How to calculate, use, and report variance explained effect size indices and not die trying

Abstract

Many consumer research and social science journals are increasingly urging behavioral researchers to submit effect sizes among their reported results. Yet most researchers are less familiar with effect sizes than with significance tests, even in choosing among them. This article clarifies the concepts, formulae, and appropriate usage of the “variance explained” effect size indices, eta-squared, omega-squared, and epsilon-squared (${\eta }^2,{\omega }^2,{\epsilon }^2$), and their partial effect size variants (${\eta }_p^2,{\omega }_p^2,{\epsilon }_p^2$). Equations are presented, explained, and illustrated. Software is provided to facilitate the calculation of the indices in SAS, SPSS, and R, and suggestions and updated guidance are offered to scholars regarding reporting practices. The primary contribution of this article is to clarify the role of variance explained effect sizes in behavioral research so that scholars can be confident in precisely understanding the content of these measures in their analysis and reporting.