The ANOVA formula (which is a ratio) compares the amount of variability between groups (which is due to the grouping factor) with the amount of variability within groups (which is due to chance). If that ratio is 1, then the amount of variability due to within-group differences is equal to the amount of variability due to between-groups differences, and any difference between groups is not significant. As the average difference between groups gets larger (and the numerator of
