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EDUCATIONAL GUIDANCE

AN EXPERIMENTAL STUDY IN THE ANALYSIS

AND PREDICTION OF ABILITY OF

HIGH SCHOOL PUPILS

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

*?•

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

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

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

.67

.58

.67

.53

.58

.67

.50

.53

.58

.67

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.

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.

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-

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

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

o
o ♦

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.

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.

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, — — ~ '

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

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

Ew+Hv

Et = f(E a +Ev+W-mean 1 ) =1(9+9+4-19) =2.0.

Grading

.5
-1
.5
.5

.5
.5
.5
.5
.5
.5

4
4

1 For table of means see p. 68.

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

E w

{ :i

10.5

4
6

Et = f (10.5+10+3-19) =3.0.

Special Tests and Their Significance

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

.5
.5

.5
.5
.5

.5
.5

.5
.5
.5

9
7.5

E< = f(9 + 10 +7.5 -19) =5.0.

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

.5
.5

-1
-1
-1

.5
-1

.5
.5

Ev
6

3.0

5
6

5.5

Special Tests and Their Significance

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

-1

.5
— 1

2
-1

(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.

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

H v

.5
-1
.5
.5

5
.5

-1

-.5

1.5

Special Tests and Their Significance

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

H v

H w

1.5

.5
.5

-.5
.5

10.0

5.5

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

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.

H v

H w

{:!

10.5

3.5

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.

H v

H w

H a

-1

U 6

{--l

-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

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

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

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

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

2
1
4
7
9
2
1

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.

37.

Life

38.

Lippincott's

39.

Literary Digest

40.

McClure's

41.

Metropolitan

42.

Modern Priscilla

43.

Moving Picture
World

44.

Munsey's

45.

Musician

46.

National Geographic

47.

Outing

48.

Outlook

49.

Photographic Times

50.

Pictorial Review

51.

Popular Mechanics

52.

Popular Science
Monthly

53.

Printer's Ink

54.

Puck

55.

Red Book

56.

Review of Reviews

57.

St. Nicholas

58.

Saturday Ev'g Post

59.

Science

60.

Scientific American

61.

Scribner's

62.

Smart Set

63.

Strand

64.

System

65.

Technical World

66.

Theatre

67.

Woman' s Home Com-
panion

Wilshire's

World's Work

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:

.887

.893

.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.

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

Locke

F. H. Smith

Franklin

Stanley

Haggard

Wallace

M. Warde

McCutcheon

Thompson-Seton

Wiggin

Stevenson

Vance

White

Dickens

Farnol

London
Kipling
Stockton

Garland

Dumas

Dickens
Churchill
L. Scott
Dumas

Gaskell
Barbour

Churchill

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

2.0

-.2

- .2

- .8

1.4

2.2

- .4

- .8

- .4

- .8

- .2

- .8

- .2

- .8

1.5

-1.2

- .8

1.2

- .8

-1.7

- .4

- .2

- .4

- .8

- .6

-1.5

- .8

1.2

- .2

- .6

- .4

- .8

- .6

1.2

1.3

— .8

- .3

- .8

1.2

- .6

- .8

1.2

-1.7

- .4

1.4

Special Tests and Their Significance

Author

Title

Grade

Eng.

