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

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 impac...

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Bibliographic Details
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) 01.02.2023
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
Online Access:Get full text
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Summary: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.
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ISSN:0214-9915
1886-144X
1886-144X
DOI:10.7334/psicothema2022.292