Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power - Blanca, María; Arnau, Jaume; García-Castro, F.; Alarcón, Rafael; Bono, Roser (Psicothema, 2023)
Repeated measures designs are commonly used in health and social sciences research. Although there are other, more advanced, statistical analyses, the F-statistic of repeated measures analysis of variance (RM-ANOVA) remains the most widely used procedure for analyzing differences in means. The impact of the violation of normality has been extensively studied for between-subjects ANOVA, but this is not the case for RM-ANOVA. Therefore, studies that extensively and systematically analyze the robustness of RM-ANOVA under the violation of normality are needed. This paper reports the results of two simulation studies aimed at analyzing the Type I error and power of RM-ANOVA when the normality assumption is violated but sphericity is fulfilled. Study 1 considered 20 distributions, both known and unknown, and we manipulated the number of repeated measures (3, 4, 6, and 8) and sample size (from 10 to 300). Study 2 involved unequal distributions in each repeated measure. The distributions analyzed represent slight, moderate, and severe deviation from normality. Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality. RM-ANOVA is generally robust to non-normality when the sphericity assumption is met.