Sample Size Determination for Examining Interaction Effects in Factorial Designs Under Variance Heterogeneity

Abstract

Moderation analysis is a vital aspect of research in education, management, psychology, and related disciplines. Although several methodological artifacts have been identified and examined, heterogeneity of variance remains one of the unique and problematic factors known as detrimental to statistical power in the detection of moderating effects. To alleviate the difficulty in assessing moderation because of low statistical power, this article describes feasible solutions to sample size calculations for tests of hypothesized interactions between categorical variables under variance heterogeneity. Detailed numerical illustrations and simulation studies are presented to demonstrate the feature and usefulness of the suggested technique for 2- and 3-way factorial designs. Moreover, SAS and R programs are provided to facilitate the implementation of the proposed sample size procedure.