Using Johnson's transformation and robust estimators with heteroscedastic test statistics: An examination of the effects of non-normality and heterogeneity in the non-orthogonal two-way ANOVA design

The present study proposes a procedure that combines Johnson's transformation and the trimmed means method to deal with the problem of non-normality. An approximate test such as the Alexander-Govern test or Welch-James type test is then employed to deal with the heterogeneity of cell variance in the non-orthogonal two-way fixed effects completely randomized design. Both unweighted and weighted means analyses are considered. The empirical Type I error rates and the statistical power for comparing population means are investigated by Monte Carlo simulation. The simulated results show that Johnson's transformation with trimmed mean and the approximate test is valid in terms of Type I error rate control, and that the magnitude of the statistical power for non-normal distributions is better than that of conventional methods.