I I 
 
 WWO P DO P OOPP POP POO P •< 
 
 + + + + ++ + I I 
 
 «po p Ofl m op o o p o oo o pp«ipm p o 
 
 + + ++++ 1+1+1+ +i +i+ +++ 
 
 n wHH«poppqpq«o<!om poppo«Pppppppowp«woppppo popwpmppa 
 
 +++ + + + ++++ + ++ + + +4- ++ + + +++ + + 
 
 «ooppfQPQppm««oopoppooppopmppppoo popowopomopooop on 
 
 + + + +++++++++++++ ++ + + 
 
 mm«oppqooo«pq«M«o«ooooomeoooooooopooomwpopo<:o««opmpm 
 
 ++ ++++ + + + + + + + + ++++ 
 
 «mopppqoopmwo«mwopp<iopo«p«opoooopo<ip<:wppomoomompp9p-i; 
 
 + 
 o 
 
 + ++ ++++ ++ + + + + ++++ 
 «omop<;ooo«<i;<«<!o«poopQm«omoppMOOOpmopm«oopm«pooooop^ 
 
 ++ ++++++ + + + + +++ i + +++ + + ++ 
 
 <PPOO^POWOCQPO^m«WOOOOO«PPQOPOPPHWOCQR«HWPPOPWWOOWCQW<t; 
 
114 
 
 Educational Guidance 
 
 N ■* O 00 CO l> 00 03 OS l> N to t- to-* co com to CO OOt-NN 
 IT3 »C ■* ■* IT3 iO t~ ■* lO t~ tO W3 tO ^ to »C tO tO *C *0 l©lOU3U3 
 
 iHt0C0OO"5O^O-*e<lrtt~iHOiHrtt0Oi-IT)(r-lt0rH000> 
 
 rt - < 7 I I II I I rt I I III 
 
 * °7 
 
 0--HOlNiOIN(NO"50i-<IMtDC<l>HiH'*000<-IN-*NCOi-ieO 
 
 I I 
 
 I I I I I I 
 
 (Irv— 4 TAT ^Hr-lt0C0T-lOIMC0OC0t0C0C<110Ni-lr-(C0O(NC0rH'*OC0>0 
 °~ W II I I I I ^ I I I I I I 
 
 t~->j( HMHOU3 i-INlO^CO «■*!-! rt O N i-l "3 •* 
 
 I 17 I ^ 1117 I 
 
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 C4MMi-l<H HWNOH 0>0i-l tOHNMNH 
 I I I I I I I 
 
