Alexander and Govern's Approximation: Providing an Alternative to ANOVA Under Variance Heterogeneity

Abstract A Monte Carlo simulation was conducted to compare the Type I error rate and power of the 1994 approximation developed by Alexander and Govern as an alternative to the ANOVA F test. It was compared with the ANOVA F, Kruskal-Wallis, Welch, Brown-Forsythe, and James second-order tests. The authors concentrated on the impact of various factors on Type I error rate and power. The factors included variance inequality, sample-size pairings with group variances, degree of skewness/kurtosis, and number of treatment groups. Under variance heterogeneity, Alexander-Govern's test was not only comparable to the performance of the Welch test and the James second-order test but was superior in certain instances.