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the three groups, a derivation of the Pearson formula

was used (52), r=2 Av(^Y i a and b being the reduced

measures in the test and typewriting. The following table

gives the correlations of the tests with abilities in type-

writing.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 27

II. Correlations.

Group 1. Group 2. Group 3.

k

O & Q fe g < <t& fe pq pq pq

Verb-object .41 .43 .46 .55 .21 .57 .46 .28 .32 .34 .33 .35

No. check. .45 .47 .37 .53 -.01 .30 .45 .28 .34 .41 .34 .39

Color naming .30 .43 .55 .41 .29 .61 .40 .39 .39 .40 .36 .38

Action-agent .42 .43 .29 .41 .00 .40 .39 .13 .29 .26 .29 .28

Agent-action .29 .19 .40 .31 -.02 .28 .30 .02 .20 .24 .18 .26

Form subs. .21 .27 .11 .37 .30 .42 .24 .04 .14 .17 .17 .20

Hard dir. .11 .14 .19 .13 .34 .32 .14 -.20 -.20 -.08 .16 .19

Mixed rel. -.09 .21 .17 .25 .04 .00 .13 -.07 -.12 -.09 .03 -.04

Opposites .17 .11 .07 .15 .19 .54 .12 -.09 -.09 -.11 -.07 .06

No. of subj. 42 40 40 40 29 27 40 38 38 38 65 65

E. Discussion of correlations.

a. Significant tests for typewriting and significant tests

for stenography and grammar.

In comparing the correlations obtained between tests and

typewriting with the correlations between tests and stenog-

raphy and grammar, if a line is drawn horizontally across

the paper in the middle of the list of tests, in each of the

preceding tables, it will be observed that, in most cases, the

tests which correlated best with stenography and grammar

and worst with typewriting lie below this line and the tests

which correlate best with typewriting and worst with

stenography and grammar lie above this line. The two tests

which are not language tests, number checking and form sub-

stitution, do not correlate well, except in one instance, with

stenography and grammar, but one correlates very well and

the other fairly well with typewriting.

b. Typewriting, group 1.

In considering the first four months' correlations in type-

writing one is met with the uniformity of the results for any

one test during those four months. If a test correlates well

with one month's measures of abilities in typewriting, it can

be predicted that it will correlate well with another month's

measures; if a test correlates poorly with one month's

measures it can be predicted that it will correlate poorly

with another month's measures.

28 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

The March correlations with the verb-object, number

checking, agent-action and hard directions tests show no

correspondence with the correlations for these tests for the

first four months. This can be accounted for as follows:

The March typewriting test was an especially difficult one

which probably means that it called for reactions which the

subjects had not formed the habits of making or that it called

for the functioning of processes which did not exist or which

were not well developed. Since the exercise was exceptional

it could be expected that the results of the exercise would be

exceptional and it is quite possible that the correlations would

be exceptional and that the uniformity of correlation would

be absent. It will also be observed that the number of sub-

jects dropped from forty to twenty-nine this month.

The April correlations show a good degree of correspond-

ence with the correlations for the first four months except

for the form substitution, hard directions, and opposites

tests. Here again it will be observed that only twenty-seven

subjects took the exercise. This reduction in the number of

subjects taking the exercise does not mean entirely a process

of the elimination of the poorer typists; some of the the

poorer typists had dropped out of the course and some of the

best typists were in the University offices working as typists.

Inspection of the table will show that in the first three tests

in the list, those which correlate highest with typewriting,

and correlations are usually higher each month as the sub-

jects acquire more speed in typing.

c. Typewriting, groups 2 and 3.

In the tests which correlate well in group 2 the correla-

tions with the best week's measure of ability are higher than

the correlations with the five weeks' measure of ability, and

the correlations with the best day's measure of ability are

higher than either the correlations of the five weeks' or the

best week's measure of ability. In the same tests in group 3

the correlations with the best day's measure of ability are

higher than correlations with the fifth and sixth weeks' meas-

ure of ability. The best day measures the ability when a spurt

is made and the best spurt over a long period of time is prob-

ably the best indexf of a subject's ultimate ability that can be

found in practice of groups of this sort. Since the correla-

tions are higher in these short intense periods it is concluded

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 29

that the tests tend to measure the physiological ability in

typewriting.

d. Typewriting, groups 1, 2 and 3.

The seventh column in the table, the average of the cor-

relations for October, November, December and February

was obtained as a means of comparison of group 1 with

groups 2 and 3 rather than comparing any one month's cor-

relations of group 1 with the correlations of group 2 and 3.

In groups 2 and 3 the correlations, for the first four tests in

the list, in every case, are lower than those of group 1. With

slight exceptions the tests which are correlated well in one

group are correlated well in other groups and the tests which

are correlated poorly in one group are correlated poorly in

other groups.

F. Partial correlations.

The four tests which were correlated highest with type-

writing ability were used in deriving a multiple correlation

with the measures obtained in the typewriting exercise of

February in group 1.