 
 < 
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 Q 
 
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 9 § 
 
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 6s 
 
 C0t>.'*C0'>!tltO'<ilrHC<)lO^HiHCONC0lOC0««5iHi-ICOC0^IN'* 
 
 ?D='-PM I III I I I I I I I I 
 
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 •snoo 
 
 •posijM OOCQQPO «10«m«0«pqfflOOOOMFQO« 
 
 + +i i. + 
 
 •3IV pqpo<OQOOPqQOP500PqO-DQO «pqmQ«« 
 
 IJL+ i. ++ ++ 
 
 •wo oomoo o ooOmo QQ oo«o 
 + + 
 
 + JL 
 
 OO O OWOO 
 + j_ I 
 
 + £ + 
 
 •^i oo woo omoomo 
 
 + ++£ + „ 
 
 •Sag p50ompqomwfqpqpqmmOpqOPaP5000mmOfflO 
 
 + ' + +++ J„+.i,++ JL 
 
 •tnoao— -h OQO^OOO«mOO«OQOQOOOPOOQOOO 
 + + + 
 
 •a rnqo^mom <-pqpq^MOPQOO«wom«pqqwo 
 
 J. J. _L _i_ J. 
 
 •tnosQ— 'W « O^OOPQ WPQOfflOQOQWOOQWOQQOQ 
 
 co-*iocot^ooc>©i-ie<ico-f<iotor~oooO'H<Nco-*iotDt>oo 
 
 OOOOOOOOOOOOOOOOS0050503C1C5005000000QOO 
 HHHHHHH>-IHHriHHHHririCqiNIN«MC<C4ININ 
 
Appendix 
 
 115 
 
 lOiOcDcO^OJNOOOWCOOOOOt^^COWWWWCOOOJ 
 
 ta 
 
 NNNM'*eN«lOH(B00NHMN'*«'*NNON 1 OH 
 
 I I I 
 
 I I I 
 
 t HWeOWHrt^NHH^^HHOHHCOHHOOOH 
 
 •3|| Ml || I III 
 
 ■V= -Vi I, i i II iii | | | | | 
 
 I I I I 
 
 H3 
 
 e 
 o 
 O 
 
 < 
 
 < 
 
 Q 
 
 H 
 
 m 
 
 H 
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 00 U3 © i-H CO CO CO >-l © IQ >-l -»J< i-: C3 ■<* © © H«MH 
 rH I I I rH ■ I - — • I r 1 T 1 
 
 I I I 
 
 117 1 
 
 H i_, HnnnouiH ^ ionncc(nin(N(d 1-1 coco no 
 
 ^ a II I I I I I I 
 
 ■8 
 
 J? . t-«i-I (N ■* •* CO <-H tO r-l O CM <N CO N <N ■* © IQ rH O tO 1-1 1-1 
 
 I »v= 4 w I 111 11 1 11 
 
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 lay -tnoa 
 
 mo 
 
 « O fflO«Q«P3PQ<! 
 
 + + + + +++ 
 
 ommoomommooommmommoooo<:m«5 
 
 + 
 
 1 1 
 
 + 
 
 ++ 
 
 oisnjAi oQ W opq*.-«<<moo<JomoMOpqm«mfflwm« 
 
 'oo 
 
 "H N Pa« '3080 
 
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 •niBJO 
 ■dtnoQ 
 
 1+ + + + + 1++ 
 
 «<!OPQQ«OP5000<!«0<!0-<OPmOOOOO 
 
 + ++++ ++ + +++ ++++ 
 
 pq«OOOOOmmOOmOmmmOOmmmmmm-< 
 
 I 1 1 _1_ J I L -(- 
 
 a o ooq« 0000m mo poo ooo 
 
 JL +++++1 +L+ i + + 
 
 oomooppooomoomoooopooomoo 
 
 i + i i +1+ 1+ + + + 
 
 oommmoffl^oooomoomoopoooooo 
 
 + + ' +++ 
 
 1+++ + + ++L+ ++ + 
 
 ooomoopmoomoomooooooooomm 
 
 + + ++ + ++ +1+ ++ + 
 
 v»n oomoooomoomoomoomoomooomm 
 
 + + + 
 
 ■»iv— jm oooopoQ pmpmmpopopPmmmooo 
 
 + + + 
 
 •3 oommmoQ<50omomoommoQmpmmm*< 
 
 111 _|_ _1_ I _L -|- 
 
 •3iv— w. ommoooomomommoooooomommo< 
 
 05©i-nNco-*"5cot^ooo>©'->(Nco-*incDt>coo5©'-|ejco 
 
 N(NCN<C<1NINCSIIN<N(N(NINNNININNN<NCN1(NC<ININN 
 
116 
 
 Educational Guidance 
 
 HIGH AND ELEMENTARY SCHOOL GRADES 
 
 High School 
 1st year 
 
 Fm Fb Fav 
 
 EXPRESSED AS DEVIATIONS FROM MEAN 
 
 7th Gr. 6th Gr. 5th Gr. 
 
 4 
 
 9 
 
 10 
 
 12 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 24 
 
 25 
 
 29 
 
 36 
 
 38 
 
 39 
 
 40 
 
 41 
 
 42 
 
 45 
 
 46 
 
 47 
 
 53 
 
 65 
 
 76 
 
 89 
 
 98 
 
 103 
 
 106 
 
 109 
 
 110 
 
 112 
 
 113 
 
 116 
 
 123 
 
 125 
 
 127 
 
 128 
 
 129 
 
 130 
 
 135 
 
 138 
 
 143 
 
 145 
 
 147 
 
 148 
 
 151 
 
 152 
 
 153 
 
 154 
 
 156 
 
 157 
 
 160 
 
 162 
 
 166 
 
 168 
 
 169 
 
 172 
 
 173 
 
 174 
 
 3 
 
 -10 
 
 1 
 
 3 
 
 -4 
 10 
 
 -1 
 1 
 
 -3 
 
 10 
 7 
 7 
 3 
 3 
 5 
 
 -6 
 
 
 -1 
 7 
 
 -4 
 5 
 
 -4 
 
 -3 
 
 2 
 
 12 
 
 -3 
 
 4 
 
 4 
 
 3 
 
 -5 
 
 
 
