Anova Tests for Homogeneity of Variance: Nonnormality and Unequal Samples

This paper presents an exposition and an empirical comparison of two potentially useful tests for homogeneity of variance. Control of Type I error rate, P(EI), and power are investigated for three forms of the Box test and for two forms of the jackknife test with equal and unequal n's under conditions of normality and nonnormality. The Box test is shown to be robust to violations of the assumption of normality. The jackknife test is shown not to be robust. When n's are unequal, the problem of heterogeneous within-cell variances of the transformed values and unequal n's affects the jackknife and Box tests. Previously reported suggestions for selecting subsample sizes for the Box test are shown to be inappropriate, producing an inflated P(EI). Two procedures which alleviate this problem are presented for the Box test. Use of the jack-knife test with a reduced alpha is shown to provide power and control of P(EI) at approximately the same level as the Box test. Recommendations for the use of these techniques and computational examples of each are provided.