Analysing multivariate repeated measures designs when covariance matrices are heterogeneous

Methods for the analysis of within‐subjects effects in multivariate groups by trials repeated measures designs are considered in the presence of heteroscedasticity of the group variance‐covariance matrices and multivariate non‐normalilty. Under a doubly multivariate model approach to hypothesis testing, within‐subjects main and interaction effect procedures are largely robust to the effects of heteroscedasticity when group sizes are equal, even when the data are non‐normal. These tests are, however, highly sensitive to the effects of covariance heterogeneity when the design is unbalanced and the data are normally distributed; Type I error rates will deviate even more from the nominal significance level when the data are obtained from a skewed distribution. An approximate degrees of freedom multivariate statistic given by Johansen (1980) is shown to be robust to the combined effects of the homogeneity and normality assumption violations for unbalanced designs, provided that the smallest of the group sizes is sufficiently large.