 -2 
 
 -1 
 8 
 6 
 2 
 6 
 2 
 5 
 
 
 -1 
 
 
 -2 
 4 
 
 
 -1 
 6 
 
 -2 
 
 2 
 
 -5 
 
 -1 
 
 -10 
 
 -1 
 
 -4 
 
 -6 
 
 8 
 
 4 
 
 -2 
 
 -1 
 
 8 
 
 4 
 
 4 
 
 4 
 
 8 
 
 
 
 4 
 
 -1 
 
 -10 
 
 1 
 
 -2 
 
 1 
 
 4 
 
 -2 
 
 -6 
 
 -2 
 
 -1 
 
 3 
 
 -6 
 
 
 
 9 
 
 -2 
 
 -2 
 
 -2 
 
 -4 
 
 -4 
 
 -4 
 
 -2 
 
 9 
 
 -2 
 
 5 
 
 6 
 
 7 
 
 5 
 
 
 
 * 5 
 
 -2 
 
 1 
 
 2 
 
 5 
 
 2 
 
 -2 
 
 1 
 
 
 
 
 
 3 
 
 3 
 
 -8 
 
 2 
 
 7 
 
 
 
 -5 
 
 1 
 
 3 
 
 -5 
 
 9 
 
 3 
 
 -2 
 
 -2 
 
 7 
 
 5 
 
 5 
 
 
 
 4 
 
 -1 
 
 
 
 -3 
 
 -6 
 
 1 
 
 -3 
 
 2 
 
 6 
 
 
 
 -5 
 
 -3 
 
 -2 
 
 -1 
 
 -3 
 
 
 
 10 
 
 -2 
 
 1 
 
 2 
 
 -1 
 
 -4 
 
 -2 
 
 
 
 9 
 
 -3 
 
 2 
 
 6 
 
 7 
 
 3 
 
 3 
 
 3 
 
 2 
 
 1 
 
 1 
 
 3 
 
 -1 
 
 
 
 
 
 -2 
 
 3 
 
 4 
 
 -1 
 
 -5 
 
 1 
 
 5 
 
 7m 
 
 
 
 1 
 
 —2 
 
 
 
 -2 
 
 -3 
 
 1 
 
 
 
 1 
 
 
 
 
 
 -3 
 
 -3 
 
 -2 
 
 
 
 
 
 2 
 
 2 
 
 2 
 
 1 
 
 
 
 -3 
 
 2 
 
 1 
 
 1 
 
 2 
 
 2 
 
 
 
 
 
 -1 
 
 1 
 
 
 
 
 
 
 
 1 
 
 -1 
 
 
 
 -1 
 
 
 
 -1 
 
 -2 
 
 -1 
 
 -1 
 
 
 
 -2 
 
 
 
 1 
 
 -1 
 
 2 
 
 -1 
 
 4 
 
 1 
 
 
 
 1 
 
 
 
 1 
 
 
 
 
 
 
 
 7b 7h 
 
 6m 6b 6a 
 
 5m 5b 5h 
 
 4th Gr. 
 
 4b 4h 
 
 3 
 
 2 
 
 -3 
 
 
 
 3 
 
 -4 
 
 -3 
 
 1 
 
 2 
 
 -1 
 
 3 
 
 -2 
 
 -3 
 
 -5 
 
 1 
 
 
 
 
 
 4 
 
 -1 
 
 -1 
 
 2 
 
 -3 
 
 
 
 1 
 
 2 
 
 3 
 
 -1 
 
 
 
 3 
 
 -2 
 
 -2 
 
 6 
 
 -2 
 
 6 
 
 3 
 
 2 
 
 2 
 
 -3 
 
 2 
 
 3 
 
 -1 
 
 -2 
 
 -1 
 
 3 
 
 -2 
 
 -2 
 
 2 
 
 2 
 
 -2 
 
 1 
 
 -2 
 
 -1 
 
 
 
 1 
 
 
 
 
 
 3 
 
 1 
 
 -4 
 
 -1 
 
 
 
 
 
