VII. THE HIERARCHY OF ABILITIES
It has been stated that though all, or nearly all, mental functions so far measured and correlated, yield positive coefficients, all do not show an equal amount of positive correlation. Certain mental functions, for example, are shown to yield coefficients of as much as .80, for a total correlation with others of a series; while some yield coefficients as low as .10, approaching absence of relationship. To explain these facts, Spearman formulated the concept of a hierarchy of relatedness to a “general factor.” Those abilities showing slight correlation with others in series of tests, were thought of as but loosely related to “general intelligence,” and as constituting “special abilities.” They might be displayed by persons inferior in general, or might be lacking in persons otherwise superior.
Here again, the facts are not in question. It is admitted by all that functions show different amounts of positive correlation with one another, and of total correlation with members of a series. Not all experts agree, however, with Spearman’s theoretical explanation of the phenomena. Thomson has recently shown, by tossing dice of various colors, that in this game of chance (in which there is no “general factor,” but only many independent factors), hierarchical order of correlation coefficients is almost sure to be obtained, for combinations resulting from throws. Thomson, therefore, holds that the theory of a “general factor,” participating in all the separate performances of an individual, is not proved from the facts about correlation coefficients. He proposes the following, regarded by him as an alternative: “The mind, in carrying out any activity such as a mental test, has two levels at which it can operate. The elements of activity at the lower level are entirely specific, but those at the higher level are such that they may come into play in different activities. Any activity is a sample of these elements. The elements are assumed to be additive like dice, and each to act on the ‘all or none’ principle, not being in fact further divisible.”
It is not quite easy to see that this theory, finally proposed by Thomson, which might be termed the “two level” theory, is very different from Spearman’s “two factor” theory, nor why the terms “higher” and “lower” should be introduced. But demonstration of the probability of obtaining a hierarchy of correlations simply from the tossing together by chance of independent factors, as with dice, adds new data for consideration. It might be that non-biological principles of probability are sufficient to explain the hierarchical order of correlations, among many tests administered to a given group, just as they are apparently sufficient to account for the particular form in which ability in any single test is distributed through the human species.
But if this is so, how account for the consistency with which certain abilities, like ability to draw, are repeatedly shown to correlate but slightly, while others, like completing sentences, repeatedly yield high total correlation? How account for the fact that there is marked coherence among certain groups of tests, such as “tests dealing with words only,” and “tests dealing with numbers only,” as contrasted with the relative lack of coherence among “tests, some dealing with number, and some with words”? It would seem that these phenomena must be at bottom biological. It cannot, for instance, be demonstrated that yellow dice and red dice thrown, wherever and by whomever cast, tend always to correlate high, while green and maroon dice tend always to correlate low with each other, and with yellow and red dice. Nor can it be demonstrated that dice colored, let us say, from one end of the spectrum tend always to correlate high among themselves, but much lower with the dice colored from the other end of the spectrum, wherever and by whomever cast.
Furthermore, die-casting will not give a relationship in which throws resulting in low scores are paired with low scores, and so on, from low through high, high scores being also paired with high scores, as when organisms are tried. The correlation among throws of dice arises from a different form of relationship, in which the improbable throws, resulting in either very high or very low scores, are paired indifferently,[[6]] this indifference not being able, however, to produce zero correlation, because of the infrequency of extreme scores. The frequently occurring, mediocre scores in both series are, however, very similar, the most frequently occurring score for both being, indeed, the same. Since the mediocre scores tend to occur both frequently and together, because of the laws of chance, they produce positive correlations, differing in amount from series to series (also because of the laws of chance). But when organisms are tested, as has been repeatedly demonstrated, the serial relationship between two functions holds through high and low, and this, also, must be biological, and not explainable by laws of chance.
The demonstrations from die-casting are extremely significant, as warning us not to depend wholly for our inferences upon the amount of positive coefficients of correlation, nor the possibility of arranging them in hierarchical order. Both of these features of apparent relationship may come of chance, within a single series. Other features of relationship must be examined in the attempt to infer biological law, especially the consistency with which given traits correlate to a given degree with others, when investigated by different examiners, in various groups; and the form of the relationship, whether all the way from highest to lowest, or only in central tendency.