The calculation of the regression equation with five vari-

ables is, Measure in typewriting = .3721 (measure in verb-

object) + .0109 (measure in color naming) + .0848 (measure

in number checking) -j- .0852 (measure in action-agent).

Or for practical purposes, after multiplying by 24.3, a conven-

ient constant; Measure in typewriting = 9 (measure in

verb-object) + .3 (measure in color naming) + 2. (measure

in number checking) -|- 2 (measure in action-agent). After

performing the arithmetic this gives a correlation of .61 with

a probable error of .07.

30 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

5. Applicability of the results.

The correlation method has been used to measure the

degree of association between performance in the tests and

typing ability and it is now necessary to obtain the line of re-

gression or the line of best fit in order to predict, for any in-

dividual in the group, her most probable performance in typ-

ing from her performance in the tests.

The accompanying diagrams, appended hereto, show fre-

quency distributions in groups 1, 2 and 3 of the reduced meas-

ures in the combination of the four tests, as obtained by the

weights assigned by the method of partial correlation, and the

reduced measures in typewriting, the former being plotted on

the x axis and the latter on the y axis. From the general

sweep of the scatter diagrams, it is evident that, as the meas-

ures in typewriting increase or decrease the measures in the

combination of the four tests increase or decrease. The

straight line AB, giving the best fit to the data, is fitted to the

points in the diagrams by means of the formula y=mx-f-b

which for group 1 becomes y = .68x + .OOb.*

The expression best fit is seldom defined. Its significance

varies with the problem in hand and it generally means a

fit which is convenient and which for the problem to be solved,

gives satisfactory results. The principle upon which the

values of m and b are determined is so to choose m and b as

to make the mean square deviation of the observations from

the resulting straight line a minimum. The pertinancy of

this principle for the problem of prediction is plain since

when observations are distributed according to the normal

law, the Tables of the Probability Integral enable us to com-

*y = mx -f b or y "y = r ^ x x where y, x and try, <rx are the means

and the standard deviations, respectively of the y's and x's.

pute the probability of a deviation equal to any multiple or

submultiple of the root mean square deviation. Moreover,

as in all problems of prediction it is desirable to have the root

mean square deviation as small as possible it is obvious that

a straight line which fits given data so as to make the mean

square deviation of the points from a straight line a minimum

is, for the problem of predicting one variable from a knowl-

edge of the other, a good fit to the data.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 31

We have found the best fitting straight line connecting

performances in the tests and ability in typewriting by means

of the formula y=mx+b. For any given value of x, repre-

senting a performance in the tests, we can predict, by means of

this formula, the most probable performance which will be

achieved in typing. The problem is not completely solved by

finding the equation connecting the two variables. We are

not content to predict the most probable values of y, but we

wish to know, in addition, the degree of accuracy of the pre-

dictions. The scatter formula supplies an answer to this lat-

ter question. The formula S (scatter) = o-y ^2 (30)* shows

the accuracy with which, using the equation to the best fitting

straight line, the magnitude of the one variable may be pre-

dicted from a knowledge of the other. Substituting the val-

ues, for group 1, in the formula gives S=84.t When the as-

sociation between the two variables is perfect, or when r =

1., S = and all of the points lie on the straight line, and by

means of the equation to the best fitting straight line, we can

predict exactly the value of y corresponding to a given value of

x. But it is an exceedingly rare case when r = 1, and when

r lies between these two limiting values, we can still predict

the results with a knowledge of the probabilities in favor

of the prediction. When the association between the two

variables is not perfect, r falls between the limiting values

1, and the equation to the best fitting straight line enables

the computation of the most probable value of y corresponding

to a given value of x and the value S shows the accuracy with

which, using this equation to the best fitting straight line,

the magnitude of the one variable may be predicted from a

knowledge of the other or enables us to say within what limits

any proportion of the measures are scattered about the

straight line. The degree of association between performance

in the tests and typing ability is measured by the correlation

formula whose value is r = .61: the formula by means of

which typing ability can be predicted from performance in

the tests is y=.68x+.00b: and the error of the predictions

is measured by means of the scatter formula the value of

which in this case is S = 84.

It is known from the Table of the Probability Integral

that when the distribution of the points about the straight line

*For the derivation of this formula the reader is referred to Chapter 2.

fS = <ry \/T^ = 106.5 Vi-.6i2 = 84.

32 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

is normal, 99.7 per cent of the observations lie within a de-

viation from the straight line equal to 3S, 95 per cent lie

between 2S, and 68 per cent lie between S. Since S =

84, 2S = 168. In the chart for group 1 the lines 2S are

drawn parallel to the line AB and 168 points above and below

it, respectively, on the y axis.

