Nonparametric Competitors to the Two-Way ANOVA

Key words: two-way designs, ANOVA, nonparametric testsThe ANOVA F and several nonparametric competitors for two-way designs were compared for empirical a and power.Simulation of 2 X 2, 2 X 4, and 4X4 designs was done with cell sizes of 5 and 10 when sampling from normal, exponential, and mixed normal distributions.Conservatism of both a 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 a for some designs and distributions, especially for small n.The ANOVA F suffers from conservative a and power for the mixed normal distribution, but it is generally recommended.The applied researcher has often expressed concerns about meeting the assumptions of the parametric fixed effects two-way ANOVA.Given the linear model of Y ijk = |± + a,-+ p* + aP ; * + %, the assumptions on the error are that e ijk i NID(0, a]) for each cell.These concerns about assumptions have been addressed in research on ANOVA, including development of alternatives to the ANOVA and examination of the ANOVA under assumption violations.Nonparametric competitors to the two-way ANOVA relax the assumptions on e ijk by assuming that they are independent, identically distributed random variables from some continuous distribution.Nonparametrics for the twoway layout include rank tests by Puri and Sen (1985), rank transform tests by Conover and Iman (1981), and aligned rank tests.The latter area has grown out of a suggestion by Hodges and Lehmann (1962) and includes a test for interaction by Mehra and Sen (1969), tests for main effects in an additive model by Mehra andSarangi (1967) andSen (1968), tests for interaction in mixed models by Koch (1969) and Koch and Sen (1968), a test for interaction in the presence of main effects by McSweeney (1967), and linear-model-based tests of main effects and interaction by Hettmansperger (1984).Generally, nonparametric methods have gained attention due to their ability to analyze data that is questionable with respect to the normality assumption.These nonparametric competitors to the two-way ANOVA would be desirable alternatives for nonnormal data likely to be found in applied