Discovery of “Hierarchical” order among correlation coefficients—Use of the formula for the correction of observational errors to prove the existence of a general factor—Researches between 1904 and 1912—A criterion for hierarchical order applied to numerous researches—Complications in the original theory.

DISCOVERY OF HIERARCHICAL ORDER AMONG CORRELATION COEFFICIENTS

THE controversy as to whether ability in any individual is general, or specific, or in groups or “ faculties ” is a very old one, but for the purposes of the present chapter it is not necessary to go back prior to 1904, in which year there was published the first f of a series of articles in which Professor C. Spearman has developed his Theory of General Ability, or Theory of Two Factors, as it is alternatively named.

Professor Spearman's method in that paper was to measure a number of mental abilities, some of them school subjects, others artificial tests, in a number of persons, and calculate the correlation coefficients of each of these activities with each of the others. These correlation coefficients, he then noticed, had a certain relationship among themselves, a relationship which may be called hierarchical order, and is explained in detail later. He saw, quite rightly, that the presence of a general factor would produce this hierarchical order among the coefficients, and, reversing this argument, he concluded that the presence of hierarchical order proved the existence of a general factor.

In this first series of investigations Professor Spearman used the following groups of subjects: 24 village school-children of both sexes, age limits 10•0 to 13•10; 23 boys of a high class preparatory school, age limits 9•5—13•7; and 27 adults of both sexes, age limits 21—78.