The accuracy of the forecasts is measured by S = oTy'TT 2

where o-y is the standard deviation of a concrete series, and r

is the correlation between the two series. S measures the

accuracy of the predictions because it shows how the predic-

tion formula enables us to reduce their variability. If there

were no predicting formula the variability of the series that

we wish to know would be o-y but by the use of the formula the

variability of the predictions is only o-y fr*. The factor TI^T*

measures the reduction in variability that is gained by means

of the predicting formula. If, therefore, we wish to compare

the accuracy of predictions of two different series, ay being

constant, the measure of the relative accuracy is given by

jT^i and the smaller the value of v^r 2 > the greater the ac-

curacy of the predictions. The same idea may be put in a

different way by saying that the greater the value of r, the

greater the accuracy of the predictions.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 33

Fig. 1

34 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

ISO

-ISO-

/

-is

X

X

t I

-aoo -i

I

-io -so

III''

TESTS

Fig. 2

Scatter Diagram for Group 2. r = .47. y = .59x + .OOb.

2s = 186. Pop. = 38.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 35

I

-ISO **i

1

-/do -So

I I I I

+So 4190 -HSb tloo

Fig. 3

Scatter Diagram for Group 3. r = .45. y = .515x -j- .OOb.

2s 187. Pop. = 65.

36 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

In group 1 all but five subjects received passing grades in

typewriting which, in terms of the diagram, means that all

subjects scoring above 150 on the y axis accomplished sat-

isfactory work. We will take this point, for the group, as

being the lowest point to which any one subject may reach

and still do satisfactory work in typing, then it can be predict-

ed with 95 per cent accuracy that all the subjects who score

-(-25 in the combination of the four tests will score between

150 and +185 in typewriting or will accomplish satisfac-

tory work in typewriting (intersection of the line 2S with

+25 on the x axis = 150 on the y axis and the intersection

of the line +2S with +25 on the x axis = +185 on the y

axis) . Or for any specific individual such as one, for instance,

who receives a score of +225 in the tests, we can predict that

she will be able to accomplish a score of +150 in typewriting

(intersection of the line of best fit with +225 on the x axis =

+150 on the y axis) and we know with 95 per cent accuracy

that her accomplishment in typewriting will not be lower

than 12 nor higher than +304 (intersection of the line

2S with +225 on the x axis = 12 on the y axis and the in-

tersection of the line +2S with +225 on the y axis +304 on

the y axis) . For convenience the reduced measures have been

used. After the arithmetic of balancing the scores in the

tests has been computed the same thing may be accomplished

with the actual scores in the tests and in typewriting.

There appears to be a great deal of difference in the opin-

ions of psychologists as to just how much of a coefficient of

correlation, with its probable error, constitutes a significant

correlation, some psychologists having reported figures lower

than .25 as being significant coefficients of correlation. Some

of this, confusion can be cleared up by means of this method,

and the practical significance of coefficients of correlation may

be determined.

The problem of vocational guidance is to give an individual

counsel as to what sort of an occupation or profession his

potential capacities fit him for, so that he can be definitely

informed that he will be successful in certain lines of endeavor

and unsuccessful in certain other lines, or in more specific

cases for any one occupation such as assembling, typewriting,

teaching psychology, etc., whether the individual will be a

success or a failure and to just what degree he will be a success

or a failure in that specific occupation. Unless the chances

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 37

of an individual succeeding or not succeeding are very accu-

rately determined it does the individual very little good to

know that his chances for success are such and such a percent,

as seventy-nine or eighty-two percent, etc. For the problem

in hand, in the typewriting occupation, this sort of counsel

given to an individual may result in her spending an amount

of time ranging from a few months upward in training and

then she may finally learn that she is one of those unfortunate

ones outside of the seventy-nine percent and that she will

never become a successful typist. It is evident that of ten in-

dividuals examined if we can predict that the chances for

success in each case is, say, approximately eighty-nine per-

cent and they are all counselled to take up, the study of type-

writing and go through a period of training and at the end

of the training period nine develop into successful typists and

one becomes a failure at typing then as far as this one in-

dividual is concerned she has been misguided and her time and

expense of training has been wasted to say nothing of the

effect that the failure may have on her temperament and

character.

Vocational guidance should mean accurate scientific pre-

diction for each individual and if, in the future, applied psy-

chology, in the field of vocational guidance, would escape the

many abuses that have been heaped upon it in the past it will

not attempt to establish a system of vocational guidance

until it can be almost perfectly sure of each and every one of

its predictions. To establish such a system of vocational

guidance which is to make no grave errors it will probably

be necessary to have a coefficient of correlation well above

ninety with a very small probable error and with a small scat-

ter value; just what coefficient of correlation, probable error,

and scatter value will be necessary will probably be impossible

to accurately determine until the actual work has been accom-

plished and the scatter diagrams drawn and interpreted.

