If the normality assumption of the single-factor ANOVA is violated, then the Kruskal-Wallis test is a good alternative as long as the sample sizes are large and the distributions are similar.

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The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA that does not assume normality, making it suitable when the normality assumption is violated. It can be effectively used when sample sizes are large and distributions across groups are similar, as it relies on rank-based methods.

If the Normality Assumption of the Single-Factor ANOVA Is Violated