g Factor (psychometrics) - Spearman's Law of Diminishing Returns

Spearman's Law of Diminishing Returns

A number of researchers have suggested that the proportion of variation accounted for by g may not be uniform across all subgroups within a population. Spearman's law of diminishing returns (SLDR), also termed the ability differentiation hypothesis, predicts that the positive correlations among different cognitive abilities are weaker among more intelligent subgroups of individuals. More specifically, SLDR predicts that the g factor will account for a smaller proportion of individual differences in cognitive tests scores at higher scores on the g factor.

SLDR was originally proposed by Charles Spearman, who reported that the average correlation between 12 cognitive ability tests was .466 in 78 normal children, and .782 in 22 "defective" children. Detterman and Daniel rediscovered this phenomenon in 1989. They reported that for subtests of both the WAIS and the WISC, subtest intercorrelations decreased monotonically with ability group, ranging from approximately an average intercorrelation of .7 among individuals with IQs less than 78 to .4 among individuals with IQs greater than 122.

SLDR has been replicated in a variety of child and adult samples who have been measured using broad arrays of cognitive tests. The most common approach has been to divide individuals into multiple ability groups using an observable proxy for their general intellectual ability, and then to either compare the average interrelation among the subtests across the different groups, or to compare the proportion of variation accounted for by a single common factor, in the different groups. However, as both Deary et al. (1996). and Tucker-Drob (2009) have pointed out, dividing the continuous distribution of intelligence into an arbitrary number of discrete ability groups is less than ideal for examining SLDR. Tucker-Drob (2009) extensively reviewed the literature on SLDR and the various methods by which it had been previously tested, and proposed that SLDR could be most appropriately captured by fitting a common factor model that allows the relations between the factor and its indicators to be nonlinear in nature. He applied such a factor model to a nationally representative data of children and adults in the United States and found consistent evidence for SLDR. For example, Tucker-Drob (2009) found that a general factor accounted for approximately 75% of the variation in seven different cognitive abilities among very low IQ adults, but only accounted for approximately 30% of the variation in the abilities among very high IQ adults.