HOW TO USE THE MENTIMETER TESTS
The Mentimeter tests differ from the Alpha tests, or from the Beta test
of the United States Army, from the Otis test, or from any other system
of tests now available, chiefly in their flexibility. Rather than
present to the public a certain fixed and invariable group of eight or
ten tests which are to be used wherever a measure of general
intelligence is to be employed, as has been done in other cases, the
present authors have chosen to present a wide variety of tests from
which each reader may select those for his use which actually give the
best results.
It is not probable that exactly the same tests would select men of high
intelligence in the graduate work of a university as would be needed to
select the intelligent men in a logging camp in the wilds of Canada or
our own Northwest. The present authors do not profess to know just how
much of each mental trait is required to make up a perfect superior
intelligence, and for that reason they have not attempted to propose any
single group of tests as the best measure of intelligence. The reader is
asked to “try out” such tests in the Mentimeter series as seem to him to
offer greatest promise of usefulness, and then to make up his own “team
of tests” in such manner as will best reveal the kind of intelligence in
which he is interested.
For the benefit of those who wish some suggestions as to the tests which
would probably be most useful in the main lines of work to which
intelligence tests may be applied, the authors here propose certain
tentative or suggestive lists which would seem to them to offer great
promise of successful use. For the classification of clerical workers in
business and industry, the following tests should at least be given
thorough trial:
MENTIMETER NO. TITLE
6. Completion of Form Series
7. Checking Identity of Numbers
8. Digit-Symbol Substitution
9. Completion of Number Relation Series
16. Naming Opposites
23. Completion of Sentences
24. Analogies
28. Arithmetic Reasoning
It is possible, of course, that some employer who makes the trial will
find a half dozen other tests that show more accurate results in
classifying clerical workers than will be shown by any test in the above
list, but such a thing will probably not happen, for the type of test
which has been useful in similar situations will probably prove useful
again. If such a thing did happen, however, the employer would be
foolish and unscientific to retain the list suggested above when he knew
of a better list.
In the classification of the intelligence of labourers, the authors
would suggest that the following tests be given fair trial:
MENTIMETER NO. TITLE
2. Pictorial Absurdities
3. Maze Threading
5. Dividing Geometric Figures
6. Completion of Form Series
9. Completion of Number Relation Series
18. Range of Information
28. Arithmetic Reasoning
29. Practical Judgment
For classifying public school pupils according to their general
intellectual power and ability to learn, the authors propose that the
following tests be employed until a different selection has been proved
to be superior:
MENTIMETER NO. TITLE
2. Pictorial Absurdities
3. Maze Threading
8. Digit-Symbol Substitution
16. Naming Opposites
20. Reading Directions
23. Completion of Sentences
28. Arithmetic Reasoning
29. Practical Judgment
As being more strictly education tests rather than tests of intelligence
the reader’s attention is invited to the following list:
MENTIMETER NO. TITLE
10. Addition
17. Spelling
19. Reading: Vocabulary
21. Reading: Interpretation
25. Handwriting
26. English Composition
27. Poetic Discrimination
28. Arithmetic Reasoning
The most profitable list from the point of view of social entertainment
would seem to be the following:
MENTIMETER NO. TITLE
2. Pictorial Absurdities
3. Maze Threading
5. Geometrical Figures
6. Completion of Form Series
18. Range of Information
20. Reading Directions
22. Disarranged Sentences
23. Sentence Completion
24. Analogies
27. Poetic Discrimination
29. Practical Judgment
30. Logical Conclusions
Whatever the purpose for which the tests are to be used, the best
results can be obtained only by securing from the original publishers
the carefully printed forms prepared by the authors of the tests.
Mimeographed copies of test blanks or privately printed blanks are
certain to differ so much from the true form that the results obtained
therewith cannot be directly compared with the official results.
Long experience has likewise demonstrated, fairly clearly, that the best
results will be obtained in any industrial organization or educational
staff by making one person chiefly responsible for the proper
administration of the intellectual and educational measurements. If a
personnel director is at hand who can study his tests just as
scientifically as he studies his men, progress and improvement in the
methods and results are inevitable.
Measurements of intelligence are by no means the only or final criteria
by which the successful personnel manager wins success in his work and
saves money for his employers. He makes use of every piece of
information about his men that it is possible for him to pick up
anywhere. The trade tests particularly offer a wide field in which
measurements of intelligence may be supplemented and made more useful.