From the results of this research, it is interesting to know

that we can predict that individual A who scores 140 in the

psychological tests will most probably attain an ultimate abil-

ity in typing of forty words per minute, and in 99.7 percent of

the cases she will attain an ultimate ability in typing varying

between not more than thirty-one to forty-nine words per

minute, and that individual B, who scores ninety-six in the

psychological tests will probably attain an ultimate ability in

38 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

typing of thirty-two words per minute and in 99.7 percent of

all such cases she will attain an ultimate ability in typing

varying not more than between twenty-three to forty-one

words per minute. But it will readily be seen that these pre-

dictions are of very little practical value for the individual

in that they afford her very little definite information about

just what ultimate ability she, individually, will attain. From

our data we can readily predict that in all probability A will

become a better typist than B but still it is quite possible for

A to develop into a poorer typist than B. The results of this

research show, then, that the correlations are not high enough

and the scatter value is not small enough to warrant the es-

tablishment of a system of vocational guidance whereby an in-

dividual can be advised, with any sufficient degree of safety,

to undertake or not to undertake to prepare herself to become

a typist.

The problem of vocational guidance, then, is supplied by the

individual who wants to know of what his potential capacities

consist and what sorts of occupations he is fitted to follow

successfully and what sorts of occupations he is not fitted to

follow successfully. The problem of vocational selection is of an

other sort, here the need is supplied by the profession or the

industrial concern and not directly by the individual. The

problem of vocational selection is given a certain number

of applicants in excess of the number required for a specific

job, to select those who, on the whole, are best fitted to succeed.

In practical life the employment manager has a number of

vacancies open for a specific job and of a limited number of

applicants for that job his problem is to select from the ap-

plicants those who, on the whole, are most likely to succeed.

If ten jobs in the typewriting department are open and twenty

typists are induced to apply for the jobs the problem is to se-

lect the ten who, on the whole, will do the best work. If this

can be accomplished there will be an ideal state of affairs.

However, this ideal has never been reached in any system of

vocational selection. If we have something which works

with some degree of success, with such a degree of success

never before attained by any other method, which has been

checked up scientifically, then we are justified from a prag-

matic view point in using it until a better method appears.

If we can have a system of vocational selection which can pick

from the twenty applicants (ten poor ones and ten good ones)

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 39

a majority of the good ones and weed out a majority of the

poor ones we have something which works and which is val-

uable. If by our method of selection of ten typists from

twenty applicants eight finally turn out to be very good typ-

ists, one a typist of medium ability, and one a poor typist then

we have erred to some extent but on the whole we have made

a selection which is a good one. By pure chance we would

probably have selected five good typists and five poor typists

and practically all of the traditional methods of selecting

typists appear to do nothing more than this even if they ac-

complish this much.

It is evident from the foregoing data that this method of

empirical vocational tests gives a far more reliable criterion

of vocational selection in the field of typewriting than has

been obtained by any other method. If a commercial concern

finds it necessary to employ a number of typists a test in typ-

ing may be given, as so many concerns do, which may or may

not determine the actual ability in typing at the moment.

This will insure the concern that they are not hiring people

who, at the moment are wholly inefficient. However, if we are

looking forward to the ultimate ability which the typists will

achieve it is not safe to hire a person to do typing on the basis

of the performance of a sample of typing for the typing abil-

ity of a person when she first enters the employ of a concern

is often no index of the ability that she may develop.f Along

with the test in typing the team of tests may be administered

and from the results the employer may predict with 95 per-

cent accuracy or with 99.7 percent accuracy, or with any other

degree of accuracy that is required whether or not the appli-

cants will develop into good typists and in addition within just

what limits their capacities in typing will enable them to de-

velop in this field, these predictions being made in definite

quantitative terms such as the net number of words written

per minute.* The prediction of ability by means of the tests

will do injustice to some individuals but it will vindicate it-

fin group 3 there was a coefficient of correlation of .28 with a prob-

able error of .10 between the first day's output and the best day's output,

the latter measure being taken within a period of six weeks.

*The supply of typists in New York City in the last few years has

been sufficient to enable a high degree of selection to be made. During

the time in which the experiment was carried on in the commercial con-

cern, in 1917, applications were received from two hundred and eighty-

two typists for ninety-six positions which were open during that period.

40 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

self by the percentage of best applicants, and the percentage

of poorest applicants which it will be able to detect.

Some concerns require an average of twenty-two words of

connected discourse to be written per minute, others require

thirty-five words, others forty-three words, and so on. Some

concerns require twenty words of unconnected discourse to be

written per minute, other concerns require ninety-five strokes

of indexing work to be written per minute and so on. There

are then various degrees of quantitative and qualitative typ-

ing required by various concerns and a typist who is capaci-

tated to satisfy the requirements of one concern may not be

capacitated to satisfy the requirements of another concern.

