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Description: When comparing independent groups, researchers in psychology commonly use Analysis of Variance (ANOVA), which assumes data is normally distributed, and variances are equal across conditions. When these assumptions are not met, the classical ANOVA (F-test) can be severely biased, which leads to invalid statistical inferences. However, despite their importance, test assumptions are rarely explicitly considered in scientific articles. We discuss why the assumptions of normality and homogeneity of variances will often not hold in psychological research. We explain when and why this is problematic, especially for the assumption of homogeneity of variances. Our simulations show that Welch’s ANOVA (W-test) controls the Type 1 error rate better than the F-test when the assumption of homogeneity of variance is not met, and loses little robustness compared to the F-test when the assumptions are met. Because assumption tests for the equality of variances often fail to provide an informative answer, we argue that the W-test should be the default choice in psychology.