15-29 12 0

30-44 15 0

45-59 16 0

60-74 13 0

75-89 11 1

90-104 9 4

105-119 7 8

120-134 6 14

135-149 4 23

150-164 2 24

165-179 1.3 13

180-194 0.5 7

195-212 0.2 1 ----- --- 100 100

The "drafted men", consisting of men between the ages of twenty-one and thirty-one, fairly represent the adult male white population of the country, except in two respects. Many able young men were not included in the draft, having previously volunteered for officers'

training camps or for special services. Had they been included, the percentages making the higher scores would have gone up slightly. On the other hand, many men of very low intelligence never reached the receiving camps at all, being inmates of inst.i.tutions for the feebleminded or excluded from the draft because of known mental deficiency; and, of those who reached {280} the camps, many, being illiterate, did not take the Alpha test. It is for this reason that the graph for drafted men stops rather short at the lower end; to picture fairly the distribution of intelligence, it should taper off to the left, beyond the zero of the Alpha test.

[Ill.u.s.tration: Fig. 46.--Distribution of the scores of drafted men, and also of college freshmen, in the Alpha test. The height of the broken line above the base line is made proportional to the percent of the group that made the score indicated just below along the base line. (Figure text: army median--65, freshman median--150)]

College freshmen evidently are, as they should be, a highly selected group in regard to intelligence. The results obtained at different colleges differ somewhat, and the figures here given represent an approximate average of results obtained at several colleges of high standing. The median {281} score for freshmen has varied, at different colleges, from 140 to 160 points.

[Footnote: The "median" is a statistical measure very similar to the average; but, while the average score would be obtained by adding together the scores of all the individuals and dividing the sum by the number of individuals tested, the median is obtained by arranging all the individual scores in order, from the lowest to the highest, and then counting off from either end till the middle individual is reached; his score is the median. (If the number of individuals tested is an even number, there are two middle individuals, and the point midway between them is taken as the median.) Just as many individuals are below the median as above it.

The median is often preferred to the average in psychological work, not only because it is more easily computed, but because it is less affected by the eccentric or unusual performances of a few individuals, and therefore more fairly represents the whole population.]

It will be noticed in the graph that none of the freshmen score as low as the median of the drafted men. All of the freshmen, in fact, lie well above the median for the general population. A freshman who scores below 100 points finds it very difficult to keep up in his college work. Sometimes, it must be said, a freshman who scores not much over 100 in the test does very well in his studies, and sometimes one who scores very high in the test has to be dropped for poor scholarship, but this last is probably due to distracting interests.

No such sampling of the adult female population has ever been made as was afforded by the draft, and we are not in a position to compare the average adult man and woman in regard to intelligence. Boys and girls under twelve average almost the same, year by year, according to the Binet tests. In various other tests, calling for quick, accurate work, girls have on the average slightly surpa.s.sed boys of the same age, but this may result from the fact that girls mature earlier than boys; they reach adult height earlier, and perhaps also adult intelligence.

College women, in the Alpha test, score on the average a few points below college men, but this, on the other hand, may be due to the fact that the Alpha test, being prepared for men, includes a few questions that lie rather outside the usual range of women's interests. On the whole, tests have given very little evidence of any significant difference between the general run of intelligence in the two s.e.xes.

Limitations of the Intelligence Tests

Tests of the Binet or Alpha variety evidently do not cover the whole range of intelligent behavior. They do not test {282} the ability to manage carpenter's or plumber's tools or other concrete things, they do not test the ability to manage people, and they do not reach high enough to test the ability to solve really big problems.

Regarding the ability to manage concrete things, we have already mentioned the performance tests, which provide a necessary supplement to the tests that deal in ideas expressed in words. It is an interesting fact that some men whose mental age is below ten, according to the Binet tests, nevertheless have steady jobs, earn good wages, and get on all right in a simple environment. There are many others, with a mental age of ten or eleven, who cannot master the school work of the upper grades, and yet become skilled workmen or even real artists. Now, it takes mentality to perform skilled or artistic work; only, the mentality is different from that demanded by what we call "intellectual work".