Of two men who are to-day working in the same trade, receiving the same
wages and making the same score on their trade tests, that one is more
promising who has the higher intelligence score. On the other hand, of
two equally intelligent men, as measured by the intelligence tests, that
one who has attained within a given time the higher proficiency in his
trade is superior.
The chief value of the group intelligence tests will probably always be
in the classification of large groups of persons into smaller,
well-defined groups, the members of which groups may then be studied
more carefully and by more exact methods in the hands of a trained
psychologist, if necessary. Until the group method of examination was
developed, making it possible to test the intellectual ability of every
employee without tremendous expense in time and money, it would have
been most foolish to talk about maintaining a continuous inventory of
the mental strength of an organization, and yet such an inventory is now
possible—just as possible as the record of the condition and capacity of
each machine owned by the company.
Prospective users of the Mentimeters need to bear in mind that mental
powers are far less constant in their amounts than are the dimensions
and measurements of a piece of steel or lumber. Even the length of a
steel rail varies between winter and summer, but the variation that
occurs in the strength of mental connections from day to day or from
hour to hour is very much greater than the variations of the steel rail.
Except by chance one would not obtain exactly the same score a second
time in taking a Mentimeter test, or any other test of mental ability.
Being for the most part constructed on the “increasing difficulty” plan,
however, the Mentimeters will prove much less influenced by recency of
drill and nearness to the lunch hour than will most other tests,
especially less than those speed tests which measure how many simple
tasks one can do within a given time limit. The Mentimeter ideal is to
test power rather than speed.
No single set of tests should be used as final and conclusive in the
public schools with regard to the kind of work which a given boy or girl
should undertake. The Mentimeter tests may be used as a first
“drag-net,” but those caught in this net should then be carefully
studied by the most refined methods known to psychologists before being
recommended for particular types of special instruction or sent to
special schools. One of the most hopeful signs in the entire educational
field is the number of cities that are employing psychologists to follow
up the results of group examinations in the schools. Many of the state
universities have established bureaus to serve the local communities[1]
in such matters. The very finest measurements are of no avail unless
something is done about the results disclosed.
Footnote 1:
There has recently been established in Teachers College, Columbia
University, New York City, a Bureau of Educational Service, the
Director of which would be glad to answer questions or advise with any
one interested in measuring intelligence or educational results,
regardless of the state or community in which one may live.
For each of the Mentimeter tests, the authors have classified the
possible scores into five general groups: Superior, High Average,
Average, Low Average, and Inferior. This classification is very rough
and should not be wrongly interpreted. An individual who is tested with
three or four or more of the Mentimeter tests should not be expected to
receive the same classification in each test. In the Handwriting test,
for example, a person might well be expected to make a rating of
“Superior” in _quality_ of writing while making only “Low Average” in
_speed_ of writing. The same person might well make a score on the test
of Poetic Discrimination which would classify him as “Inferior.”
Although there is a tendency for people who are superior in one line to
have high abilities in other lines, it is only a general tendency, which
will not hold good in all cases and with regard to all varieties of
ability.
For the most accurate scientific work the reader will probably disregard
entirely the fivefold classification of scores mentioned above. The
finer distinctions made by the numerical scores will be studied, and
interpretations will be made for the specific purposes of the examiner.
It is probable, for example, that comparatively few children at the age
of eight years would be classified as being better than “Inferior,” if
these rough general classifications were to be the only record kept of
performance on these tests. On the other hand, very few clerical workers
of proved ability and success would make a classification as low as
“Average,” except possibly in a few specialized-ability tests. The
important point to be considered by the teacher of a second-grade class,
or by an employer of clerical workers, or by any other person who wishes
to make serious use of these tests, is the relation of the scores in the
test to the relative abilities of the persons in the special group
tested. The tentative classification of scores made at the end of each
section of the chapter which follows this is for human beings in general
and will not fit well any specialized group of persons.
