What does the F Ratio compare in ANOVA?

What does the F Ratio compare in ANOVA?

• A. Between-group variance divided by within-group variance.
• B. The correlation between scores and treatment groups.
• C. The sum of squares between and within.
• D. The ratio of the total variance to the sample size.

Answer: (A)

In ANOVA, the F ratio tells you whether the differences you see among group means are larger than what would be expected from random variation within groups. It does this by comparing two sources of variance: how much the group means differ from the grand mean (between-group variance) and how much individual scores vary within each group (within-group variance). The F statistic is the ratio of the between-group mean square to the within-group mean square. If the group means are all the same, this ratio stays around 1 because both sources of variance are similar. If the treatment has an effect, the between-group variance grows while the within-group variance stays the same, making the F value larger and indicating the observed differences are unlikely to be due to chance. So the F ratio corresponds to between-group variance divided by within-group variance. The other statements describe different concepts (correlation between scores and groups, sums of squares, or total variance relative to sample size) and do not define the F statistic.

In ANOVA, the F ratio tells you whether the differences you see among group means are larger than what would be expected from random variation within groups. It does this by comparing two sources of variance: how much the group means differ from the grand mean (between-group variance) and how much individual scores vary within each group (within-group variance). The F statistic is the ratio of the between-group mean square to the within-group mean square. If the group means are all the same, this ratio stays around 1 because both sources of variance are similar. If the treatment has an effect, the between-group variance grows while the within-group variance stays the same, making the F value larger and indicating the observed differences are unlikely to be due to chance. So the F ratio corresponds to between-group variance divided by within-group variance. The other statements describe different concepts (correlation between scores and groups, sums of squares, or total variance relative to sample size) and do not define the F statistic.