When the assumption of sphericity has been violated in a mixed-design RM-ANOVA with four time periods, an alternative analysis is:

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MANOVA (Multivariate Analysis of Variance) is an appropriate alternative analysis when the assumption of sphericity is violated in a mixed-design Repeated Measures ANOVA, especially with multiple time points or conditions. It handles the intercorrelations among dependent variables more effectively.

When the Assumption of Sphericity Has Been Violated in a Mixed-Design