In order to assist readers who have no statistical training in the
evaluation for their special purposes of any particular Mentimeter test,
a few pages will be devoted to an elementary statement of how to try out
scientifically the relationship between a test, on the one hand, and
demonstrated ability in any special line of endeavour, on the other. It
may be stated here again that not all traits of mind are important in
every task that must be done in life. Some positions require only a
little intellectual ability while others require a great deal, and some
tasks require very great development of a few traits which may be very
little called for in other equally important tasks. The authors have
used their best judgment as to which tests will probably select the type
of persons needed in a certain type of position, but the judgments of
other equally experienced men would be just as good. The final proof of
reliability in a test can come only by actual trial of that test upon
men of various degrees of demonstrated ability in the trade or
profession concerned. What follows is a statement of how to measure this
correspondence between demonstrated degree of success and score in a
test, or between the scores of the same persons in two or more different
tests.
No measure of relationship between success in life and success in a test
can be any more accurate than the original measures of success from
which the calculation is made. If the measures of success in life are
unreliable, then the measure of their relationship to success in a test
will be even more unreliable. The more definite and certain one can be
of his measures of success, the more reliable will his measure of
relationship be.
In productive labour, especially where payment is based upon the number
of standard articles produced in a day, or upon the number of standard
operations performed in a given time, the records of actual performance
are probably the best measures of success available as a standard
against which to judge the reliability of a test. The record for one day
or for one week would be less reliable usually than the record for a
month or a longer period.
In many business organizations and industries there is no such
satisfactory standard of success as individual production records, and
in such cases it is necessary to make use of the judgments of foremen,
supervisors, or superintendents. These are far less satisfactory records
of efficiency and are subject to gross errors and prejudices, but they
are the only available measures of many workers. If the rating as to
ability is the consensus of the judgments of two or more supervisors,
each making his rating without any reference to that made by any other
person, the result is much more reliable than the rating of any single
supervisor would be.
Very grave errors creep into a rating of efficiency where the ratings
are made by different supervisors, each supervisor rating only a few
men. Even where a detailed schedule of qualities is listed, each to be
given a definite weight or importance in making up the total rating, as
in the Army Rating Scale, the degree of ability which one man’s
experience leads him to call “Average” will call forth a rating of
“Superior” from another equally able supervisor whose experience has
been with slightly different people. If individuals A, B, and C are
rated by the first supervisor and individuals D, E, and F by the second,
it is not at all safe to assume that C is rated fairly in relation to D.
Only when two individuals are rated by the same supervisors upon the
same scale and under the same conditions is it legitimate or safe to
assume that their relative abilities are well indicated by the ratings.
Assuming that the reader has obtained a reliable order of merit for the
individuals he is using as a check upon the value of the Mentimeter
tests, no test should be considered useful which does not result in
approximately this same order of merit. The tests are, of course, so
short and so crude that it is not to be expected that any test will,
except by chance, show exactly the same order of ability as the
production records or supervisor’s ratings furnish, but some tests will
show much closer correspondence than others. Those tests which
correspond most closely should be employed, while those tests which do
not correspond at all should not be employed, regardless of any
statement of the authors or any preconceived ideas of the reader as to
what tests ought to foretell ability in any particular line of work. The
proof of a test or of any method of prognostication lies in the degree
to which it actually arranges people in the order of their relative
efficiency in the tasks for which one seeks to foretell success.
A mere glance at a record such as that shown below for twenty-eight
sixth-grade pupils would show that there was a real relationship between
the scholarship marks, the teacher’s estimate of intelligence, and the
results of educational measurements taken by an outsider.
