Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power

• Published in: Psicothema Vol. 1; no. 35; pp. 21 - 29
• Main Authors: Blanca, María, Arnau, Jaume, García-Castro, F., Alarcón, Rafael, Bono, Roser
• Format: Journal Article
• Language: English
• Published: Spain Colegio Oficial de Psicólogos (PSICODOC) 01.01.2023; Colegio Oficial de Psicólogos del Principado de Asturias
• Subjects: Analysis of Variance; Between-subjects design; Computer Simulation; Humans; Psychology; Psychology, Clinical; Psychology, Developmental; Psychology, Experimental; Psychology, Multidisciplinary; Research Design; Sample Size; Variance analysis; Within-subjects design; potencia; diseño intrasujeto; ANOVA; robustness; violation of normality; within-subject design; power; robustez; violación de la normalidad
• ISSN: 0214-9915; 1886-144X; 1886-144X
• DOI: 10.7334/psicothema2022.292

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.