Robust Means Modeling: An Alternative to Hypothesis Testing Of Mean Equality in the Between-Subjects Design under Variance Heterogeneity and Nonnormality

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The study describes the various alternatives to the between-subjects ANOVA F test that have been performing reasonably well in the literature under different experimental conditions of sample sizes, variance ratios or nonnormality. Drawing from structural equation modeling (SEM), the robust means modeling (RMM) approach is developed, in which the assumption of variance homogeneity is not part of the model or its estimation. Specifically, univariate structured means modeling (SMM) is applied to the independent groups design with robust estimation strategies such as the Browne's asymptotic distribution free (ADF) estimator (1982, 1984) and its alternatives for non-normal continuous variables in order to achieve robustness to the biasing effects of nonnormality. A Monte Carlo simulation investigation is conducted to compare the Type I error rate and the power of the ANOVA-based methods as well as the proposed RMM approaches. Various factors including variance inequality, sample-size pairings with group variances, and degree of nonnormality are manipulated in the simulation. The results show that the proposed RMM methods are indeed superior to the ANOVA-based methods across conditions, especially when the distribution is asymmetric nonnormal.