 -1 
 
 2 
 
 -4 
 
 -2 
 
 1 
 
 1 
 
 -3 
 
 -3 
 
 -2 
 
 -2 
 
 -1 
 
 -2 
 
 1 
 
 -1 
 
 
 
 -1 
 
 1 
 
 
 
 -3 
 
 1 
 
 
 
 
 
 2 
 
 
 
 
 
 -1 
 
 -3 
 
 
 
 
 
 -1 
 
 1 
 
 
 
 
 
 -1 
 
 -4 
 
 
 
 -1 
 
 -1 
 
 -2 
 
 
 
 -1 
 
 -1 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 1 
 
 2 
 
 1 
 
 -1 
 
 -4 
 
 1 
 
 1 
 
 -1 
 
 -4 
 
 
 
 -2 
 
 2 
 
 2 
 
 3 
 
 -4 
 
 -1 
 
 -3 
 
 -2 
 
 -3 
 
 
 
 1 
 
 1 
 
 -1 
 
 -3 
 
 -2 
 
 -1 
 
 -3 
 
 2 
 
 1 
 
 2 
 
 4 
 
 1 
 
 
 
 -1 
 
 -3 
 
 1 
 
 
 
 1 
 
 
 
 
 
 
 
 -1 
 
 
 
 1 
 1 
 
 -4 
 -1 
 
 
 
 
 
 
 3 
 1 
 1 
 -1 
 
 
 
 
 1 
 
 
 
 -1 
 
 
 
 1 
 
 3 
 
 
 7 
 
 -6 
 
 -3 
 3 
 5 
 
 -6 
 3 
 
 -4 
 3 
 
 -5 
 3 
 
 -1 
 
 -2 
 3 
 
 
 -1 
 
 -1 
 
 -3 
 2 
 1 
 
 -3 
 2 
 
 -2 
 1 
 
 -1 
 
 -3 
 2 
 5 
 
 -1 
 4 
 2 
 3 
 
 
 -5 
 2 
 2 
 
 
 -3 
 
 
 -4 
 
 -1 
 
 
 1 
 
 
 1 
 
 2 
 
 -3 
 
 2 
 
 2 
 
 -3 
 
 -3 
 
 2 
 
 1 
 
 -4 
 
 
 1 
 
 
 -1 
 1 
 
 -3 
 
 2 
 2 
 
 -2 
 2 
 
 -2 
 1 
 
 
 -2 
 
 
 1 
 
 -2 
 
 
 
 -2 
 
 -1 
 1 
 1 
 2 
 
 -3 
 
 
 
 -2 
 
 
 
 1 
 
 -1 
 
 -2 
 
 -1 
 
 -2 
 
 
 
 -4 
 
 -3 
 
 
 -1 
 
 
 -1 
 
 
 -1 
 1 
 
 
 -2 
 -1 
 
 2 
 
 
 -1 
 
 
 
 1 
 -1 
 
 -4 
 
 2 
 
 3 
 
 -1 
 
 -3 
 
 6 
 
 -3 
 
 -2 
 
 3 
 
 
 
 -5 
 
 3 
 
 2 
 
 3 
 
 -3 
 
 2 
 
 -5 
 
 3 
 
 2 
 
 -3 
 
 
 
 3 
 
 
 
 
 
 -2 
 
 -3 
 
 3 
 
 -2 
 
 -2 
 
 -2 
 
 -6 
 
 
 
 6 
 
 
 
 3 
 
 1 
 
 
 
 
 
 -6 
 
 1 
 
 -2 
 
 -4 
 
 -5 
 
 -5 
 
 -1 
 
 -5 
 
 6 
 
 -4 
 
 2 
 
 -6 
 
 -6 
 
 2 
 
 -4 
 
 -2 
 
 -1 
 
 -2 
 
 -6 
 
 -2 
 
 
 
 1 
 1 
 1 
 
 -2 
 4 
 
 
 1 
 
 
 -2 
 
 -2 
 
 2 
 1 
 1 
 
 -1 
 2 
 1 
 
 -2 
 1 
 
 
 -2 
 1 
 
 -1 
 1 
 3 
 
 -2 
 1 
 1 
 
 -3 
 1 
 2 
 
 -2 
 2 
 
 -2 
 
 -1 
 
 
 -3 
 2 
 1 
 
 -2 
 
 -3 
 
 2 
 
 -2 
 
 -2 
 2 
 
 
 -3 
 
 
 