SCORES AND RATINGS OF SIXTH-GRADE CLASS
═════════════════╤═════════════════╤═════════════════╤═════════════════
NAME OF PUPIL │ EDUCATIONAL │TEACHER’S RANKING│ SUMMARY OF
│ MEASUREMENTS │ OF INTELLIGENCE │ TEACHER’S MARKS
│ SCORE │(1 IS BRIGHTEST) │ IN SCHOLARSHIP
│ (NO. OF ERRORS) │ │
─────────────────┼─────────────────┼─────────────────┼─────────────────
Adelaide │ 36. │ 19│ 85
Ruth │ 16.5│ 15│ 90
Alexander │ 25.5│ 7│ 93
LaMonte │ 46.5│ 6│ 93
Earl │ 76.5│ 18│ 77
│ │ │
Joseph │ 20.5│ 20│ 85
Amadeo │ 75. │ 14│ 85
Leo │ 48. │ 3│ 93
William │ 53.5│ 9│ 82
Isabel │ 25. │ 21│ 76
│ │ │
Ida │ 36.5│ 4│ 94
Hazel │ 15. │ 10│ 90
Frederick │ 65. │ 26│ 86
Charles │ 58.5│ 13│ 85
Edward │ 30. │ 1│ 95
│ │ │
Benjamin │ 62.5│ 24│ 76
Bruce │ 56. │ 22│ 87
Alden │ 55. │ 12│ 87
George │ 60.5│ 17│ 87
Alice │ 29. │ 11│ 88
│ │ │
Almira │ 15.5│ 5│ 96
Helen │ 16.5│ 2│ 90
Elizabeth │ 65.5│ 23│ 75
Amelia │ 24.5│ 8│ 92
Edwin │ 19. │ 16│ 89
│ │ │
Robert │ 67. │ 28│ 71
Edna │ 47. │ 27│ 78
Samuel │ 72. │ 25│ 80
─────────────────┴─────────────────┴─────────────────┴─────────────────
The things which are not so evident at a glance are the degrees of
relationship between these three types of measures. Is the relation of
educational measurements to the teacher’s estimates greater than the
relation of the measurements to the marks in scholarship given by the
teacher? In order to measure precisely the relative degrees of
correspondence between various measures and estimates of the abilities
of individuals, it is quite evident that something more accurate and
exact than mere inspection is necessary.
For an explanation of the method by which the exact relationship may be
worked out mathematically between the results of a test and the true
abilities of the individuals tested, the reader is referred to pages
326–331 in the appendix. The discussion which will be found there of the
method of calculating a coefficient of coördination will not be
difficult to understand nor will the method be difficult of application
for any one who wishes to measure the exact reliability of any of the
Mentimeter tests or of any other test. For many purposes such a record
as is shown on the preceding page, giving the score of the individual in
each test used, will reveal the essential facts regarding the
correspondence between test results and demonstrated ability. The reader
should be cautious, however, about accepting a conclusion drawn from
casual observation of such a table as that shown on the preceding page
without checking up the accuracy of this conclusion by actually working
out the coefficient of coördination according to the method shown in the
appendix.
When the reader has tried out, upon a fairly large group of persons of
known ability, the Mentimeter tests which seem to him to promise
greatest usefulness, and when he has made his calculations and
discovered which tests actually do classify his people most accurately,
it will then be possible for him to make an intelligent scientific
selection of tests for practical use. Let us suppose, for example, that
an employer wishes to have a set of tests whereby he may select
intelligent sales-girls. By giving the ten or twelve tests which seem
most hopeful for the purpose to fifty or sixty saleswomen, who have been
in his employ long enough to demonstrate their relative degrees of
ability and intelligence, the five or six tests may be chosen whose
results show the closest relation to their demonstrated ability for
intelligent salesmanship.
The results obtained by the separate tests chosen should also be
compared, for two tests may measure practically the same mental trait
and have a very high coördination with each other. In such a case, it
would seem almost a useless waste to retain in the group two tests which
measured the same phase of ability. The one of the pair which showed the
less close relationship to the true ranking might be dropped from the
list without much loss to the total effectiveness of the group of tests.
A group of tests thus carefully selected would prove very helpful and
effective in the selection of untrained material for training or in the
classification of experienced employees according to their intellectual
qualifications for the type of position held by the people on whom the
validity of the tests had been proved.
The advantage of such a well-selected “team” of tests is not so much
that it selects various grades of ability more accurately than
supervisors could select it after many months of experience in trying to
train the new material, but that the tests make a satisfactory
classification immediately, which saves the salaries and time of those
applicants who would certainly fail in the training period. Even with
the very best coefficients of coördination between the tests and actual
demonstrated ability in the trade or position, the tests will not be
infallible. On the other hand, no supervisor’s judgment would be
infallible, either. And the supervisor would be much more likely to make
errors through personal likes and dislikes than the impersonal tests
could possibly be.
The tests are an invaluable aid, when they are themselves chosen with
the scientific care outlined above, although it would be a short-sighted
policy for any firm to trust entirely to the results of intelligence
tests in the employment of its personnel. Appearance, voice, education,
manners, physical size, and many other qualities are sometimes quite as
important as the degree of intelligence, and the intelligence tests do
not measure other elements of personality than the mental qualities.