Managing people requires tact and leadership, which are obviously mental traits, though not easily tested. It is seldom that a real leader of men scores anything but high in the intelligence tests, but it more often happens that an individual who scores very high in the tests has little power of leadership. In part this is a matter of physique, or of temperament, rather than of intelligence, but in part it is a matter of _understanding_ people and seeing how they can be influenced and led.

Though the intelligence tests deal with "ideas", they do not, as so far devised, reach up to the great ideas nor make much demand on the superior powers of the great thinker. If we could a.s.semble a group of the world's great authors, scientists and inventors, and put them through the Alpha test, it is probable that they would all score high, but not higher than the upper ten per cent, of college freshmen. Had their IQ's been determined when they were children, {283} probably all would have measured over 180 and some as high as 200, but the tests would not have distinguished these great geniuses from the gifted child who is simply one of a hundred or one of a thousand.

The Correlation of Abilities

There is no opposition between "general intelligence", as measured by the tests, and the abilities to deal with concrete things, with people, or with big ideas. Rather, there is a considerable degree of correspondence. The individual who scores high in the intelligence tests is likely, but not certain, to surpa.s.s in these respects the individual who scores low in the tests. In technical language, there is a "positive correlation" between general intelligence and ability to deal with concrete things, people and big ideas, but the correlation is not perfect.

_Correlation_ is a statistical measure of the degree of correspondence. Suppose, for an example, we wish to find out how closely people's weights correspond to their heights. Stand fifty young men up in single file in order of height, the tallest in front, the shortest behind. Then weigh each man, and shift them into the order of their weights. If no shifting whatever were needed, the correlation between height and weight would be perfect. Suppose the impossible, that the shortest man was the heaviest, the tallest the lightest, and that the whole order needed to be exactly reversed; then we should say that the correlation was perfectly inverse or negative.

Suppose the shift from height order to weight order mixed the men indiscriminately, so that you could not tell _anything_ from a man's position in the height order as to what his position would be in the weight order; then we should have "zero correlation". The actual result, however, would be that, while the height order would be {284} somewhat disturbed in shifting to the weight order, it would not be entirely lost, much less reversed. That is, the correlation between height and weight is positive but not perfect.

Statistics furnishes a number of formulae for measuring correlations, formulae which agree in this, that perfect positive correlation is indicated by the number + 1, perfect negative correlation by the number - 1, and zero correlation by 0. A correlation of +.8 indicates close positive correspondence, though not perfect correspondence; a correlation of +.3 means a rather low, but still positive, correspondence; a correlation of -.6 means a moderate tendency towards inverse relationship.

The correlation between two good intelligence tests, such as the Binet and the Alpha, comes out at about +.8, which means that if a fair sample of the general population, ranging from low to high intelligence, is given both tests, the order of the individuals as measured by the one test will agree pretty closely with the order obtained with the other test. The correlation between a general intelligence test and a test for mechanical ability is considerably lower but still positive, coming to about +.4. Few if any real negative correlations are found between different abilities, but low positive or approximately zero correlations are frequent between different, rather special abilities.

In other words, there is no evidence of any antagonism between different sorts of ability, but there is plenty of evidence that different special abilities may have little or nothing in common.

[Footnote]

Possibly some readers would like to see a sample of the statistical formulae by which correlation is measured. Here is one of the simplest. Number the individuals tested in their order as given by the first test, and again in their order as given by the second test, and find the difference between each individual's two rank numbers. If an individual who ranks no. 5 in one test ranks no.

12 in the other, the difference in his rank numbers is 7. Designate this difference by the letter D. and the whole number of individuals tested by n. Square each D, and get the sum of all the squares, calling this sum "sum of D2[squared]". Then the correlation is given by the formula,

1 - ( ( 6 X sum of D[squared] ) / (n x ( n[squared] - 1)) )

As an example in the use of this formula, take the following:

Individuals Rank of each Rank of each D D[squared]

tested individual in individual in first test second test

Albert 3 5 2 4

George 7 6 1 1

Henry 5 3 2 4

James 2 1 1 1

Stephen 1 4 3 9

Thomas 4 2 2 4

William 6 7 1 1

n = 7