AN IMPROVED GENERAL APPROXIMATION TEST FOR THE MAIN EFFECT IN A SPLIT-PLOT DESIGN

Type I error rates for a test of a main effect of the within-subjects factor in a split-plot design were estimated for four tests-the <(epsilon)over tilde>-adjusted test, the General Approximation test, the Improved General Approximation test, and the Corrected Improved General Approximation test-under conditions in which dispersion matrices were unequal between groups. The main effect null hypothesis was H-o: mu(1) = ... = mu(p) where mu(k) is an element of the p x 1 vector mu = G(-1)Sigma(g) mu(g), G is the number of levels of the between-subjects factor, and mu(g) is the mean vector for the population from which the gth sample was drawn. Control of the Type I error rate by the <(epsilon)over tilde>-adjusted test was poor except when the sample sizes were equal. When the sample sizes were not equal the Improved General Approximation and Corrected Improved General Approximation tests controlled the Type I error rate much better than did the <(epsilon)over tilde>-adjusted test.