In one-way ANOVA, what does the F-ratio compare and what does a large F-ratio suggest?

In one-way ANOVA, the F-ratio compares variability between group means to variability within groups. It is computed as the mean square between groups divided by the mean square within groups. A large F-ratio suggests that the differences between groups are large relative to the variation within groups, so the independent variable is likely related to, or caused, the group differences rather than chance. This supports rejecting the null hypothesis.

The F-ratio in one-way ANOVA is the ratio of the mean square between groups (SSB divided by its degrees of freedom) to the mean square within groups (SSW divided by its degrees of freedom). Between-groups variability reflects differences among the group means around the overall grand mean and is attributable to the independent variable. Within-groups variability reflects individual differences, measurement error, and other factors. When the between-groups differences are large relative to within-group variation, a large F-ratio results, indicating that the observed differences are unlikely to be due to chance alone and that the independent variable probably has an effect.