In ANOVA, the F ratio is the ratio of which variances?

• A. Variation between groups to variation within groups
• B. Variation within groups to variation between groups
• C. Between-group mean square to within-group mean square
• D. Total variance to error variance

Answer: (A)

The F ratio in ANOVA compares how much the group means differ from each other to how much individual scores vary within each group. In practice, this is formalized as the variance among group means (the between-groups variation) divided by the variance within groups (the within-groups variation). If the groups truly come from the same population, these two sources of variability are similar, and F hovers around 1. If the between-group variation is much larger, F becomes large, indicating that the group means differ more than would be expected by chance.

So the correct idea is the ratio of variation between groups to variation within groups. (The other options either reverse the ratio, refer to mean squares rather than variances, or mix in total/error concepts that aren’t how F is defined.)