CONTRAST ANALYSIS FOR ADDITIVE NONORTHOGONAL 2-FACTOR DESIGNS IN UNEQUAL VARIANCE CASES

This study considered the problem of performing all pairwise comparisons of column means for an additive non-orthogonal two-by-four factorial ANOVA model where cell variances were heterogeneous. Extensions of the Games & Howell (1976) procedure, the Dunnett (1980) T3 and C procedures, the Holland & Copenhaver (1987) technique, the Hayter (1986) procedure, and the James (1951) second-order test were considered. Using computer-simulated data, Type I error rates and statistical power for these multiple comparison procedures were estimated. Examined in this study were 132 different combinations of sample size, variance patterns, group mean patterns, and design types. The family-wise Type I error rate for each of these procedures was generally maintained under the nominal .05 level. In terms of statistical power, the Games-Howell procedure generally provided the greatest any-pair power, while the extension of the Hayter technique provided the greatest average power per contrast and was most efficient in identifying all significant pairwise differences (all-pairs power).