Refinements to Effect Sizes for Tests of Categorical Moderation and Differential Prediction

Abstract

We provide a follow-up treatment of Nye and Sackett’s (2017) recently proposed d_Mod standardized effect-size measures for categorical-moderation analyses. We offer several refinements to Nye and Sackett’s effect-size equations that increase the precision of d_Mod estimates by accounting for asymmetries in predictor distributions, facilitate the interpretation of moderated effects by separately quantifying positive and negative differences in prediction, and permit the computation of nonparametric effect sizes. To aid in the implementation of our refinements to d_Mod, we provide software written in the R programming language that computes Nye and Sackett’s effect sizes with all of our refinements and that includes options for easily computing bootstrapped standard errors and bootstrapped confidence intervals.