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 surpass 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
sum of D[squared] = 24
n[squared] - 1 = 48
6 x sum of D[squared] = 144
6 x sum of D[squared] / n ( n[squared] - 1 )
= 1 - 144/(7 x 48)
= +.57
In order to get a full and true measure of the
correlation between two tests, the following
precautions are necessary:
(1) The same individuals must be given
both tests.
(2) The number of individuals tested must be as
great as 15 or 20, preferably more.
(3) The individuals should be a fair sample of
the population in regard to the abilities
tested; they should not be so selected as to
represent only a small part of the total range
of ability.
(4) The tests should be thorough enough to
determine each individual's rank in each test,
with a high degree of certainty. Sloppy testing
gives a correlation nearer zero than it should
be, because it "pies" the true orders to some
extent.
[End footnote]
General Factors in Intelligence
If now we try to analyze intelligence and see in what it consists, we can best proceed by reviewing the intelligence tests, and asking how it is that an individual succeeds in them. Passing the tests is a very specific instance of [{286}] intelligent behavior, and an analysis of the content of the tests should throw some light on the nature of intelligence.
The first thing that strikes the eye in looking over the tests is that they call for so many different reactions. They call on you to name objects, to copy a square, to tell whether a given statement is true or false, to tell wherein two objects are alike or different. The first impression, then, is that intelligence consists simply in doing a miscellaneous lot of things and doing them right.