A heteroscedastic, rank-based approach for analyzing 2 x 2 independent groups designs

The ANOVA F is a widely used statistic in psychological research despite its shortcomings when the assumptions of normality and variance heterogeneity are violated. A Monte Carlo investigation compared Type I error and power rates of the ANOVA F, Alexander-Govern with trimmed means and Johnson transformation, Welch-James with trimmed means and Johnson Transformation, Welch with trimmed means, and Welch on ranked data using Johansen’s interaction procedure. Results suggest that the ANOVA F is not appropriate when assumptions of normality and variance homogeneity are violated, and that the Welch/Johansen on ranks offers the best balance of empirical Type I error control and statistical power under these conditions.