The Measurement of Intelligence

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SCORING. The test is passed _if the rule is grasped by the time the
sixth sheet is reached_; that is, the subject may pass after five
incorrect responses, provided the sixth is correct and the governing
rule can then be given. It is not permissible to ask for the rule until
all six parts of the experiment have been given. Nothing must be said
which could even suggest the operation of a rule. Often, however, the
subject grasps the principle after two or three steps and gives it
spontaneously. In this case it is unnecessary to proceed with the
remaining steps.

REMARKS. This test was first used by the writer in a comparative study
of the intellectual processes of bright and dull boys in 1905, but it
was not standardized until 1914. Rather extensive data indicate that it
is a genuine test of intelligence. Of 14-year-old school children
testing between 96 and 105 I Q, 59 per cent passed this test; of
14-year-olds testing below 96 I Q, 41 per cent passed; of those testing
above 105, 71 per cent passed. That is, the test agrees well with the
results obtained by the scale as a whole. Of "average adults" only
10 per cent fail; and of "superior adults," fewer than 5 per cent. As a
rule, the higher the grade of intelligence, the fewer the steps
necessary for grasping the rule. Of the superior adults, only
35 per cent fail to get the rule as early as the end of the fourth step.

The test is little affected by schooling, and apart from differences in
intelligence it is little influenced by age. Other advantages of the
test are the keen interest it always arouses and its independence of
language ability. It has been used successfully with immigrant subjects
who had been in this country but a few months.

We have named the experiment an "induction test." It might be supposed
that the solution would ordinarily be arrived at by deduction, or by an
_a-priori_ logical analysis of the principle involved. This, however, is
rarely the case. Not one average adult out of ten reasons out the
situation in this purely logical manner. It is ordinarily only after one
or more mistakes have been made and have been exposed by the examiner
holding up the unfolded paper to view that the correct principle is
grasped. In the absence of deductive reasoning the subject must note
that each unfolded sheet contains twice as many holes as the previous
one, and must infer that folding the paper again will again double the
number. The ability tested is the ability to generalize from
particulars where the common element of the particulars can be discerned
only by the selective action of attention, in this case attention to the
fact that each number is the double of its predecessor.

XIV, 3. GIVING DIFFERENCES BETWEEN A PRESIDENT AND A KING

PROCEDURE. Say: "_There are three main differences between a president
and a king; what are they?_" If the subject stops after one difference
is given, we urge him on, if possible, until three are given.

SCORING. The three differences relate to power, tenure, and manner of
accession. Only these differences are considered correct, and the
successful response must include at least two of the three. We disregard
crudities of expression and note merely whether the subject has the
essential idea. As regards power, for example, any of the following
responses are satisfactory: "The king is absolute and the president is
not." "The king rules by himself, but the president rules with the help
of the people." "Kings can have things their own way more than
presidents can," etc.

It may be objected that the reverse of this is sometimes true, that the
king of to-day often has less power than the average president.
Sometimes subjects mention this fact, and when they do we credit them
with this part of the test. As a matter of fact, however, this answer is
seldom given.

Sometimes the subject does not stop until he has given a half-dozen or
more differences, and in such cases the first three differences may be
trivial and some of the later ones essential. The question then arises
whether we should disregard the errors and pass the subject on his later
correct responses. The rule in such cases is to ask the subject to pick
out the "three main differences."

Sometimes accession and tenure are given in the form of a single
contrast, as: "The president is elected, but the king inherits his
throne and rules for life." This answer entitles the subject to credit
for both accession and tenure, the contrast as regards tenure being
plainly implied.

Unsatisfactory contrasts are of many kinds and are often amusing. Some
of the most common are the following:--

"A king wears a crown." "A king has jewels." "A king sits on a
throne." ("A king sets on a thorn" as one feeble-minded boy put
it!) "A king lives in a palace." "A king has courtiers." "A king
is very dignified." "A king dresses up more." "A president has
less pomp and ceremony." "A president is more ready to receive
the people." "A king sits on a chair all the time and a
president does not." "No differences; it's just names." "A
president does not give titles." "A king has a larger salary."
"A king has royal blood." "A king is in more danger." "They have
a different title." "A king is more cruel." "Kings have people
beheaded." "A king rules in a monarchy and a president in a
republic." "A king rules in a foreign country." "A president is
elected and a king fights for his office." "A president appoints
governors and a king does not." "A president lets the lawyers
make the laws." "Everybody works for a king."