 
 
 
 
 1 
 
 -2 
 
 -2 
 
 
 
 1 
 
 
 
 -4 
 
 -4 
 
 -3 
 
 -4 
 
 -2 
 
 1 
 
 -4 
 
 2 
 
 -1 
 
 -4 
 
 -2 
 
 -1 
 
 -2 
 
 3 
 
 -1 
 
 1 
 
 5 
 
 2 
 
 2 
 
 -1 
 
 -1 
 
 -3 
 
 2 
 
 -1 
 
 -3 
 
 3 
 
 -2 
 
 -2 
 
 -1 
 
 -1 
 
 -1 
 
 -3 
 
 -3 
 
 -3 
 
 -2 
 
 -1 
 
 
 
 -1 
 
 -3 
 
 1 
 
 
 
 1 
 
 -1 
 
 2 
 
 1 
 
 -3 
 
 2 
 
 
 
 1 
 
 1 
 
 -1 
 
 1 
 
 4 
 
 2 
 
 8 
 
 -4 
 
 -3 
 
 3 
 
 2 
 
 -6 
 
 -3 
 
 -4 
 
 2 
 
 -4 
 
 2 
 
 -5 
 
 
 
 3 
 
 -6 
 
 1 
 
 2 
 
 -3 
 
 2 
 
 3 
 
 
 
 5 
 
 -3 
 
 -2 
 
 -3 
 
 -5 
 
 -6 
 
 2 
 
 -4 
 
 -3 
 
 2 
 
 
 
 
 
 -4 
 
 
 
 -1 
 
 -1 
 
 -5 
 
 -5 
 
 -4 
 
 -3 
 
 2 
 
 
 
 -1 
 
 -1 
 
 -6 
 
 -2 
 
 1 
 
 -1 
 
 -2 
 
 -3 
 
 -6 
 
 -1 
 
 -3 
 
 -4 
 
 1 
 
 1 
 
 -0 
 
 1 
 
 -3 
 
 -2 
 
 -1 
 
 3 
 
 -2 
 
 -3 
 
 -3 
 
 -1 
 
 2 
 
 ~0 
 
 _1 
 
 4 
 
 1 
 
 -3 
 
 -3 
 
 1 
 
 -3 
 
 1 
 
 1 
 
 1 
 
 4 
 
 -1 
 
 1 
 
 1 
 
 -3 
 
 -1 
 
 1 
 
 -1 
 
 1 
 
 1 
 
 1 
 
 1 
 
 -1 
 
 -2 
 
 -1 
 
 -1 
 
 -3 
 
 -1 
 
 -3 
 
 -1 
 
 -1 
 
 -1 
 
 1 
 
 1 
 
 -1 
 
 1 
 
 1 
 
 2 
 
 1 
 
 1 
 
 1 
 
 1 
 
 
 
 1 
 
VITA 
 
 Truman Lee Kelley, born May 25, 1884, Whitehall, Michi- 
 gan. 
 
 Was graduated from the Muskegon High School, scientific 
 course, and from the Hackley Manual Training School, in 1902. 
 Business and business college until entrance into the University 
 of Minnesota, College of Engineering, September, 1903. Entered 
 sophomore class of the University of Illinois, College of Science, 
 September, 1904. After several withdrawals and reentrances 
 received the degrees of A.B., "special honors in mathematics," 
 1909, and A.M., major in psychology, 1911. Scholar and candi- 
 date for Ph.D. degree, Teachers College, Columbia University, 
 1912-13. 
 
 When not in attendance at school variously engaged in mechan- 
 ical industries, farming, business and teaching. Adjunct professor 
 of mathematics, Georgia School of Technology, 1909-10; assis- 
 tant in psychology, 1910-11, and instructor in summer session, 
 1911, University of Illinois; teacher of mathematics, Fresno, 
 California, High School, 1911-12; consulting psychologist, Cul- 
 ver Military Academy, 1913-14; and instructor in educational 
 psychology, Teachers College, Columbia University, summer 
 session, 1914. 
 
 Master's thesis, slightly modified, appeared in November, 
 1913, issue of the Psychological Review, under the title "The 
 Association Experiment; Individual Differences and Correla- 
 tions."