In a two-way factor ANOVA, the variances of the populations are assumed to be equal unless the error variation is zero.

Name: In a two-way factor ANOVA, the variances of the populations are assumed to be equal unless the error variation is zero.
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In a two-way factor ANOVA, the assumption of equal variances (homogeneity of variances) across groups is required, but this is not related to whether the error variation is zero. The assumption does not change based on the error variation.

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