In a two-factor ANOVA design, the variances of the populations are assumed to be equal unless there is interaction present.

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In a two-factor ANOVA design, the assumption of equal variances (homogeneity of variances) is required regardless of whether there is an interaction effect present. This assumption pertains to the variances within each of the groups formed by the combinations of factors, not to the interaction between factors.

In a Two-Factor ANOVA Design, the Variances of the Populations