Robust Means Modeling: An Alternative for Hypothesis Testing of Independent Means Under Variance Heterogeneity and Nonnormality

This study proposes robust means modeling (RMM) approaches for hypothesis testing of mean differences for between-subjects designs in order to control the biasing effects of nonnormality and variance inequality. Drawing from structural equation modeling (SEM), the RMM approaches make no assumption of variance homogeneity and employ robust estimation/rescaling strategies in order to alleviate reliance on normality. A Monte Carlo simulation is conducted to compare the Type I error rate and the power of the proposed six RMM test statistics to five analysis of variance (ANOVA)-based statistics, the latter of which have also employed trimmed means and Winsorized variances to enhance robustness. Various simulation factors manipulated include variance inequality, sample-size pairings with group variances, degree of nonnormality, alpha level for hypothesis tests, and effect size. Results show that the proposed RMM methods are indeed superior to the traditional ANOVA-based methods.