It is surprising to see how often trivial differences like the above are
given. About thirty "average adults" out of a hundred, including
high-school students, give at least one unsatisfactory contrast.

The test has been criticized as depending too much on schooling. The
criticism is to a certain extent valid when the test is used with young
subjects, say of 10 or 12 years. It is not valid, however, if the use of
the test is confined to older subjects. With the latter, it is not a
test of knowledge, but of the discriminative capacity to deal with
knowledge already in the possession of the subject. It would be
difficult to find an adult, not actually feeble-minded, who is ignorant
of the facts called for: That the king inherits his throne, while the
president is elected; that the tenure of the king is for life, and that
of the president for a term of years; that kings ordinarily have, or are
supposed to have, more power. Even the relatively stupid adult knows
this; but he also knows that kings are different from presidents in
having crowns, thrones, palaces, robes, courtiers, larger pay, etc., and
he makes no discrimination as regards the relative importance of these
differences.

The test is psychologically related to that of giving differences in
year VII and to the two tests of finding similarities; but it differs
from these in requiring a comparison based on fundamental rather than
accidental distinctions. The idea is good and should be worked out in
additional tests of the same type.

The test first appeared in the Binet revised scale of 1911. Kuhlmann
omits it, and besides our own there are few statistics bearing on it.
Our results show that if two essential differences are required, the
test belongs where we have placed it, but that if only one essential
difference is required, the test is easy enough for year XII.

XIV, 4. PROBLEM QUESTIONS

PROCEDURE. Say to the subject: "_Listen, and see if you can understand
what I read._" Then read the following three problems, rather slowly and
with expression, pausing after each long enough for the subject to find
an answer:--

(a) "_A man who was walking in the woods near a city stopped
suddenly, very much frightened, and then ran to the nearest
policeman, saying that he had just seen hanging from the limb
of a tree a ... a what?_"
(b) "_My neighbor has been having queer visitors. First a doctor
came to his house, then a lawyer, then a minister (preacher or
priest). What do you think happened there?_"
(c) "_An Indian who had come to town for the first time in his
life saw a white man riding along the street. As the white man
rode by, the Indian said--'The white man is lazy; he walks
sitting down.' What was the white man riding on that caused
the Indian to say, 'He walks sitting down'?_"

Do not ask questions calculated to draw out the correct response, but
wait in silence for the subject's spontaneous answer. It is permissible,
however, to re-read the passage if the subject requests it.

SCORING. _Two responses out of three must be satisfactory._ The
following explanations and examples will make clear the requirements of
the test:--

(a) _What the man saw hanging_

_Satisfactory._ The only correct answer for the first is "A man
who had hung himself" (or who had committed suicide, been
hanged, etc.). We may also pass the following answer: "Dead
branches that looked like a man hanging."

A good many subjects answer simply, "A man." This answer cannot
be scored because of the impossibility of knowing what is in the
subject's mind, and in such cases it is always necessary to say:
"_Explain what you mean._" The answer to this interrogation
always enables us to score the response.

_Unsatisfactory._ There is an endless variety of failures: "A
snake," "A monkey," "A robber," or "A tramp" being the most
common. Others include such answers as "A bear," "A tiger," "A
wild cat," "A cat," "A bird," "An eagle," "A bird's nest," "A
hornet's nest," "A leaf," "A swing," "A boy in a swing," "A
basket of flowers," "An egg," "A ghost," "A white sheet,"
"Clothes," "A purse," etc.

(b) _My neighbor_

_Satisfactory._ The expected answer is "A death," "Some one has
died," etc. We must always check up this response, however, by
asking what the lawyer came for, and this must also be answered
correctly.

While it is expected that the subject will understand that the
doctor came to attend a sick person, the lawyer to make his
will, and the minister to preach the funeral, there are a few
other ingenious interpretations which pass as satisfactory. For
example, "A man got hurt in an accident; the doctor came to make
him well, the lawyer to see about damages, and then he died and
the preacher came for the funeral." Or, "A man died, the lawyer
came to help the widow settle the estate and the preacher came
for the funeral." We can hardly expect the 14-year-old child to
know that it is not the custom to settle an estate until after
the funeral.

