Beyond step-down analysis: a new test for decomposing the importance of dependent variables in MANOVA

Abstract

Multivariate analysis of variance (MANOVA) is often categorized as a tool for experimental psychologists. However, it also continues to be a popular statistical procedure used by organizational scientists. Unfortunately, when the dependent variables (DV) are correlated with one another, interpreting the significant omnibus test in MANOVA becomes difficult. The present article proposes a novel way of interpreting a significant MANOVA that draws from work dedicated to understanding the relative importance of correlated predictors in multiple regression. Relative importance analyses are specifically designed to overcome the limitations caused by correlated variables and permit researchers to appropriately partition shared variance. We derive and extend relative weight analysis to MANOVA designs and demonstrate how these weights may be used to draw inferences concerning the relative contribution of each DV to the overall multivariate effect. Through our example, we illustrate how researchers must consider the correlations among the DVs when interpreting a significant multivariate effect, and our procedure provides an effective mechanism for doing just that.