Heteroscedastic Test Statistics for One-Way Analysis of Variance: The Trimmed Means and Hallʹs Transformation Conjunction

To deal with nonnormal and heterogeneous data for the one-way fixed effect analysis of variance model, the authors adopted a trimmed means method in conjunction with Hallʹs invertible transformation into a heteroscedastic test statistic (Alexander-Govern test or Welch test). The results of simulation experiments showed that the proposed technique can control Type I error rates on the nominal level in various conditions. Moreover, there was a small gain with respect to the empirical power compared with competing techniques, especially for extremely skewed distributions. The authors recommend the proposed technique especially for calculating accurate confidence interval estimates.