The following excellent response was given by an enlightened
young eugenist: "A marriage; the doctor came to examine them and
see if they were fit to marry, the lawyer to arrange the
marriage settlement, and the minister to marry them." The
following logical responses occurred once each: "A murder. The
doctor came to examine the body, the lawyer to get evidence, and
the preacher to preach the funeral." "An unmarried girl has
given birth to a child. The lawyer was employed to get the man
to marry her and then the preacher came to perform the wedding
ceremony." Perhaps some will consider this interpretation too
far-fetched to pass. But it is perfectly logical and,
unfortunately, represents an occurrence which is not so very
rare.

If an incorrect answer is first given and then corrected, the
correction is accepted.

_Unsatisfactory._ The failures again are quite varied, but are
most frequently due to failure to understand the lawyer's
mission. Of 66 tabulated failures, 26 are accounted for in this
way, while only 6 are due to inability to state the part played
by the minister. The most common incorrect responses are: "A
baby born" (accounting for 5 out of 66 failures); "A divorce"
(very common with the children tested by Dr. Ordahl, at Reno,
Nevada!); "A marriage"; "A divorce and a remarriage"; "A
dinner"; "An entertainment"; "Some friends came to chat," etc.
In 20 failures out of 66, marriage was incorrectly connected
with a will, a divorce, the death of a child, etc.

The following are not bad, but hardly deserve to pass: "Sickness
and trouble; the lawyer and minister came to help him out of
trouble." Or, "Somebody was sick; the lawyer wanted his money
and the minister came to see how he was." A few present a still
more logical interpretation, but so far-fetched that it is
doubtful whether they should count as passes; for example: "A
man and his wife had a fight. One got hurt and had to have the
doctor, then they had a lawyer to get them divorced, then the
minister came to marry one of them." Again, "Some one is dying
and is getting married and making his will before he dies."

(c) _What the man was riding on_

The only correct response is "Bicycle." The most common error is
_horse_ (or _donkey_), accounting for 48 out of 71 tabulated
failures. Vehicles, like _wagon_, _buggy_, _automobile_, or
_street car_, were mentioned in 14 out of 71 failures. Bizarre
replies are: "A cripple in a wheel chair"; "A person riding on
some one's back," etc.

REMARKS. The experiment is a form of the completion test. Elements of a
situation are given, out of which the entire situation is to be
constructed. This phase of intelligence has already been discussed.[74]

[74] See IX, 5, and XII, 4.

While it is generally admitted that the underlying idea of this test is
good, some have criticized Binet's selection of problems. Meumann thinks
the lawyer element of the second is so unfamiliar to children as to
render that part of the test unfair. Several "armchair" critics have
mentioned the danger of nervous shock from the first problem. Bobertag
throws out the test entirely and substitutes a completion test modeled
after that of Ebbinghaus. Our own results are altogether favorable to
the test. If it is used in year XIV, Meumann's objection hardly holds,
for American children of that age do ordinarily know something about
making wills. As for the danger of shock from the first problem, we have
never once found the slightest evidence of this much-feared result. The
subject always understands that the situation depicted is hypothetical,
and so answers either in a matter-of-fact manner or with a laugh.

The bicycle problem is our own invention. Binet used the other two and
required both to be answered correctly. The test was located in year XII
of the 1908 scale, and in year XV of the 1911 revision. Goddard and
Kuhlmann retain it in the original location. The Stanford results of
1911, 1912, 1914, and 1915 agree in showing the test too difficult for
year XII, even when only two out of three correct responses are
required. If the original form of the experiment is used, it is
exceedingly difficult for year XV. As here given it fits well at
year XIV.

XIV, 5. ARITHMETICAL REASONING

PROCEDURE. The following problems, printed in clear type, are shown one
at a time to the subject, who reads each problem aloud and (with the
printed problem still before him) finds the answer without the use of
pencil or paper.

(a) _If a man's salary is $20 a week and he spends $14 a week,
how long will it take him to save $300?_
(b) _If 2 pencils cost 5 cents, how many pencils can you buy for
50 cents?_
(c) _At 15 cents a yard, how much will 7 feet of cloth cost?_

Only one minute is allowed for each problem, but nothing is said about
hurrying. While one problem is being solved, the others should be hidden
from view. It is not permissible, if the subject gives an incorrect
answer, to ask him to solve the problem again. The following exception,
however, is made to this rule: If the answer given to the third problem
indicates that the word _yard_ has been read as _feet_, the subject is
asked to read the problem through again carefully (aloud) and to tell
how he solved it. No further help of any kind may be given.