Warning should also be given against using a particular set of
intelligence tests, selected because they show high correspondence with
ability in salesmanship, for example, as a measure of the intellectual
qualities of candidates for some other position. Sets of tests, selected
because they have been found accurate in classifying soldiers or school
children for instruction, may not be of maximum usefulness in
classifying machinists or business managers. The Mentimeter tests offer
a wide variety, from which it is proposed that only those shall be used
which have actually proved useful in classifying candidates for the
particular task concerned. There is no reason to believe that exactly
the same type of intelligence is required in all positions.
Having chosen certain promising tests for experiment, having proved the
validity of these tests by checking up the relation of their results to
the true abilities of a group of old employees or persons whose relative
capacities are known perfectly, and having selected those tests whose
results relate most directly to intellectual ability and least directly
to one another, one may begin to employ the tests thus selected for the
sorting and classification of new recruits or applicants. The question
which will at once confront the reader who is not experienced in the
employment of statistics of this sort is “How shall the test results be
recorded and interpreted?”
The answer to the question regarding test records is that the exact
score of each person should be kept for each test to which that person
is “exposed.” One difficulty with the records kept of certain other
group intelligence tests is that only the final total score is retained,
while all the wealth of detail furnished by the different tests included
in the series is lost. The total score on a series of six or eight
intelligence tests is worth keeping, but the separate scores on each of
the six or eight may prove to be even more illuminating than the total
score. Two candidates may make the same total score on a series of tests
but the one may make his points chiefly in memory tests with little help
from the tests calling for complex thought, while the other may do very
poorly in the memory work and very well in the thought tests. If only
the total score on the series were retained, the usefulness of the
series would be practically destroyed for many purposes.
For the interpretation of the result recorded on any test, one will need
to use some short but intelligible scheme for stating the true relation
of the score of any individual to the scores of the remainder of his
group or to the scores of the other group of old employees used as a
standard in selecting the tests to be regularly employed. It is not
always safe to say merely that Mr. K—— is below the average of his
group. As an extreme case of how unjust this might be, let us suppose
that in one of the Mentimeter tests, A made a score of 0; B made a score
of 2; C, a score of 1; D, 2; E, 3; F, 0; G, 10; H, 2; I, 3; J, 9; and K,
3. The average score of this small group, obtained by adding the eleven
scores and dividing by 11, is 3.18. Mr. K—— therefore obtained a score
which was below the average of the group, even though fewer than 20 per
cent. of his group made better scores than he. _The average score is too
much influenced by extremely low or extremely high scores._
To arrive at a proper perspective for interpreting the score of any
individual, it is necessary first of all to have a _distribution_ of the
scores made by all the persons in the group with which the individual is
to be compared. Such a distribution should show how frequently each
possible score was made. The table on the left illustrates the idea of a
distribution, using as material the scores quoted above for eleven
individuals tested by a Mentimeter test. This table shows that one
person had a score of 10, that one other had a score of 9, and that 3
was the next highest score made. The mode, or most common score, in this
distribution is a 2 or a 3, which fact makes K’s score of 3 appear as
quite typical of his group. The modal or most frequent score is a really
useful score with which to compare the record of any individual,
although it is not as safe a measure of the central tendency of a
distribution as is the median score.
DISTRIBUTION
═════════════╤═════════════
SIZE OF SCORE│ FREQUENCY
─────────────┼─────────────
10│ 1
9│ 1
8│ 0
7│ 0
6│ 0
5│ 0
4│ 0
3│ 3
2│ 3
1│ 1
0│ 2
─────────────┼─────────────
TOTAL │ 11
─────────────┴─────────────
The median score of a distribution is the middle score, than which there
are just as many larger as smaller. The median score is found by
beginning at one end of a distribution and counting through half of the
frequencies. To count through half of the eleven frequencies in the
above distribution would bring us into the midst of the three who had
scores of 2, and therefore 2 is the median score with which K’s score,
or the score of any other individual, should be compared.
The reader who is mathematically inclined may wish to find the median
point in the distribution, the point which bisects the distribution. To
find this, one needs to study his facts carefully and make such
assumptions as seem most probable for the facts which are not perfectly
apparent. For example, of the three persons who scored 2 points, one
individual may have had the third problem thought out and have been in
the very act of writing the correct answer to it when the time was up,
while another may have just finished problem two without having begun to
read the third problem, and the third person may have been right in the
middle of his thought about problem three. Not knowing what the exact
truth is, we may assume that of the three who had a score of 2, one’s
true score was between 2 and 2.33, another’s was between 2.33 and 2.66
and that the third’s was between 2.67 and 3.00.
