Testing Repeated Measures Hypotheses When Covariance Matrices are Heterogeneous

For balanced designs, degrees of freedom-adjusted univariate F tests or multivariate test statistics can be used to obtain a robust test of repeated measures main and interaction effect hypotheses even when the assumption of equality of the covariance matrices is not satisfied. For unbalanced designs, however, covariance heterogeneity can seriously distort the rates of Type I error of either of these approaches. This article shows how a multivariate approximate degrees of freedom procedure based on Welch (1947 , 1951 )- James (1951 , 1954) , as simplified by Johansen (1980) , can be applied to the analysis of unbalanced repeated measures designs without assuming covariance homogeneity. Through Monte Carlo methods, we demonstrate that this approach provides a robust test of the repeated measures main effect hypothesis even when the data are obtained from a skewed distribution. The Welch-James approach also provides a robust test of the interaction effect, provided that the smallest of the unequal group sizes is five to six times the number of repeated measurements minus one or provided that a reduced level of significance is employed.