Detecting Between-Groups Heteroscedasticity in Moderated Multiple Regression With a Continuous Predictor and a Categorical Moderator

Abstract

Moderated multiple regression (MMR) is frequently used to test moderation hypotheses in the behavioral and social sciences. In MMR with a categorical moderator, between-groups heteroscedasticity is not uncommon and can inflate Type I error rates or reduce statistical power. Compared with research on remedial procedures that can mitigate the effects of this violated assumption, less research attention has focused on statistical procedures that can be used to detect between-groups heteroscedasticity. In the current article, we briefly review such procedures. Then, using Monte Carlo methods, we compare the performance of various procedures that can be used to detect between-groups heteroscedasticity in MMR with a categorical moderator, including a heuristic method and a variant of a procedure suggested by O’Brien. Of the various procedures, the heuristic method had the greatest statistical power at the expense of inflated Type I error rates. Otherwise, assuming that the normality assumption has not been violated, Bartlett’s test generally had the greatest statistical power when direct pairing occurs (i.e., when the group with the largest sample size has the largest error variance). In contrast, O’Brien’s procedure tended to have the greatest power when there was indirect pairing (i.e., when the group with the largest sample size has the smallest error variance). We conclude with recommendations for researchers and practitioners in the behavioral and social sciences.