Hist

Eliot

Daniel Deronda

1.4

Stevenson

David Balfour

Dickens

David Copperfield

1.1

- .4

Ferber

Dawn O'Hara

- .6

- .7

Aguilar

Days of Bruce

- .3

1.1

Cervantes

Don Quixote

1.2

Dickens

Dombey and Son

1.1

- .4

Major

Dorothy Vernon of Haddon Hall

- .6

Bacheller

Dri and I

Eben Holden

- .2

- .5

Alcott

Eight Cousins

- .2

- .8

Tennyson

Enoch Arden

1.3

- .8

Longfellow

Evangeline

Drummond

Evolution of Man

Spenser

Faerie Queene

2.1

- .8

Poe

Fall of the House of Usher

1.2

- .8

Gaboriau

File Number 113

Fothergill

First Violin

- .4

- .8

Chaplin

Five Hundred Dollars

-1.5

- .9

Porter

Freckles

- .4

- .8

Read

Foul Play

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

Dodge

Hans Brincker

- .8

- .5

Porter

Harvester

Thackeray

Henry Esmond

1.4

Shakespere

Henry V

2.3

Kelly

Her Little Young Ladyship

- .4

- .8

Redpath

History of America

3.5

Hollow of Her Hand

-1.4

- .9

Leblau

Hollow Needle

- .2

Ford

Honorable Peter Sterling

- .4

- .2

Mulford

Hopalong Cassidy

- .9

- .8

Doyle

Hound of the Baskervilles

- .2

Hawthorne

House of Seven Gables

1.2

- .8

Rohlfs

House of the Whispering Pines

-1.2

Clemens

Huckleberry Finn

- .5

Clemens

Innocents Abroad

- .8

Davis

In the Fog

- .4

Crawford

In the Palace of the King

- .2

Deland

Iron Woman

- .4

- .8

Scott

Ivanhoe

1.2

McCutcheon

Jane Cable

-1.7

- .8

Bronte

Jane Eyre

- .8

Ford

Janice Meredith

- .4

1.2

Craik

John Halifax, Gentleman

- .8

Kipling

Jungle Book

- .8

Educational Guidance

Author

Title

Grade

Eng. Hist

Scott

Kenilworth

1.2 1

Smith

Kennedy Square

- .4

Stevenson

Kidnapped

Kipling

Kim

Irving

Knickerbocker History of New York

Williamson

Lady Betty Across the Water

-1.4

Scott

Lady of the Lake

1.2

Cummins

Lamplighter

- .9 -

Lytton

Last Days of Pompeii

.8 1

Cooper

Last of the Mohicans

Reed

Lavender and Old Lace

-1.7

Letters of Abraham Lincoln

.5 2

Johnston

Little Colonel in Arizona

- .9 -

Little Colonel at Boarding School

- .9

Kipling

Light that Failed

.2 -

Dickens

Little Dorrit

1.1 -

Alcott

Little Men

.1 -

Barrie

Little Minister

Fox

Little Shepherd of Kingdom Come

- .4 -

Alcott

Little Women

Blackmore

Lorna Doone

Parrish

Love under Fire

— .8

Rice

Lovey Mary

- .6

Austen

Mansfield Park

Rinehart

Man in Lower Ten

-1.0 -

London

Martin Eden

Dickens

Martin Chuzzlewit

1.1

Bosher

Mary Cary

- .8 -

Zangwill

Master

.2 -

Corelli

Master Christian

-1.2 -

Eliot

Mill on the Floss

1.4 -

Marryat

Mr. Midshipman Easy

-1.2

Hugo

Miserables, Les

1.3 1

Lincoln

Mr. Pratt

-1.2 -

Barclay

Mistress of Shenstone

— 7 —

Rice

Mrs. Wiggs of the Cabbage Patch

- .6

Abbott

Molly Make-believe

- .6 -

Collins

Moonstone

- .2 -

Norris

Mother

- .4

Mother Carey's Chickens

- .4 -

Spearman

Mountain Divide

- .8

Shakespere

Much Ado About Nothing

2.3 -

Verne

Mysterious Island

-1.2 -

Beach

Ne'er Do Well

- .9 -

Net

-1.2

Thackeray

Newcomes

1.4 -

Dickens

Nicholas Nickleby

1.1

Hugo

Notre Dame

1.3

Homer

Odyssey

2.3

Dickens

Old Curiosity Shop

1.1

Page

Old Gentleman of the Black Stock

- .2

Dickens

Oliver Twist

1.1

Burnham

Open Shutters

- .8

Special Tests and Their Significance

Author

Title

Grade

Eng.

Hist.