If we count out the five who scored 3 or higher, we shall still require
half of the distance represented by the next highest individual in order
to have counted out 5.5 (half of 11). If our assumption is true, then,
we shall need to count half way down from 3.00 to 2.67 in order to find
the median point, 2.83. The calculation of the median point is not
necessary, however, unless there is a very large number of cases in the
distribution and unless very accurate comparisons must be made. In
passing it may be said that the calculation of the median point at 2.83
is just as sensible and just as accurate as the calculation of the
average point at 3.18, and that the median point is a much more useful
measure of the distribution than the more commonly used average.
The user of the Mentimeter tests will not, under ordinary circumstances,
be satisfied with interpreting an individual’s score merely by
indicating its direction from the median, mode or average of a group. It
will not usually be sufficient to say “He made the modal or most popular
score,” or “His score was lower than the average,” or even “His score
was higher than the median.” Some indication will be desired as to how
much better or poorer a given score is than the median, or just what
percentage of the standard group made better scores. An illustration of
the method to be employed in such calculations and a review of the
method of finding the median is given below in connection with a
distribution of scores on one of the Mentimeter tests. (See Mentimeter
No. 24, page 234.)
═════════════════╤═════════════════╤═════════════════╤═════════════════
I │ II │ III │ IV
─────────────────┼─────────────────┼─────────────────┼─────────────────
SIZE OF SCORE │FREQUENCY: NO. OF│ TOTAL NO. FROM │ TOTAL % FROM
ANALOGIES TEST │COLLEGE GRADUATES│ LOWEST SCORES │ LOWEST SCORES
─────────────────┼─────────────────┼─────────────────┼─────────────────
30│ 2│ 129│ 100
29│ 4│ 127│ 98.5
28│ 10│ 123│ 95.3
27│ 22│ 113│ 87.6
26│ 32│ 91│ 70.6
│ │ │
25│ 20│ 59│ 45.8
24│ 18│ 39│ 30.3
23│ 8│ 21│ 16.3
22│ 4│ 13│ 10.1
21│ 2│ 9│ 7.0
│ │ │
20│ 1│ 7│ 5.4
19│ 2│ 6│ 4.7
18│ 1│ 4│ 3.1
17│ 1│ 3│ 2.3
16│ ...│ ...│ .....
│ │ │
15│ 1│ 2│ 1.6
14│ ...│ ...│ .....
13│ ...│ ...│ .....
12│ 1│ 1│ .8
11│ ...│ ...│ .....
│ ———│ │
TOTAL │ 129│ │
─────────────────┴─────────────────┴─────────────────┴─────────────────
Having distributed the scores obtained by a group of college graduates
on the Analogies test, the next important step toward their
interpretation is the totaling of the frequencies up to and including
those of each possible size, as shown in the third column of the
accompanying table. The fourth column is then prepared showing the
corresponding _percentages_ of the total number (129) of persons tested,
for each of the total frequencies shown in column III. The table as a
whole is then to be read from left to right. As an example, one may
begin at 20 in the first column and read as follows: “1 college graduate
made a score of exactly 20 points, making in all 7 individuals who
obtained a score of 20 points or less, which (7) is 5.4 per cent. of the
129 individuals tested.” Dropping the eye to the next percentage below
this line in column IV, one can interpret the score of the individual
who made a score of 20 as follows: “This is a poor showing for a college
graduate, for of 129 college graduates tested only 4.7 per cent. made a
lower score.”
A very popular method of interpreting a score is to tell in what quarter
or, as the statisticians would say, in what “quartile” of the
distribution a given score is found. The upper or first quartile of a
distribution is the range of scores below which 75 per cent. of those
tested have fallen. The second quartile is the range of scores below
which 50 per cent. are found but above which 25 per cent. of those
tested are found. The third quartile is the range below which only 25
per cent. are found and above which 50 per cent. are found, and the
fourth or lowest quartile is the range of scores in which are found the
lowest 25 per cent. of the scores made. The first and second quartiles
are above the median, while the third and fourth quartiles are below the
median. Obviously the individual who scored 20 points in the Analogies
test, and is included in the lowest 5.4 per cent. is also in the lowest
quartile of the college graduate scores. The point dividing the first
and second quartiles is called the 75 percentile, while the point
dividing the third and fourth quartiles is called the 25 percentile. As
was stated above, the median or 50 percentile divides the second and
third quartiles.
