The Effects of Differential Between-Groups Skewness on Heteroscedastic, Trimmed Means, and Rank-Based Between Groups Procedures

Abstract The effect of differential between-group skewness was investigated for the traditional t- and ANOVA F tests, the Welch procedure without trimming (Welch, 1938) and with trimming and Winsorized variances (Yuen, 1974), the Welch-James (James, 1951) with trimming and transformation, the Yuen procedure with bootstrapping, trimming, and transformation (Keselman, Wilcox, Othman, & Fradette, 2002), and the Welch procedure with ranked data (Zimmerman & Zumbo, 1992). Empirical Type I error and power rates for these procedures were compared under varied conditions of non-normality, heterogeneity, group size imbalance, and positive and negative pairing of variance and group size. In particular, these conditions were combined with conditions of between-group skewness that was equal, dissimilar, and dissimilar and directionally opposite. Monte Carlo simulations revealed that when skewness across groups was unequal, there were deleterious effects on Type I error and power for models with two, four, and seven groups for the traditional t-test and ANOVA F, which had unacceptable rates of Type I error and power compared to other procedures. Further, procedures that accommodate heteroscedasticity fall short compared to those that can simultaneously accommodate heterogeneity and skewness. Finally, empirical power is highest for the Welch procedure on ranked data in most data conditions. It is recommended that investigators routinely investigate their data for violations and adopt robust procedures such as the Welch test on ranks to test differences of central tendency.