Darwin

Origin of Species

- .6

- .4

Alcott

Our Helen

- .8

Dickens

Our Mutual Friend

1.1

- .4

E. Smith

Palace Beautiful

-1.2

- .8

Cooper

Pathfinder

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

Flammarion

Popular Astronomy

- .9

-1.4

Austen

Pride and Prejudice

- .8

Clemens

Prince and the Pauper

- .8

Johnson

Prodigious Hickey

-1.2

- .8

Aldrich

Prudence Palfrey

- .5

Harrison

Queed

- .4

Scott

Quentin Durward

1.1

1.2

Sienkiewics

Quo Vadis

1.2

Hornung

Raffles

-1.7

- .4

Jackson

Ramona

Wiggin

Rebecca of Sunnybrook Farm

- .2

- .8

Lytton

Rienzi

1.2

Parkman

Robin Hood

- .8

Thompson-Seton

Rolf in the Woods

- .2

- .4

Le Gallienne

Romance of Zion Chapel

- .8

EHot

Romola

1.9

Barclay

Rosary

-1.2

- .8

Alcott

Rose in Bloom

- .8

Hope

Rupert of Hentzau

-1.0

- .4

Hawthorne

Scarlet Letter

1.1

Porter

Scottish Chiefs

- .4

-1.2

London

Sea Wolf

- .4

Kipling

Seven Seas

- .8

Haggard

She

-1.4

- .4

Wright

Shepherd of the Hills

- .8

Goldsmith

She Stoops to Conquer

1.1

- .4

Eliot

Silas Marner

1.9

- .2

Porter

Song of the Cardinal

- .8

London

Son of the Sun

- .8

Barr

Souls of Passage

- .9

- .8

Reed

Spinner in the Sun

-2.2

- .8

Cooper

Spy

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

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

Educational Guidance

Author

Title

Grade

Eng.

Hist

Thoughts of Marcus Aurelius

- .1

Dumas

Three Guardsmen

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

Ouida

Under Two Flags

- .4

Henty

Under Drake's Flag

-2.4

Alcott

Under the Lilacs

- .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

London

White Fang

- .8

Thompson-Seton

Wild Animals I Have Known

- .2

- .4

King

Wild Olive

- .8

Scott

Woodstock

1.1

1.2

Rohlfs

Woman in the Alcove

-1.6

Hawthorne

Wonder Book

1.1

- .8

Alger

Young Adventurer

-2.2

- .8

Bennett

Your United States

- .2

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

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

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 .

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.

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

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

Lecturer

Librarian

Milliner

Musician

2
5

Member of navy

Nurse

Politician

Secretary

Singer

4
5

4
6

2
4

Charity worker

Dressmaker

Teacher

Domestic science

English

Kindergarten

Physical training or dancing

7
6

Girls

4
6
9

5
5

4
2

2
7
9
8
1
3

2
6
8
8
2
3

1
2
1
1
1
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.

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

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

3
2

4
2
2

5
48
4
3
3
7
3
2
2
4
5
5
7

336
4.5

5
4

16
7
2
1
6
4

1
2
5
2

5
6
3
7
2
1
7
1
2
7
4

2
1
1

Mi Ei Hi

246
3.3

149 109

Special Tests and Their Significance

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

3.7

5.7

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

6
9
6

Educational Guidance

Pupil's
mark

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

9
15

6
6

3
12

30
3

30
15

18
24

3
15
12

144

426

243

66 44 194

Special Tests and Their Significance

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

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

Grade given
by

pupil

3
1

3
2

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

3
2.5

15.5

-29

100
20

197

-11

324

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)

Grade of

Same for

Factor Con-
tributing
to Total
Grade

160
30

190
2.9

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

59 39

135

Special Tests and Their Significance

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

Pupil

1
2

1
1
1

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
1

10.5

-33

66
13

102

-15

176

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

1
3

3
1

3
2
3
3

3
3
3
3

3
3

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:

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

t-l

E°

1 Beginning 2d

year

Gt25

18.5

3/2

1/2

170

260

2 Mid-year 1st

year

At89

3/2

1/2

150

220

3 Entering 1st

year

At72

3/2

1/2

160

200

4 Beginning 2d

year

Gt26

3/2

5.5

1/2

100

190

280

5 Entering 1st

year

At88

17.5

3/2

6.5

1/2

170

240

Special Tests and Their Significance

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

22.5
9

68
153
141

Devia-

Means

tions from

Mean

Divisors

-1

7.5

3/2

1/2

160

-7

200

-59

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.

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.

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

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.

Alg.

Geo.

Eng.

