True or False: The within-groups variance is different for all three F ratios.

The statement is false because the within-groups variance is typically consistent across all groups, especially when conducting an ANOVA (Analysis of Variance). In the context of an ANOVA, the within-groups variance represents the variability of scores within each group and is calculated as a pooled variance that encompasses all individual groups being compared.

When analyzing data, the F ratios are calculated by comparing the variance between groups to the within-groups variance. Since the within-groups variance does not change across different comparisons or F ratios (main effects or interactions), it remains the same for all calculated F values in a standard ANOVA framework. Therefore, the assertion that the within-groups variance differs for all three F ratios is incorrect, leading to the conclusion that the answer is false.