SCORING. _Two of the three_ problems must be solved correctly within the
minute allotted to each. No credit is allowed for correct method if the
answer is wrong.

REMARKS. We have selected these problems from the list used by Bonser in
his _Study of the Reasoning Ability of Children in the Fourth, Fifth,
and Sixth School Grades_.[75]

[75] Columbia University Contributions to Education, no. 37, 1910.

Our tests of 279 "at age" children between 12 and 15 years reveal the
surprising fact that the test as here used and scored is not passed by
much over half of the children of any age in the grades below the
high-school age. Of the high-school pupils 19 per cent failed to pass,
21 per cent of ordinarily successful business men (!), and 27 per cent
of Knollin's unemployed men testing up to the "average adult" level. To
find average intelligence cutting such a sorry figure raises the
question whether the ancient definition of man as "the rational animal"
is justified by the facts. The truth is, _average_ intelligence does not
do a great deal of abstract, logical reasoning, and the little it does
is done usually under the whip of necessity.

At first thought these problems will doubtless appear to the reader to
be mere tests of schooling. It is true, of course, that in solving them
the subject makes use of knowledge which is ordinarily obtained in
school; but this knowledge (that is, knowledge of reading and of
addition, subtraction, multiplication, and division) is possessed by
practically all adults who are not feeble-minded, and by many who are.
Success, therefore, depends upon the ability to apply this knowledge
readily and accurately to the problems given--precisely the kind of
ability in which a deficiency cannot be made good by school training. We
can teach even morons how to read problems and how to add, subtract,
multiply, and divide with a fair degree of accuracy; the trouble comes
when they try to decide which of these processes the problem calls for.
This may require intelligence of high or low order, according to the
difficulty of the problem. As for the present test, we have shown that
almost totally unschooled men of "average adult" intelligence pass this
test as frequently as high-school seniors of the same mental level.

XIV, 6. REVERSING HANDS OF CLOCK

PROCEDURE. Say to the subject: "_Suppose it is six twenty-two o'clock,
that is, twenty-two minutes after six; can you see in your mind where
the large hand would be, and where the small hand would be?_" Subjects
of 12- to 14-year intelligence practically always answer this in the
affirmative. Then continue: "_Now, suppose the two hands of the clock
were to trade places, so that the large hand takes the place where the
small hand was, and the small hand takes the place where the large hand
was. What time would it then be?_"

Repeat the test with the hands at 8.10 (10 minutes after 8), and again
with the hands at 2.46 (14 minutes before 3).

The subject is not allowed to look at a clock or watch, or to aid
himself by drawing, but must work out the problem mentally. As a rule
the answer is given within a few seconds or not at all. If an answer is
not forthcoming within two minutes the score is failure.

SCORING. The test is passed if _two of the three_ problems are solved
within the following range of accuracy: the first solution is considered
correct if the answer falls between 4.30 and 4.35, inclusive; the second
if the answer falls between 1.40 and 1.45, and the third if the answer
falls between 9.10 and 9.15.

REMARKS. It appears that success in the test chiefly depends upon
voluntary control over constructive visual imagery. Weakness of visual
imagery may account for the failure of a considerable percentage of
adults to pass the test. Visual imagery, however, is not absolutely
necessary to success. One 8-year-old prodigy, who had 12-year
intelligence, arrived in forty seconds at a strictly mathematical
solution for the second problem, as follows: "If it is 2.46, and the
hands trade places, then the little hand has gone about one fourth of
the distance from 9 o'clock to 10 o'clock. One fourth of 60 minutes is
15 minutes, and so the time would be 15 minutes after 9 o'clock." Such a
solution is certainly possible by the use of verbal imagery of any type.

The test shows a high correlation with mental age, but more than most
others it is subject to the influence of cribbing. For this reason,
other positions of the clock hands should be tried out for the purpose
of finding substitute experiments of equal difficulty. Until such
experiments have been made, it will be necessary to confine the
experiment to the three positions here presented.

Schooling seems to have no influence whatever on the percentage of
passes.