3rd &
4th
Yr.

2nd
Yr.

|Yr.

1st.
Yr.
i Yr.

1 yr.

1 Yr.

§Yr.

i Yr.

1 Yr.

i Yr.

\ Yr.

Groups

2 and 3

4 and 5

A +

2.44

1.99

AJ +

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

.80

.96

.51

1.28

.55

.78

.68

.67

1.29

.29

.67

Bk-

.57

.44

.23

.92

.38

.06

.08

.58

.07

.15

.21

- .05

.77

- .05

.28

CJ+

.17

- .24

- .08

.15

- .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

- .77

-1.09

-2.16

-1.46

-1.11

-1.99

- .88

-2.16

-1.33

-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§ +

-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

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

grade:

1.41

1.80

1.57

2.03

A-B = .86

A-B=1.04

A-B=1.05

A-B=1.22

.55

.76

.52

.81

B-C = .71

B-C=1.00

B-C= .80

B-C= .91

- .16

- .24

- .28

- .10

C-D = .86

C-D=1.10

C-D= .99

C-D= .89

-1.02

-1.34

-1.27

- .99

D-E = .93

D-E=1.27

D-E=1.06

D-E=1.04

-1.95

E-F = .88

-2.61

-2.33

-2.03

-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

.83

1.13

1.12

Average of all = 1.02

Appendix

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

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.

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

2
3
4

.67
.58
.53
.50

.67
.58
.53

.67
.58

.67

<r's

0"3

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

Appendix

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

.92

.95

.74

.79

.74

.76

.66

.73

.66

.68

.63

.69

.63

.65

.61

.67

.61

.63

.59

.66

.59

.61

.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,

Educational Guidance

The various coefficients of correlation and standard deviations required; are
given in the following table:

7.0

A'
B'

c's Estimated

A
.39
.41
.39

.17
.41
10.3

.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\

(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'

.25

-.06

.13

.22

.19

.06

.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:

°" 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 a

.84

.59

.86

.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 a

.31

.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

Spts.

Ents.

Vocs.

F.ofA.

Wds.

Mags.

.20

.14

.24

.04

.26

.37

.13

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.

.24

.20

.21

.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 .

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

Mi Ei

.15

.46

.21

.32

.54 .63

5.23

4.64 3.13

.02

.27

.21

.30

.54

.63

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.

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

Educational Guidance

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+ + ++ I + +

'3 OOOPQPPOpOfQOP OWH

++ + + +

•3 IV _- H QQOpqoOCQOHOOpmOPP

Appendix 111

II I rt I I l ri l l^l I I

HW^HiflWHNO N^tOifiiOHOtBHONnHHOH

I I I I II III I

CO IN i-l -H CO OS rH IN t» CO Tj< r-l CM •* •* lfl> i-H eB CO IN U5 IN IN CO CO

I I I I I I I I I I I

0000'<llC«IN'*«OHfflNNiOINN!ONOO'00*'*NNTl<
II I I I ~ If

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II II I I I I I

O rH CO CO ■* CO ■* O "* CO fi CO rH ■* CO •* CN CO rH CO b- IN CO CN

II II I I I I I

CN-*0-*CNOOOCOt>.COlO^OlNOCOM(NT}(TjliO'*COCOT)<iN
rt I II I II I I I I

■*U5TjlOCNINiNOt»COCO!OcNO'*>OCO'*<N'cH'*iNtNWCOCN
I I I l H l I I I I I f I I I I

