Standardized effect sizes for moderated conditional fixed effects with continuous moderator variables

Abstract

Wilkinson and Task Force on Statistical Inference (1999) recommended that researchers include information on the practical magnitude of effects (e.g., using standardized effect sizes) to distinguish between the statistical and practical significance of research results. To date, however, researchers have not widely incorporated this recommendation into the interpretation and communication of the conditional effects and differences in conditional effects underlying statistical interactions involving a continuous moderator variable where at least one of the involved variables has an arbitrary metric. This article presents a descriptive approach to investigate two-way statistical interactions involving continuous moderator variables where the conditional effects underlying these interactions are expressed in standardized effect size metrics (i.e., standardized mean differences and semi-partial correlations). This approach permits researchers to evaluate and communicate the practical magnitude of particular conditional effects and differences in conditional effects using conventional and proposed guidelines, respectively, for the standardized effect size and therefore provides the researcher important supplementary information lacking under current approaches. The utility of this approach is demonstrated with two real data examples and important assumptions underlying the standardization process are highlighted.