A Conjoint Test for Testing the Equality of Mean and Variability in a One-Way ANOVA Layout

The robustness with respect to Type I error and the power of a proposed test statistic in testing the conjoint hypotheses of mean and variability equality were examined in this simulation study. The conjoint test utilizes the maximum p-value from separate tests of equality of means and equality of variability as its p-value to control the Type I error rates. The number of groups (2, 4, 6, 8, and 10), number of subjects per group (10, 20, 40 and 80), and distribution shapes (4) were manipulated. Data with equal means and equal variances, equal means and unequal variances, and unequal means and equal variances were simulated to obtain the Type I error rates; whereas data with unequal means and unequal variances were simulated to obtain the empirical power. Results showed that the conjoint test yielded low Type I error under all three conditions across the manipulated variables. The conjoint test provided "reasonable" power when the sample size per group was large. An appendix presents a sample computer program for the analysis. (Contains five references and seven tables.) (Author/SLD)