The tests have developed a definite scale of efficiency in typing,

from lower to higher grades. Since each of the various con-

cerns requires a different average ability in its typists, higher

or lower than that required by other concerns, it will be neces-

sary, before the tests can be adequately applied, first to deter-

was used (52), r=2 Av(^Y i a and b being the reduced

measures in the test and typewriting. The following table

gives the correlations of the tests with abilities in type-

writing.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 27

II. Correlations.

Group 1. Group 2. Group 3.

k

O & Q fe g < <t& fe pq pq pq

Verb-object .41 .43 .46 .55 .21 .57 .46 .28 .32 .34 .33 .35

No. check. .45 .47 .37 .53 -.01 .30 .45 .28 .34 .41 .34 .39

Color naming .30 .43 .55 .41 .29 .61 .40 .39 .39 .40 .36 .38

Action-agent .42 .43 .29 .41 .00 .40 .39 .13 .29 .26 .29 .28

Agent-action .29 .19 .40 .31 -.02 .28 .30 .02 .20 .24 .18 .26

Form subs. .21 .27 .11 .37 .30 .42 .24 .04 .14 .17 .17 .20

Hard dir. .11 .14 .19 .13 .34 .32 .14 -.20 -.20 -.08 .16 .19

Mixed rel. -.09 .21 .17 .25 .04 .00 .13 -.07 -.12 -.09 .03 -.04

Opposites .17 .11 .07 .15 .19 .54 .12 -.09 -.09 -.11 -.07 .06

No. of subj. 42 40 40 40 29 27 40 38 38 38 65 65

E. Discussion of correlations.

a. Significant tests for typewriting and significant tests

for stenography and grammar.

In comparing the correlations obtained between tests and

typewriting with the correlations between tests and stenog-

raphy and grammar, if a line is drawn horizontally across

the paper in the middle of the list of tests, in each of the

preceding tables, it will be observed that, in most cases, the

tests which correlated best with stenography and grammar

and worst with typewriting lie below this line and the tests

which correlate best with typewriting and worst with

stenography and grammar lie above this line. The two tests

which are not language tests, number checking and form sub-

stitution, do not correlate well, except in one instance, with

stenography and grammar, but one correlates very well and

the other fairly well with typewriting.

b. Typewriting, group 1.

In considering the first four months' correlations in type-

writing one is met with the uniformity of the results for any

one test during those four months. If a test correlates well

with one month's measures of abilities in typewriting, it can

be predicted that it will correlate well with another month's

measures; if a test correlates poorly with one month's

measures it can be predicted that it will correlate poorly

with another month's measures.

28 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

The March correlations with the verb-object, number

checking, agent-action and hard directions tests show no

correspondence with the correlations for these tests for the

first four months. This can be accounted for as follows:

The March typewriting test was an especially difficult one

which probably means that it called for reactions which the

subjects had not formed the habits of making or that it called

for the functioning of processes which did not exist or which

were not well developed. Since the exercise was exceptional

it could be expected that the results of the exercise would be

exceptional and it is quite possible that the correlations would

be exceptional and that the uniformity of correlation would

be absent. It will also be observed that the number of sub-

jects dropped from forty to twenty-nine this month.

The April correlations show a good degree of correspond-

ence with the correlations for the first four months except

for the form substitution, hard directions, and opposites

tests. Here again it will be observed that only twenty-seven

subjects took the exercise. This reduction in the number of

subjects taking the exercise does not mean entirely a process

of the elimination of the poorer typists; some of the the

poorer typists had dropped out of the course and some of the

best typists were in the University offices working as typists.

Inspection of the table will show that in the first three tests

in the list, those which correlate highest with typewriting,

and correlations are usually higher each month as the sub-

jects acquire more speed in typing.

c. Typewriting, groups 2 and 3.

In the tests which correlate well in group 2 the correla-

tions with the best week's measure of ability are higher than

the correlations with the five weeks' measure of ability, and

the correlations with the best day's measure of ability are

higher than either the correlations of the five weeks' or the

best week's measure of ability. In the same tests in group 3

the correlations with the best day's measure of ability are

higher than correlations with the fifth and sixth weeks' meas-

ure of ability. The best day measures the ability when a spurt

is made and the best spurt over a long period of time is prob-

ably the best indexf of a subject's ultimate ability that can be

found in practice of groups of this sort. Since the correla-

tions are higher in these short intense periods it is concluded

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 29

that the tests tend to measure the physiological ability in

typewriting.

d. Typewriting, groups 1, 2 and 3.

The seventh column in the table, the average of the cor-

relations for October, November, December and February

was obtained as a means of comparison of group 1 with

groups 2 and 3 rather than comparing any one month's cor-

relations of group 1 with the correlations of group 2 and 3.

In groups 2 and 3 the correlations, for the first four tests in

the list, in every case, are lower than those of group 1. With

slight exceptions the tests which are correlated well in one

group are correlated well in other groups and the tests which

are correlated poorly in one group are correlated poorly in

other groups.

F. Partial correlations.

The four tests which were correlated highest with type-

writing ability were used in deriving a multiple correlation

with the measures obtained in the typewriting exercise of

February in group 1.