Columns III and IV in the foregoing table assist one quite materially in
calculating the median and the other percentile points. To find the
median, one will need to count half way through the distribution, in
this case to count out 64.5 scores (129/2 = 64.5). The 20 persons who
scored on 25, in the above distribution, are shown by column III to be
included in the lowest 59 scores and by column IV to be in the lowest
45.8 per cent. To include 64.5 (or 50 per cent.) of the scores, 5.5 of
the 32 individuals who scored on 26 will need to be taken (64.5 − 59 =
5.5); 5.5 is .17 of 32, so it will be necessary to take .17 of the
distance (26.0 up to 27.0) represented by a score of 26. This places the
50 percentile or median point at 26.17, if we assume that the 32
individuals obtaining a score of 26 were evenly distributed in their
exact values between 26.0 and 27.0, which is the safest assumption one
can make about these scores.
The 25 percentile is found by counting out one fourth of the
frequencies, beginning with the low-score end of the distribution. In
the case of the college graduates’ distribution on the Analogies test,
the 25 percentile is 24.63. The 75 percentile, which is found by
counting out three fourths of the frequencies from the low-score end or
one fourth from the high-score end of the distribution, is 27.26 in the
case of the analogies distribution shown above. The “middle 50 per
cent.” of the distribution, or the second and third quartiles, lie
between 24.6 and 27.3 according to these calculations. One may therefore
assert that the typical college graduate, meaning one who is within the
two middle quartiles of the college graduate distribution, should be
expected to make a score of 24, 25, 26, or 27 on the Analogies test in
the Mentimeter series.
Occasionally intellectual measurements are reported by tenths, the first
tenth being the tenth of the distribution having the highest scores,
just as the first quartile is the quarter containing the highest scores.
For practical purposes with the Mentimeter tests, however, it is
recommended (1) that the score made on each test be recorded, (2) that
the median score of the standard group, with which each individual’s
score is to be compared, be calculated, and (3) that the percentage of
the standard group making lower scores than that individual’s score be
used as an interpretation. For these simple interpretations, a table,
such as that shown on page 102 for college graduates in the Analogies
tests, practically completes the necessary calculations,[2] except for
the calculation of the median score. It will be fairly intelligible to
describe Henry Smith’s score as follows: “Smith has a score of 24 points
as compared with the median score of 26.2 points for his group. Only
16.3 per cent. of the college graduates make a poorer score than Smith,
but 69.7 per cent. make a better score.”
Footnote 2:
For the purpose of assisting the reader in keeping and interpreting
records of the Mentimeter tests, the authors have prepared a record
booklet which may be used with the tests to excellent advantage. It
will be found economical to use this booklet because of the guide
lines, headings, and practical suggestions which it contains, reducing
copying and memory work in the calculations to a minimum. It is
recommended also that calculating tables or a slide rule be used to
calculate the percentages called for in the final column of the
distribution tables. Such aids are very desirable because of their
contribution to the accuracy of results and to economy of time.
Assuming now that the reader has a fairly clear idea of how to
administer and record the results of the Mentimeter tests, the next
question to be answered is: “What shall be done about these test
records?” Measurement in any field does not change to any appreciable
degree the material which has been measured. The surveyor, for example,
who measures the area of a field makes very little impression upon the
soil over which he passes. A physician who measures the weight of an
infant does not thereby increase that weight or diminish it. In the same
way the psychologist who applies a Mentimeter test to a filing clerk,
does not by that act increase the efficiency of that clerk.
Measurements, of themselves, are of no value. Something must be done
about the result which is obtained or all of the expense in time and
money is of no avail.
The real purpose of a measurement is to tell facts about a situation
more exactly and with greater objectiveness than they could be told in a
description. A child may seem, on first appearance, to be under weight,
but in order to know definitely whether or not that is true it is
necessary to measure his age in terms of years, months, and days, to
measure his weight in terms of pounds and ounces, and to measure his
height in terms of feet and inches. All of these measurements taken
together, however, will not hinder the child’s growth or make him
develop more rapidly; they merely indicate what his present condition
is, without reference to what it may have been in the past or what it
may become in the future.
