Diminishing returns as a function of the association between within-individual average performance and variance

Abstract

It has been demonstrated that the worst performance rule (WPR) effect can occur as a result of statistical dependencies in the data. Here, we examine whether this might also be the case for Spearman's law of diminishing returns (SLODR). Two proposed SLODR criteria are the skewness of the estimated latent ability factor and the correlation between this latent ability and within-individual residual variance. Using four publicly available datasets, covering quite different dimensions of behavior, we show that both these criteria are affected by the correlation between within-individual average performance and variance on the test scores. However, the influence of this correlation on the two criteria goes in opposite directions, which suggests that it generally might be difficult to get results that unambiguously support SLODR. These results might have far-reaching implications for the literature, to the extent that various research findings attributed to human cognitive functioning might in fact be due to trivial statistical dependencies in data. This is an important issue to address for future research.