The calculation of the regression equation with five vari-

ables is, Measure in typewriting = .3721 (measure in verb-

object) + .0109 (measure in color naming) + .0848 (measure

in number checking) -j- .0852 (measure in action-agent).

Or for practical purposes, after multiplying by 24.3, a conven-

ient constant; Measure in typewriting = 9 (measure in

verb-object) + .3 (measure in color naming) + 2. (measure

in number checking) -|- 2 (measure in action-agent). After

performing the arithmetic this gives a correlation of .61 with

a probable error of .07.

30 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

5. Applicability of the results.

The correlation method has been used to measure the

degree of association between performance in the tests and

typing ability and it is now necessary to obtain the line of re-

gression or the line of best fit in order to predict, for any in-

dividual in the group, her most probable performance in typ-

ing from her performance in the tests.

The accompanying diagrams, appended hereto, show fre-

quency distributions in groups 1, 2 and 3 of the reduced meas-

ures in the combination of the four tests, as obtained by the

weights assigned by the method of partial correlation, and the

reduced measures in typewriting, the former being plotted on

the x axis and the latter on the y axis. From the general

sweep of the scatter diagrams, it is evident that, as the meas-

ures in typewriting increase or decrease the measures in the

combination of the four tests increase or decrease. The

straight line AB, giving the best fit to the data, is fitted to the

points in the diagrams by means of the formula y=mx-f-b

which for group 1 becomes y = .68x + .OOb.*

The expression best fit is seldom defined. Its significance

varies with the problem in hand and it generally means a

fit which is convenient and which for the problem to be solved,

gives satisfactory results. The principle upon which the

values of m and b are determined is so to choose m and b as

to make the mean square deviation of the observations from

the resulting straight line a minimum. The pertinancy of

this principle for the problem of prediction is plain since

when observations are distributed according to the normal

law, the Tables of the Probability Integral enable us to com-

*y = mx -f b or y "y = r ^ x x where y, x and try, <rx are the means

and the standard deviations, respectively of the y's and x's.

pute the probability of a deviation equal to any multiple or

submultiple of the root mean square deviation. Moreover,

as in all problems of prediction it is desirable to have the root

mean square deviation as small as possible it is obvious that

a straight line which fits given data so as to make the mean

square deviation of the points from a straight line a minimum

is, for the problem of predicting one variable from a knowl-

edge of the other, a good fit to the data.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 31

We have found the best fitting straight line connecting

performances in the tests and ability in typewriting by means

of the formula y=mx+b. For any given value of x, repre-

senting a performance in the tests, we can predict, by means of

this formula, the most probable performance which will be

achieved in typing. The problem is not completely solved by

finding the equation connecting the two variables. We are

not content to predict the most probable values of y, but we

wish to know, in addition, the degree of accuracy of the pre-

dictions. The scatter formula supplies an answer to this lat-

ter question. The formula S (scatter) = o-y ^2 (30)* shows

the accuracy with which, using the equation to the best fitting

straight line, the magnitude of the one variable may be pre-

dicted from a knowledge of the other. Substituting the val-

ues, for group 1, in the formula gives S=84.t When the as-

sociation between the two variables is perfect, or when r =

1., S = and all of the points lie on the straight line, and by

means of the equation to the best fitting straight line, we can

predict exactly the value of y corresponding to a given value of

x. But it is an exceedingly rare case when r = 1, and when

r lies between these two limiting values, we can still predict

the results with a knowledge of the probabilities in favor

of the prediction. When the association between the two

variables is not perfect, r falls between the limiting values

1, and the equation to the best fitting straight line enables

the computation of the most probable value of y corresponding

to a given value of x and the value S shows the accuracy with

which, using this equation to the best fitting straight line,

the magnitude of the one variable may be predicted from a

knowledge of the other or enables us to say within what limits

any proportion of the measures are scattered about the

straight line. The degree of association between performance

in the tests and typing ability is measured by the correlation

formula whose value is r = .61: the formula by means of

which typing ability can be predicted from performance in

the tests is y=.68x+.00b: and the error of the predictions

is measured by means of the scatter formula the value of

which in this case is S = 84.

It is known from the Table of the Probability Integral

that when the distribution of the points about the straight line

*For the derivation of this formula the reader is referred to Chapter 2.

fS = <ry \/T^ = 106.5 Vi-.6i2 = 84.

32 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

is normal, 99.7 per cent of the observations lie within a de-

viation from the straight line equal to 3S, 95 per cent lie

between 2S, and 68 per cent lie between S. Since S =

84, 2S = 168. In the chart for group 1 the lines 2S are

drawn parallel to the line AB and 168 points above and below

it, respectively, on the y axis.

