CONCLUSIONS: In terms of type I error rate analysis: Traditional ANOVA is the best when
data are homogeneous, normal, and balanced/unbalanced; Welch method performs the best when
data are heterogeneous, normal, and balanced/unbalanced; Kruskal-Wallis is most unstable when
the data are non-normal, while both ANOVA and Welch have type I error inflation problems. In
terms of power analysis, three methods may have different powers depending on the settings of
simulations.