One of the assumptions for the one-way analysis of variance is that the standard deviations - and so the variances - are not the same for all the populations.

Name: One of the assumptions for the one-way analysis of variance is that the standard deviations - and so the variances - are not the same for all the populations.
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One of the assumptions for the one-way analysis of variance (ANOVA) is that the populations have equal variances, known as the assumption of homogeneity of variances.

One of the Assumptions for the One-Way Analysis of Variance