Comparing Repeated Measures Means in Factorial Designs

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Abstract
The effects of violating multisample sphericity were investigated for multiple comparison procedures for pairwise contrasts in nonorthogonal split‐plot repeated measures designs. Results indicated that rates of Type I error of the multiple comparison procedures are affected not only by assumption violations but also by the type of nonorthogonal solution. Specifically, if one intends to test contrasts of unweighted means, as would be the case when the unequal group sizes are due to random loss, then all multiple comparison procedures investigated, including the previously recommended Bonferroni procedure, are prone to excessive rates of Type I errors. A satisfactory solution to this bias is to obtain additional data in order to achieve equal group sizes and hence an orthogonal design. For tests of contrasts of weighted repeated measures means, which would be of interest when the unequal group sizes are representative of population group sizes, the Bonferroni approach to Type I error control is satisfactory. In most instances, a Bonferroni critical value will provide a more powerful test than a multivariate critical value.