| Table from Hollingworth | |||
|---|---|---|---|
| Showing rank in each of two mental functions, within a group of fifth grade children, selected for special disability in spelling. The coefficient of correlation obtained is .081. | |||
| Name | Mental Age | Spelling Ability | |
| Yrs. | Mos. | Per Cent Correct | |
| (Stanford-Binet) | Lists Q and R (Ayres) | ||
| RL | 13 | 7 | 90.1 |
| JP | 12 | 5 | 95.2 |
| HA | 12 | 2 | 81.7 |
| MG | 11 | 6 | 31.7 |
| LK | 10 | 10 | 80.2 |
| SSh | 10 | 10 | 77.9 |
| SSc | 10 | 9 | 81.8 |
| MS | 10 | 9 | 34.1 |
| PJ | 10 | 4 | 32.6 |
| HL | 10 | 1 | 58.9 |
| RH | 9 | 8 | 93.1 |
| MU | 9 | 8 | 57.0 |
| BN | 9 | 6 | 92.1 |
| HR | 8 | 3 | 81.8 |
If there is in fact perfect correspondence, so that each pupil holds the same rank on the distribution in both functions, a perfect positive correlation is obtained, the coefficient of correlation being expressed as 1.00. If no relationship at all exists between the two functions measured, so that nothing whatever can be predicted of either from knowing about the other, the coefficient of correlation will be 0.00[[3]] If there exists a perfect negative relationship, so that the person who stands highest in one stands lowest in the other, and so forth through the series, in a perfect inverse standing of all members, then a coefficient of correlation expressed by −1.00 is obtained.
In the sample given, the coefficient of correlation obtained is .081, which not being reliably greater than zero (because of possible error due to the smallness of the group and other conditions) tells us that the two functions are in this case related to each other only very slightly, if at all. The child who stands above the average of the group in mental age, may or may not stand above the group average in spelling. With a relationship so far from unity as is expressed by a coefficient of .081, we may expect to find in this group comparatively intelligent children who are very poor spellers, and good spellers who stand low in mental age. Among children taken at random, however, a different relationship exists between spelling ability and general intelligence, as represented by mental age. The positive correlation is much higher among children not selected, as these were, for an observed discrepancy.
At the present time the more elaborate methods of partial correlation and multiple correlation are being applied to the study of relationships, where more than two functions are involved. Into the intricacies of these we shall not enter, except as concerns their results.
II. GENERAL INTELLIGENCE vs. SPECIAL APTITUDES
The original attempts to apply mathematical formulæ to the study of relationship among mental traits eventuated in divergent hypotheses. In England, Spearman, with his students and collaborators, interpreted his researches to mean that there is in mental constitution a “general factor,” which shows itself in all the performances of a given individual. This would render relatively predictable the quality of performance in all functions, from knowledge of performance in one function. “All branches of intellectual activity have in common one fundamental function (or group of functions), whereas the remaining or specific elements of the activity seem in every case to be wholly different from that in all others.... The function almost entirely controls the relative position of children at school (after making due allowance for differences of age), and is nine parts out of ten responsible for success in such a simple act as Discrimination of Pitch.... Its relation to the intellectual activity does not appear to be of any loosely connected or auxiliary character (such as willingness to make an effort, readiness in adaption to unfamiliar tests, or dexterity in the fashion of executing them), but rather to be intimately bound up in the very essence of the process.”
Spearman noted that, though all functions seemed related to this “common factor,” they were not all equally related in his results; wherefore he formulated the concept of a hierarchy of relatedness. Discussion as to the essential nature of the fundamental factor was reserved, but it was predicted from the correlations made that “general intelligence” could and would be measured for practical purposes. This interpretation was based upon the fact that among abilities which yielded to his measurement, Spearman could find only positive coefficients of correlation, when the groups were large and the human beings non-select.
In the United States, Thorndike and his collaborators were most struck by the fact that the coefficients obtained fell short, in many cases far short, of unity. They laid stress upon the imperfection of the relations revealed, and were able to show that between some functions, such as discriminating among the lengths of lines, and others, such as naming the opposites of words, the correlation dropped in groups investigated to approximately zero.
As a result of interpretation from their point of view, they wrote as follows: “One is almost tempted to replace Spearman’s statement by the equally extravagant one that there is nothing whatever common to all mental functions, or to any half of them.” They maintained that mental functions are specialized, and that when excellence in one is correlated with excellence in another, “this is due chiefly to the fact that the two involve identical elements in their execution. It is not due to one and the same ‘faculty,’ which presides over their activities.”
These two divergent interpretations of the same array of data have been cited, because the controversy involved is of first rate importance for mental measurement, for the understanding of individuals, and for education. The controversy now appears to have been one of emphasis. To recapitulate, Spearman stressed the positive aspect of the coefficients found, and declared mental traits to be distributed so that status in one is predictable from status in another. Thorndike emphasized the reduction from unity of the coefficients, and formulated the hypothesis that there is no absolutely predictable coherence among mental functions, that each is special to itself within an individual. No laboratory scientist has ever found reason for adding a third side to the controversy, by advocating seriously that mental traits are compensatory in relation to each other. Negative coefficients of correlation have never been found, except occasionally by chance or selection.[[4]] All know that the correlations among amounts of traits are positive. It is the reduction from unity which has caused the disagreements of interpretation.