Nonparametric Competitors to the Two-Way ANOVA

The ANOVA F and several nonparametric competitors for two-way designs were compared for empirical α and power. Simulation of 2 × 2, 2 × 4, and 4 × 4 designs was done with cell sizes of 5 and 10 when sampling from normal, exponential, and mixed normal distributions. Conservatism of both α and power in the presence of other nonnull effects was seen in the tests due to Puri and Sen (1985) and, to a lesser degree, in the rank transform tests (Conover & Iman, 1981). Tests by McSweeney (1967) and Hettmansperger (1984) had liberal α for some designs and distributions, especially for small n. The ANOVA F suffers from conservative α and power for the mixed normal distribution, but it is generally recommended.