Psicothema was founded in Asturias (northern Spain) in 1989, and is published jointly by the Psychology Faculty of the University of Oviedo and the Psychological Association of the Principality of Asturias (Colegio Oficial de Psicólogos del Principado de Asturias).
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Non-normal Data in Repeated Measures ANOVA: Impact on Type I Error and Power

María J. Blanca1, Jaume Arnau2, F. Javier García-Castro1, Rafael Alarcón1 and Roser Bono2

1 University of Malaga,
2 University of Barcelona

Background: 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. Method: 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. Results: Overall, the results show that the Type I error and power of the F-statistic are not altered by the violation of normality. Conclusions: RM-ANOVA is generally robust to non-normality when the sphericity assumption is met.

Antecedentes: El diseño de medidas repetidas es uno de los más usados en ciencias sociales y de la salud. Aunque hay otras alternativas más avanzadas, el análisis de varianza de medidas repetidas (ANOVA-MR) sigue siendo el procedimiento más empleado para analizar las diferencias de medias. El impacto de la violación de la normalidad ha sido muy estudiado en el ANOVA intersujeto, pero los estudios son muy escasos en el ANOVA-MR. Por ello, el objetivo de este trabajo es realizar dos estudios de simulación Monte Carlo para analizar el error de Tipo I y la potencia cuando se incumple este supuesto bajo el cumplimiento de la esfericidad. Método: El estudio 1 incluye 20 distribuciones, tanto conocidas como desconocidas, manipulando el número de medidas repetidas (3, 4, 6 y 8) y el tamaño muestral (de 10 a 300). El estudio 2 incluye diferentes distribuciones en cada medida repetida. Las distribuciones analizadas representan desviación leve, moderada y severa de la normalidad. Resultados: En general, los resultados muestran que tanto el error Tipo I como la potencia del estadístico F no se alteran con la violación de la normalidad. Conclusiones: El ANOVA-MR es generalmente robusto a la no normalidad cuando la esfericidad se satisface.


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