Robust and powerful nonorthogonal analyses

Numerous types of analyses for factorial designs having unequal cell frequencies have been discussed in the literature. These analyses test either weighted or unweighted marginal means which, in turn, correspond to different model comparisons. Previous research has indicated, however, that these analyses result in biased (liberal or conservative) tests when cell variances are heterogeneous. We show how to obtain a generally robust and powerful analysis with any of the recommended nonorthogonal solutions by adapting a modification of the Welch-James procedure for comparing means when population variances are heterogeneous.This research was supported by a Social Sciences and Humanities Research Council (SSHRC) grant (# 410-92-0430) to the first author, a Manitoba Health Research Council Scholar Award and a grant from Natural Sciences and Engineering Research Council to the second author, and a SSHRC Doctoral Fellowship (# 752-92-1628) to the third author. The authors would like to express their gratitude to Joanne Keselman and three anonymous reviewers for their many helpful substantive comments on earlier drafts of this paper.