For ANOVA to be statistically significant, the between-groups variance must be greater than the within-groups variance.

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ANOVA (Analysis of Variance) tests the null hypothesis that all group means are equal. For the result to be statistically significant, indicating that at least one group mean is different, the variance between groups (which reflects differences in means across groups) must be greater than the variance within groups (which reflects variability of observations within each group). This condition suggests that the observed differences among group means are not likely due to random chance.

For ANOVA to Be Statistically Significant, the Between-Groups Variance Must