One-Way and Two-Way ANOVA: Inferences About a Robust, Heteroscedastic Measure of Effect Size

Abstract

Consider a one-way or two-way ANOVA design. Typically, groups are compared based on some measure of location. The paper suggests alternative methods where measures of location are replaced by a robust measure of effect size that is based in part on a robust measure of dispersion. The measure of effect size used here does not assume that the groups have a common measure of dispersion. That is, it deals with heteroscedasticity. It is fairly evident that no single method reveals everything of interest regarding how groups differ. Certainly, comparing measures of location provides useful information. But as illustrated, comparing measures of effect size can provide a deeper understanding of how groups compare.