Spearman's law of diminishing returns: A statistical artifact?

Abstract

Spearman's Law of Diminishing Returns (SLODR) is the idea that the structure of human cognitive ability is more differentiated and g a weaker determinant of cognitive performance at higher levels of ability. In this study, we distinguish between ‘traditional’ methods of testing SLODR and ‘contemporary’ methods of testing SLODR. It is the former set of methods from which the vast majority of the evidence base for SLODR derives. We demonstrated that it is easy to mimic SLODR and reverse SLODR effects in these traditional methods of assessing SLODR by using data with skewed observed variable distributions. The skewness magnitudes did not need to be large to produce these effects and they fell well within the range of values that are usually considered unproblematic for parametric statistic analysis. In simulated datasets, positive subtest skewness resulted in SLODR and negative subtest skewness resulted in reverse SLODR. In contemporary methods of testing SLODR, non-linear g-loadings or a skewed g are assumed to reflect evidence for SLODR. When we applied contemporary methods of testing SLODR to these data, there was evidence of heteroscedastic residuals but no evidence of non-linear g-loadings or skewed g distributions. We broadly replicated the effects of subtest skew from these simulated datasets in real data from the Minnesota Study of Twins Reared Apart. Results imply that traditional methods of assessing SLODR cannot distinguish between effects due to subtest characteristics that have nothing to do with differences in ability structure at different levels of g and true SLODR effects. This calls into question the empirical support for SLODR.