Developing trimmed mean test statistics for two-way fixed-effects ANOVA models under variance heterogeneity and nonnormality

The Alexander-Govern test was extended to 2-way fixed-effects analysis of variance models. To deal with the impact of violating normality assumptions, variance homogeneity assumptions, or both, the author applied the trimmed mean method to the approximate tests, that is, the Alexander-Govern, Welch, and James 2nd-order tests. The empirical Type I error rates and the statistical power of the original Alexander-Govern, Welch, and James 2nd-order tests and their corresponding trimmed mean methods were investigated by Monte Carlo simulation. The simulation results showed that all 3 trimmed mean methods can control the empirical Type I error on the nominal level when the degree of nonnormality and heterogeneity is extreme, On the other hand, the untrimmed mean methods may be liberal for skewed cases and less powerful than the trimmed mean methods for heavy-tailed cases. The trimmed mean method on the approximate tests was robust with respect to estimators as well as statistics. A numerical example is provided.