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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-


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Online LibraryHerbert Wesley RogersSome empirical tests in vocational selection → online text (page 3 of 4)