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This study aims to investigate the effects of violations of the sphericityassumption on Type I error rates for different methodical approaches ofrepeated measures analysis using a simulation approach. In contrast to previoussimulation studies on this topic, up to nine measurement occasions wereconsidered. Therefore, two populations representing the conditions of aviolation vs. a non-violation of the sphericity assumption without anybetween-group effect or within-subject effect were created and 5,000 randomsamples of each population were drawn. Finally, the mean Type I error rates forMultilevel linear models (MLM) with an unstructured covariance matrix (MLM-UN),MLM with compound-symmetry (MLM-CS) and for repeated measures analysis ofvariance (rANOVA) models (without correction, withGreenhouse-Geisser-correction, and Huynh-Feldt-correction) were computed. Toexamine the effect of both the sample size and the number of measurementoccasions, sample sizes of n = 20, 40, 60, 80, and 100 were considered as wellas measurement occasions of m = 3, 6 and 9. For MLM-UN, the results illustratea massive progressive bias for small sample sizes (n =20) and m = 6 or moremeasurement occasions. This effect could not be found in previous simulationstudies with a smaller number of measurement occasions. The mean Type I errorrates for rANOVA with Greenhouse-Geisser-correction demonstrate a smallconservative bias if sphericity was not violated, sample sizes were small (n =20), and m = 6 or more measurement occasions were conducted. The results pleadfor a use of rANOVA with Huynh-Feldt-correction, especially when the sphericityassumption is violated, the sample size is rather small and the number ofmeasurement occasions is large. MLM-UN may be used when the sphericityassumption is violated and when sample sizes are large.

Violation of the sphericity assumption and its effect on Type-I error rates in repeated measures ANOVA and multi-level linear models (MLM)