Spearman's "Law of Diminishing Returns"
Spearman ( 1927, pp. 217-21) compared the disattenuated correlation matrices (based on 12 diverse cognitive tests) of 78 "normal" children and 22 "defective" children. He found that the mean r of the matrix for the normal children was +.466; for the retarded children the mean r was +.782. Deary and Pagliari ( 1991) performed principal components analyses of Spearman's correlation matrix for the normal children and the correlation matrix for the defective children. The average loadings on the first principal component (PCI) of each matrix were +.325 and +.899, respectively. Yet the PC1 was clearly the same factor in both the normal and retarded groups, as indicated by a congruence coefficient of +.988. Spearman also noted in other data sets that tests' intercorrelations (and average g loadings) were larger for younger children than for older children. These findings suggested that the higher the level of g, the less is the amount of g variance in any particular mental test.
Spearman rather grandiosely likened this phenomenon to the "law of diminishing returns," as it applies in physics and in economics. That is, the higher a person's level of g, the less important it becomes in the variety of abilities the person possesses. High-g persons have more diversified abilities, with more of the total variance in their abilities existing in non-g factors (i.e., the various group factors and specificity). Others have explained this phenomenon in terms of what has become known as the differentiation theory, that higher g level (and the increase in mental abilities from childhood to early maturity) is accompanied by an increasing differentiation of general ability and the development of special abilities independent of g. (In the elderly, the reverse occurs for novel tests and tasks; there is dedifferentiation of abilities variance and a consequent increase in various tests' g loadings.) One might say that in the course of mental development g (or fluid ability, Gf) becomes increasingly invested in specialized skills, in which proficiency becomes partly automatized through practice. The automatized aspects of the special skills lose their g loading, and the non-g part
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Publication information: Book title: The G Factor:The Science of Mental Ability. Contributors: Arthur R. Jensen - Author. Publisher: Praeger. Place of publication: Westport, CT. Publication year: 1998. Page number: 585.