What do you do if the test for equal variances indicates that the standard deviations are different? Or that the test has insufficient power? Or, perhaps you just don’t want to have to worry about performing and explaining this extra test? Let me introduce you to Welch’s ANOVA!
Welch’s ANOVA is an elegant solution because it is a form of one-way ANOVA that does not assume equal variances. And the simulations show that it works great!