Spearman’s Law of Diminishing Returns (SLODR): Examining Effects at the Level of Prediction

The current study presents the results of an incremental validity investigation using a hierarchical multiple regression design, examining standard score data from the standardization sample (N = 4,722) of the Woodcock-Johnson III Tests of Cognitive Abilities (WJ-III COG) and Achievement (WJ-III ACH). Specifically, this study examined whether or not the differentiation hypothesis known as Spearman’s law of diminishing returns (SLODR) impacts the incremental predictive validity of the Cattell-Horn-Carroll (CHC) broad cluster scores on the WJ-III COG. Consistent with the SLODR hypothesis, differential patterns of prediction were observed across ability classes (e.g., Below Average, Average, Above Average). Specifically, the general factor score (GIA) accounted for significantly less portions of achievement variance in the Above Average group (R2 = .11 to .20) when compared to estimates for the Below Average group (R2 = .24 to .32). Secondary chi-square goodness of fit tests provided additional evidence of predictive variance across ability classes. The results of this study indicate that the effects of SLODR must be accounted for when interpreting the results of the contemporary cognitive ability tests in clinical settings.