TjtiO^OJCON^^COOCNcOINlN-^C-rjHlNOT^iNrHCNOCOCN
I I I I rt I I f I I f I I

CO«5CNIN'-llNCOTt<>OOlOcO(NIN'*Tt<I>'*lNOt»iN(N(NOCN
I I I l H II II I I f

+ \+ ++I ++ ++ +

PPO ffl QOOOOOOPQ « WQQO

Q Q O O

I +

WO H O Q

+ + ++ I +

BOH HO 0««0 QOOOOOOBPQfl

+ + -M-+ ++ +M +

OQmOQOQWQ«1QOoO«««OOOOQQMOO

++++++ + + +

QompqQQOfflom«moo«««o«o«wq«mo

+ ++ ++++++

pqpq«mQQwmo«oopqqomomeQPOHWHQO

+ + + + ++ + +

Qpq«0«OfflQ«MQo «« 000<HQ«po

+ + ++ 4- ++ + +

QOttWQQQffl pqo«Oo<iJmWQ«QmHOpqoO

+ + ++ + + +

OOOOQQ O PQQQOOQPQOOfflQOHW QQ

112

Educational Guidance

■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

■V- -M i I I I I I I II

si
©

*V= W I I I

I I I I I I I IT I I

a I I rt I th IT I I I I I l rt I I IT I I I

I UU *^ II I rH rH | II II | I

I I

H -

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9 i

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o §

suoo , ,h ! _, rH , iii |T H, ,

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+ ++ + +++++ +
•[aosijAi o mm oo q omoftmomoo porno o

'«0 ft

•JJ

«1 <!QO

QPQ

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ft<JQQ

1+ + + I II + + + ++

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•TOO ++ + + + + + +

• s ooft«oo«iom ooo oomooo mopomomft

+ +++ + + + + + + +++ +++

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++ +++++ + +++ + ++ +4-

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•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

Appendix 113

cocococoocococ^r^coiNcococ<icocococococo:ocoi-icococo"OcoM^^coNcoMcocOT)<coMcOT*ro

-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

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I I I I I II I II I I I I I I I II

I I I I I I I II I I I I I I I II I 7 - 1

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l rt I rt II II II If III Mil

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

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

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J. J. _L _i_ J.

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Appendix

115

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I I I I

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JL +++++1 +L+ i + +

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i + i i +1+ 1+ + + +

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+ + ' +++

1+++ + + ++L+ ++ +

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v»n oomoooomoomoomoomoomooomm

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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.

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

-10

-4
10

-1
1

-3

10
7
7
3
3
5

-6

-1
7

-4
5

-4

-3

-5

-2

-1
8
6
2
6
2
5

-1

-2
4

-1
6

-2

-5

-1

-10

-1

-4

-6

-2

-1

-10

-2

-6

-2

-1

-6

-2

-4

-2

* 5

-2

-8

-5

-2

-1

-3

-6

-3

-5

-3

-2

-1

-3

-2

-1

-4

-2

-3

-1

-2

-1

-5

—2

-2

-3

-2

-3

-1

-2

-1

-2

-1

7b 7h

6m 6b 6a

5m 5b 5h

4th Gr.

4b 4h

-3

-4

-3

-1

-2

-3

-5

-1

-3

-1

-2

-3

-1

-2

-1

-2

-1

-4

-1

-4

-2

-3

-2

-1

-2

-1

-3

-1

-3

-1

-4

-1

-2

-1

-4

-1

-4

-2

-4

-1

-3

-2

-3

-1

-3

-2

-1

-3

-1

-3

-1

1
1

-4
-1

3
1
1
-1

-1

-6

-3
3
5

-6
3

-4
3

-5
3

-1

-2
3

-1

-3
2
1

-3
2

-2
1

-1

-3
2
5

-1
4
2
3

-5
2
2

-3

-4

-1

-3

-4

-1
1

-3

2
2

-2
2

-2
1

-2

-1
1
1
2

-3

-2

-1

-2

-1

-2

-4

-3

-1

-1
1

-2
-1

-1

1
-1

-4

-1

-3

-2

-5

-3

-5

-3

-2

-3

-2

-6

-2

-4

-5

-1

-5

-4

-6

-4

-2

-1

-2

-6

-2

1
1
1

-2
4

-2

2
1
1

-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

-3

-2

-4

-3

-4

-2

-4

-1

-4

-2

-1

-2

-1

-3

-1

-3

-2

-1

-3

-2

-1

-3

-1

-3

-1

-4

-3

-6

-3

-4

-5

-6

-3

-2

-3

-5

-6

-4

-3

-4

-1

-5

-4

-3

-1

-6

-2

-1

-2

-3

-6

-1

-3

-4

-0

-3

-2

-1

-2

-3

-1

-3

-1

-3

-1

-2

-1

-3

-1

-3

-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."