Computational approach test in one-way fixed effects ANOVA models of log-normal samples

We apply a recently developed computational approach test to the one-way fixed effects ANOVA models of log-normal data with unequal variances. The merits of the proposed test are numerically compared with the existing tests - the James second order test, the Welch test and the Alexander-Govern test - with respect to their sizes and powers in different combinations of parameters and various sample sizes. The simulation results demonstrate that the proposed method is satisfactory: its type I error probability is very close to the nominal level. We illustrate these approaches using a real example.