Various tests to check the homogeneity of variance assumption have been proposed in the literature, yet there is no consensus as to their robustness when the assumption of normality does not hold. This simulation study evaluated the performance of 14 tests for the homogeneity of variance assumption in one-way ANOVA models in terms of Type I error control and statistical power. Seven factors were manipulated: number of groups, average number of observations per group, pattern of sample sizes in groups, pattern of population variances, maximum variance ratio, population distribution shape, and nominal alpha level for the test of variances. Overall, the Ramsey conditional, O’Brien, Brown–Forsythe, Bootstrap Brown–Forsythe, and Levene with squared deviations tests maintained adequate Type I error control, performing better than the others across all the conditions. The power for each of these five tests was acceptable and the power differences were subtle. Guidelines for selecting a valid test for assessing the tenability of this critical assumption are provided based on average cell size.