Is the ANOVA F-Test Robust to Variance Heterogeneity When Sample Sizes are Equal?: An Investigation via a Coefficient of Variation

Numerous investigations have examined the effects of variance heterogeneity on the empirical probability of a Type I error for the analysis of variance (ANOVA) F-test and the prevailing conclusion has been that when sample sizes are equal, the ANOVA is robust to variance heterogeneity. However, Box (1954) reported a Type I error rate of .12, for a 5% nominal level, when unequal variances were paired with equal sample sizes. The present paper explored this finding, examining varying degrees and patterns of variance heterogeneity for varying sample sizes and number of treatment groups. The data indicate that the rate of Type 1 error varies as a function of the degree of variance heterogeneity and, consequently, it should not be assumed that the ANOVA F-test is always robust to variance heterogeneity when sample sizes are equal.