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.
VIII. PRESENT STATUS OF THE PROBLEM
Whatever may be the ultimate cause of the manifestations, educators are practically concerned with the facts. The practical implications for education of knowledge gleaned up to the present time, concerning the coherence among mental functions, have been well stated by Burt, in his recent discussion of Mental and Scholastic Tests: “The examiner should always discriminate between children who are backward in most subjects, and children who are backward in one subject, or limited group of subjects, alone. A child, for example, who suffers merely from a specialized disability in reading and spelling, such as so-called ‘word blindness,’ is to be carefully distinguished from one who is in every respect mentally defective.
“As I have shown in memoranda previously published, educational attainments depend largely upon capacities of two kinds: first, a common or general capacity, entering into every subject in different degrees, but best exhibited in those that need thought-processes of a higher order, such as the comprehension of reading matter among young children, and, among older children, problem arithmetic and literary (or rather logical) composition; secondly, specific capabilities—such as arithmetical ability, linguistic ability, manual ability, and musical ability—entering into a small group of subjects. A child who is deficient in the former will be backward in all subjects—most backward in those subjects most dependent on this central capacity (such as the subjects first named), least backward in those subjects least dependent on it (such as manual and musical subjects). A child who is deficient in one of the specific capacities alone will be backward in the limited group of implicated subjects, and in none but these.”
McCall writes as follows: “There is an objectively and practically measurable something, which constitutes the core of most aptitudes. It is overlaid with various incidental abilities, and furthered or retarded by emotional or physical characteristics of the individual. This something is general intelligence. If an individual’s intelligence is all that is known, some mistakes will be made in attempting vocational guidance, but if only one thing can be known, general intelligence is perhaps most important.... A pupil’s intelligence score is an approximate measure of the diameter of an approximate general ability circle, and is hence an approximate basis for vocational guidance.
“But any individual who assumes that all the spokes in an ability-wheel are of exactly equal length, or that instances of marked special aptitudes do not exist, or even that most individuals do not possess some tendency toward a special aptitude, would make as egregious an error as one who assumed that all individuals are markedly lopsided.”
These two summaries of the present status of this problem from the practical point of view, coming as they do, the one from a student of the British school, the other from a student of Thorndike, show how the two originally conflicting interpretations have been approaching middle ground. There is found to be a quality of the individual, which results in generally superior, mediocre, or inferior performances in his case—a positive coherence in the amounts of all traits possessed, extending even to appreciable coherence between mental and physical. General intelligence is now measured, for practical purposes, as Spearman long ago predicted. Nevertheless, there are, as Thorndike maintained and maintains, mental functions, standing in which is hardly predictable from knowledge of other capacities. In rare cases there may be complete discrepancy in rank between performance in one task and performance in other tasks, with equal training. These are the cases of special talents and defects, to which this volume is devoted.