The accuracy of the forecasts is measured by S = oTy'TT 2

where o-y is the standard deviation of a concrete series, and r

is the correlation between the two series. S measures the

accuracy of the predictions because it shows how the predic-

tion formula enables us to reduce their variability. If there

were no predicting formula the variability of the series that

we wish to know would be o-y but by the use of the formula the

variability of the predictions is only o-y fr*. The factor TI^T*

measures the reduction in variability that is gained by means

of the predicting formula. If, therefore, we wish to compare

the accuracy of predictions of two different series, ay being

constant, the measure of the relative accuracy is given by

jT^i and the smaller the value of v^r 2 > the greater the ac-

curacy of the predictions. The same idea may be put in a

different way by saying that the greater the value of r, the

greater the accuracy of the predictions.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 33

Fig. 1

34 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

ISO

-ISO-

/

-is

X

X

t I

-aoo -i

I

-io -so

III''

TESTS

Fig. 2

Scatter Diagram for Group 2. r = .47. y = .59x + .OOb.

2s = 186. Pop. = 38.

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 35

I

-ISO **i

1

-/do -So

I I I I

+So 4190 -HSb tloo

Fig. 3

Scatter Diagram for Group 3. r = .45. y = .515x -j- .OOb.

2s 187. Pop. = 65.

36 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

In group 1 all but five subjects received passing grades in

typewriting which, in terms of the diagram, means that all

subjects scoring above 150 on the y axis accomplished sat-

isfactory work. We will take this point, for the group, as

being the lowest point to which any one subject may reach

and still do satisfactory work in typing, then it can be predict-

ed with 95 per cent accuracy that all the subjects who score

-(-25 in the combination of the four tests will score between

150 and +185 in typewriting or will accomplish satisfac-

tory work in typewriting (intersection of the line 2S with

+25 on the x axis = 150 on the y axis and the intersection

of the line +2S with +25 on the x axis = +185 on the y

axis) . Or for any specific individual such as one, for instance,

who receives a score of +225 in the tests, we can predict that

she will be able to accomplish a score of +150 in typewriting

(intersection of the line of best fit with +225 on the x axis =

+150 on the y axis) and we know with 95 per cent accuracy

that her accomplishment in typewriting will not be lower

than 12 nor higher than +304 (intersection of the line

2S with +225 on the x axis = 12 on the y axis and the in-

tersection of the line +2S with +225 on the y axis +304 on

the y axis) . For convenience the reduced measures have been

used. After the arithmetic of balancing the scores in the

tests has been computed the same thing may be accomplished

with the actual scores in the tests and in typewriting.

There appears to be a great deal of difference in the opin-

ions of psychologists as to just how much of a coefficient of

correlation, with its probable error, constitutes a significant

correlation, some psychologists having reported figures lower

than .25 as being significant coefficients of correlation. Some

of this, confusion can be cleared up by means of this method,

and the practical significance of coefficients of correlation may

be determined.

The problem of vocational guidance is to give an individual

counsel as to what sort of an occupation or profession his

potential capacities fit him for, so that he can be definitely

informed that he will be successful in certain lines of endeavor

and unsuccessful in certain other lines, or in more specific

cases for any one occupation such as assembling, typewriting,

teaching psychology, etc., whether the individual will be a

success or a failure and to just what degree he will be a success

or a failure in that specific occupation. Unless the chances

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 37

of an individual succeeding or not succeeding are very accu-

rately determined it does the individual very little good to

know that his chances for success are such and such a percent,

as seventy-nine or eighty-two percent, etc. For the problem

in hand, in the typewriting occupation, this sort of counsel

given to an individual may result in her spending an amount

of time ranging from a few months upward in training and

then she may finally learn that she is one of those unfortunate

ones outside of the seventy-nine percent and that she will

never become a successful typist. It is evident that of ten in-

dividuals examined if we can predict that the chances for

success in each case is, say, approximately eighty-nine per-

cent and they are all counselled to take up, the study of type-

writing and go through a period of training and at the end

of the training period nine develop into successful typists and

one becomes a failure at typing then as far as this one in-

dividual is concerned she has been misguided and her time and

expense of training has been wasted to say nothing of the

effect that the failure may have on her temperament and

character.

Vocational guidance should mean accurate scientific pre-

diction for each individual and if, in the future, applied psy-

chology, in the field of vocational guidance, would escape the

many abuses that have been heaped upon it in the past it will

not attempt to establish a system of vocational guidance

until it can be almost perfectly sure of each and every one of

its predictions. To establish such a system of vocational

guidance which is to make no grave errors it will probably

be necessary to have a coefficient of correlation well above

ninety with a very small probable error and with a small scat-

ter value; just what coefficient of correlation, probable error,

and scatter value will be necessary will probably be impossible

to accurately determine until the actual work has been accom-

plished and the scatter diagrams drawn and interpreted.