As a sample of the great benefit which may be obtained from knowing
mental facts exactly, we may consider the traditions and present status
of our public school systems. Education has in the past been pointed,
from the very beginning in the kindergarten toward the high school and
the college and ultimately the professional school in which lawyers,
physicians, ministers, and teachers were to be prepared. The child who
by nature was not inclined toward the consideration of abstract ideas
and theories soon found that the schools were not well adapted to his
interests.
The percentage of persons in our population who cannot successfully
think and work with abstract symbols and verbal ideas is very much
greater than most of us have been inclined to believe. We have stated or
implied that any boy who would stay in school long enough might fit
himself to become a United States Senator or possibly a great newspaper
editor, or lawyer. Those pupils who found it impossible to assimilate
the type of thing that was offered by the public schools have been
eliminated and sent out into the industrial world to find materials
which would correspond to their interests.
Educators have still further made the error of saying or implying that
it was the inferior people who were thus forced out of school. The
authors of the present book wish to assert their belief that the mind of
a man whose interests lie in handling people and concrete objects is not
at all inferior on that account to the mind of the man who handles ideas
and abstract conceptions.
Measures of intelligence have in the past been chiefly those which would
be favourable to the abstract thinker. The Alpha test, used in the Army,
proved conclusively to those who studied the results most carefully,
that fully half of our population can never succeed, even moderately, in
the manipulation of abstract ideas. The large proportion of our boys and
girls who come to school are absolutely doomed to be unsuccessful and to
become discouraged in their attempts to progress in the courses which
are commonly given, and yet the public supports these schools, and the
administrators of these schools try to claim that they offer “equal
opportunity to all.” Actually the kind of opportunity offered can be
used effectively by only a small percentage of the pupils. Unless the
child has the ability to interpret symbols and juggle ideas he is
declared to be inferior and is forced out to learn for himself how to
earn a living and to secure his rights.
The Mentimeter tests and other measures of intellectual abilities
provide the means whereby pupils may be classified, at the very
beginning of their education, according to the degree to which the
formal academic training will be assimilated. These tests make it
possible to select those who do not think abstractly but who require
concrete objects or persons as the material for their mental activity.
Unless the public recognizes that it owes an appropriate education to
these people just as surely as it does to the academic few, it will not
be long until this great group, in which our present schools develop the
habit of failure and discontent, will arise to overthrow the injustices
which our past aristocratic organization of society has handed on to
them.
It is not proposed that certain individuals be selected by the
Mentimeter tests and trained psychologists and then condemned to
training of a less respectable order than that which is now offered.
What is proposed is that by the use of intelligence tests students in
schools be classified and placed in classes where they can learn things
which it is within their mental power and interests to grasp and which
will be of practical value and of social significance in the development
of good citizens; rather than to continue, as we have in the past,
condemning this large majority of our population to failure in school
and elimination from the benefits of public taxation for education.
It is no disgrace for a blind man to be unable to paint beautiful
pictures, nor is it considered a great social injustice for a man of
ordinary size to be denied the opportunity of serving as a giant in a
side show. It should not be considered by any one that being a good
valet or mule driver or boot black or street cleaner is a less
respectable calling for a man whose mind demands concrete objects for
its exercise than the expounding of the gospel or explanation of legal
technicalities is to the man whose mind is inclined toward abstract
ideas and relationships. If we are to have an effective social
organization each person must do the type of thing for which his brain
and his physical body fit him, without feeling that he is thereby either
inferior or superior to any other person. We must help one another, each
supplying that service for which he is best fitted. To continue as we
have in the past, encouraging every child to look for a “white-collar
job” at the end of his educational career is to foster the monster of
discontent and unrest which threatens to destroy the very foundations of
modern society.
If the Mentimeter tests which follow can do no more than point out for
employers and educators the limits to which those who are dependent upon
them can go in the understanding and use of abstract ideas, they will
thereby have contributed materially to the happiness and contentment of
a weary world. Along with the results of the tests there must, however,
be this feeling of responsibility for one another and the recognition of
the need for “pulling together” for the common good, each man
contributing that for which his inheritance has fitted him, else we
shall continue to force men to learn failure and discontent in our
schools and thereby destroy the social structure we have been so long in
building.