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

• A. Within-group variance to Between-group variance
• B. Total variance to error variance
• C. Between-group variance to within-group variance
• D. Between-group variance to total variance

Answer: (C)

In ANOVA, the F-statistic measures how large the variation due to differences between groups is compared with the variation that occurs within groups from random error. Concretely, it uses the between-group variance (how far group means are from the overall mean) divided by the within-group variance (how much individual observations vary around their group means). These are typically expressed as mean squares: F = MS_between / MS_within. So the ratio described is between-group variance to within-group variance. The other options don’t match this structure, since they mix in total variance or reverse the ratio.