From the results of this research, it is interesting to know

that we can predict that individual A who scores 140 in the

psychological tests will most probably attain an ultimate abil-

ity in typing of forty words per minute, and in 99.7 percent of

the cases she will attain an ultimate ability in typing varying

between not more than thirty-one to forty-nine words per

minute, and that individual B, who scores ninety-six in the

psychological tests will probably attain an ultimate ability in

38 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

typing of thirty-two words per minute and in 99.7 percent of

all such cases she will attain an ultimate ability in typing

varying not more than between twenty-three to forty-one

words per minute. But it will readily be seen that these pre-

dictions are of very little practical value for the individual

in that they afford her very little definite information about

just what ultimate ability she, individually, will attain. From

our data we can readily predict that in all probability A will

become a better typist than B but still it is quite possible for

A to develop into a poorer typist than B. The results of this

research show, then, that the correlations are not high enough

and the scatter value is not small enough to warrant the es-

tablishment of a system of vocational guidance whereby an in-

dividual can be advised, with any sufficient degree of safety,

to undertake or not to undertake to prepare herself to become

a typist.

The problem of vocational guidance, then, is supplied by the

individual who wants to know of what his potential capacities

consist and what sorts of occupations he is fitted to follow

successfully and what sorts of occupations he is not fitted to

follow successfully. The problem of vocational selection is of an

other sort, here the need is supplied by the profession or the

industrial concern and not directly by the individual. The

problem of vocational selection is given a certain number

of applicants in excess of the number required for a specific

job, to select those who, on the whole, are best fitted to succeed.

In practical life the employment manager has a number of

vacancies open for a specific job and of a limited number of

applicants for that job his problem is to select from the ap-

plicants those who, on the whole, are most likely to succeed.

If ten jobs in the typewriting department are open and twenty

typists are induced to apply for the jobs the problem is to se-

lect the ten who, on the whole, will do the best work. If this

can be accomplished there will be an ideal state of affairs.

However, this ideal has never been reached in any system of

vocational selection. If we have something which works

with some degree of success, with such a degree of success

never before attained by any other method, which has been

checked up scientifically, then we are justified from a prag-

matic view point in using it until a better method appears.

If we can have a system of vocational selection which can pick

from the twenty applicants (ten poor ones and ten good ones)

SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION 39

a majority of the good ones and weed out a majority of the

poor ones we have something which works and which is val-

uable. If by our method of selection of ten typists from

twenty applicants eight finally turn out to be very good typ-

ists, one a typist of medium ability, and one a poor typist then

we have erred to some extent but on the whole we have made

a selection which is a good one. By pure chance we would

probably have selected five good typists and five poor typists

and practically all of the traditional methods of selecting

typists appear to do nothing more than this even if they ac-

complish this much.

It is evident from the foregoing data that this method of

empirical vocational tests gives a far more reliable criterion

of vocational selection in the field of typewriting than has

been obtained by any other method. If a commercial concern

finds it necessary to employ a number of typists a test in typ-

ing may be given, as so many concerns do, which may or may

not determine the actual ability in typing at the moment.

This will insure the concern that they are not hiring people

who, at the moment are wholly inefficient. However, if we are

looking forward to the ultimate ability which the typists will

achieve it is not safe to hire a person to do typing on the basis

of the performance of a sample of typing for the typing abil-

ity of a person when she first enters the employ of a concern

is often no index of the ability that she may develop.f Along

with the test in typing the team of tests may be administered

and from the results the employer may predict with 95 per-

cent accuracy or with 99.7 percent accuracy, or with any other

degree of accuracy that is required whether or not the appli-

cants will develop into good typists and in addition within just

what limits their capacities in typing will enable them to de-

velop in this field, these predictions being made in definite

quantitative terms such as the net number of words written

per minute.* The prediction of ability by means of the tests

will do injustice to some individuals but it will vindicate it-

fin group 3 there was a coefficient of correlation of .28 with a prob-

able error of .10 between the first day's output and the best day's output,

the latter measure being taken within a period of six weeks.

*The supply of typists in New York City in the last few years has

been sufficient to enable a high degree of selection to be made. During

the time in which the experiment was carried on in the commercial con-

cern, in 1917, applications were received from two hundred and eighty-

two typists for ninety-six positions which were open during that period.

40 SOME EMPIRICAL TESTS IN VOCATIONAL SELECTION

self by the percentage of best applicants, and the percentage

of poorest applicants which it will be able to detect.

Some concerns require an average of twenty-two words of

connected discourse to be written per minute, others require

thirty-five words, others forty-three words, and so on. Some

concerns require twenty words of unconnected discourse to be

written per minute, other concerns require ninety-five strokes

of indexing work to be written per minute and so on. There

are then various degrees of quantitative and qualitative typ-

ing required by various concerns and a typist who is capaci-

tated to satisfy the requirements of one concern may not be

capacitated to satisfy the requirements of another concern.

The tests have developed a definite scale of efficiency in typing,

from lower to higher grades. Since each of the various con-

cerns requires a different average ability in its typists, higher

or lower than that required by other concerns, it will be neces-

sary, before the tests can be adequately applied, first to deter-

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