This test was first used by Binet in 1905, but was not included in
either the 1908 or 1911 series. Goddard and Kuhlmann both include the
test in their revisions, placing it in year XV. They give only two
problems (our _a_ and _c_) and require that both be answered correctly.
Neither Goddard nor Kuhlmann, however, indicates the degree of error
permitted.

Something depends upon original position of the hands. Binet used 6.20
and 2.46. For some reason the 2.46 arrangement is much more difficult
than either 8.10 or 6.22, yielding almost twice as many failures as
either of the other positions.

XIV, ALTERNATIVE TESTS: REPEATING SEVEN DIGITS

This time, as in year X, only two series are given, one of which must be
repeated without error. The two series are: 2-1-8-3-4-3-9 and
9-7-2-8-4-7-5. Note that in none of the tests of repeating digits is it
permissible to warn the subject of the number to be given.

REMARKS. Binet originally placed this test in year XII, giving three
trials, but later moved it to year XV. Goddard and Kuhlmann retain it in
year XII. Our data show that when three trials are given the test is too
easy for year XIV, but that it fits this age when only two trials are
allowed; that after the age of 12 or 14 years memory for relatively
meaningless material, like digits or nonsense syllables, improves but
little; and that above this level it does not correlate very closely
with intelligence.

CHAPTER XIX

INSTRUCTIONS FOR "AVERAGE ADULT"

AVERAGE ADULT, 1: VOCABULARY (SIXTY-FIVE DEFINITIONS, 11,700 WORDS)

PROCEDURE and SCORING, as in previous vocabulary tests.[76] At the
average adult level sixty-five words should be correctly defined.

[76] See VIII, 6.

AVERAGE ADULT, 2: INTERPRETATION OF FABLES (SCORE 8)

PROCEDURE. As in year XII, test 6. Use the same fables.

SCORING. The method of scoring is the same as for XII, but the total
score must be 8 points to satisfy the requirements at this level.

REMARKS. For discussion of test, see XII, 5.

AVERAGE ADULT, 3: DIFFERENCES BETWEEN ABSTRACT TERMS

PROCEDURE. Say: _What is the difference between_:--

(a) _Laziness and idleness?_
(b) _Evolution and revolution?_
(c) _Poverty and misery?_
(d) _Character and reputation?_

SCORING. _Three correct contrasting definitions out of four_ are
necessary for a pass. It is not sufficient merely to give a correct
meaning for each word of a pair; the subject must point out a difference
between the two words so as to make a real contrast. For example, if the
subject defines _evolution_ as a "growth" or "gradual change," and
_revolution_ as the turning of a wheel on its axis, the experimenter
should say: "_Yes, but I want you to tell me the difference between
evolution and revolution._" If the contrast is not then forthcoming the
response is marked _minus_.

The following are sample definitions which may be considered
acceptable:--

(a) _Laziness and idleness._ "It is laziness if you won't
work, and idleness if you are willing to work but haven't any
job." "Lots of men are idle who are not lazy and would like to
work if they had something to do." "Laziness means you don't
want to work; idleness means you are not doing anything just
now." "Idle people may be lazy, or they may just happen to be
out of a job." "It is laziness when you don't like to work, and
idleness when you are not working." "An idle person might be
willing to work; a lazy man won't work." "Laziness comes from
within; idleness may be forced upon one." "Laziness is aversion
to activity; idleness is simply the state of inactivity."
"Laziness is idleness from choice or preference; idleness means
doing nothing."

The essential contrast, accordingly, is that _laziness refers to
unwillingness to work; idleness to the mere fact of inactivity_.
This contrast must be expressed, however clumsily.

(b) _Evolution and revolution._ "Evolution is a gradual
change; revolution is a sudden change." "Evolution is natural
development; revolution is sudden upheaval." "Evolution means an
unfolding or development; revolution means a complete upsetting
of everything." "Evolution is the gradual development of a
country or government; revolution is a quick change of
government." "Evolution takes place by natural force; a
revolution is caused by an outside force." "Evolution is growth;
revolution is a quick change from existing conditions."
"Evolution is a natural change; revolution is a violent
change." "Evolution is growth step by step; revolution is more
sudden and radical in its action." "Evolution is a change
brought about by peaceful development, while revolution is
brought about by an uprising."

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