Robust analysis of variance: a simulation study

Traditional analysis-of-variance (ANOVA) is based on 'normality' and 'homogeneity' assumptions. If either or both of these assumptions are violated, then the one-way ANOVA may not be as powerful as robust analysis-of-variance (RANOVA) alternatives. We report the results of a simulation study of alternatives to ANOVA: Welch (W*), the first and second methods of James (J1*, 3J11*), Brown- Forsythe (BF*), a Box (B*) procedure, and the Kruskal-Wallis (KW*) procedure. Random samples from 14 distributions—uniform (0, 1), normal (0, 1), contaminated normal, SLATE, SLACU, SLASH, double exponential, Cauchy, half-normal, chi-squared (two degrees of freedom), chi-squared (four degrees of freedom) log normal, gamma (1, 2) and beta (2, 5)—were generated using a composite linear congruential generator. Corresponding test satis tics were computed and the empirical size for each test is given for three nominal a values (0.10, 0.05, 0.01). For k, we choose 3, 4 and 6. The sample sizes and combinations of sample sizes were chosen at 4, 6, 8, 10, 15 and 20. We then propose an adaptive algorithm based on an ancillary statistic that selects an ANOVA/RANOVA procedure for either symmetric or asymmetric data distributions, and for equal or unequal sample sizes.