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 Hall's 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. [Derivation of the Monotone and Invertible Function is appended.]