Stepwise and Simultaneous Multiple Comparison Procedures of Repeated Measures’ Means

Stepwise multiple comparison procedures (MCPs) for repeated measures’ means based on the methods of Hayter (1986) , Hochberg (1988) , Peritz (1970) , Ryan (1960) - Welsch (1977a) , Shaffer (1979 , 1986) , and Welsch (1977a) were compared for their overall familywise rates of Type I error when multisample sphericity and multivariate normality were not satisfied. Robust stepwise procedures were identified by Keselman, Keselman, and Shaffer (1991) with respect to three definitions of power. On average, Welsh’s (1977a) step-up procedure was found to be the most powerful MCP.

Repeated Measures Multiple Comparison Procedures: Effects of Violating Multisample Sphericity in Unbalanced Designs

Two Tukey multiple comparison procedures as well as a Bonferroni and multivariate approach were compared for their rates of Type I error and any-pairs power when multisample sphericity was not satisfied and the design was unbalanced. Pairwise comparisons of unweighted and weighted repeated measures means were computed. Results indicated that heterogenous covariance matrices in combination with unequal group sizes resulted in substantially inflated rates of Type I error for all MCPs involving comparisons of unweighted means. For tests of weighted means, both the Bonferroni and a multivariate critical value limited the number of Type I errors; however, the Bonferroni procedure provided a more powerful test, particularly when the number of repeated measures treatment levels was large.