What does the F-statistic in a one-way ANOVA test?

What does the F-statistic in a one-way ANOVA test?

• A. The F-statistic tests whether there is a linear relationship between Y and X.
• B. The F-statistic tests whether all group variances are equal.
• C. The F-statistic tests whether at least one group mean differs, by comparing between-group and within-group variation.
• D. The F-statistic tests the normality of residuals.

Answer: (C)

In a one-way ANOVA, the F-statistic measures whether the group means are all the same by comparing how much the data vary between groups to how much they vary within groups. It’s calculated as the mean square between groups divided by the mean square within groups. If all group means are equal, most variation comes from random fluctuation within groups, so the between-group variation is small and the F value is close to 1. If at least one group mean differs, the between-group variation increases, making the F statistic larger and providing evidence that not all means are equal. This is the test of the overall effect: is there some difference among the group means? It’s worth noting that a large F tells you that at least one mean differs, but it doesn’t specify which groups differ—that requires post hoc comparisons. The F-statistic here is not about a linear relationship, nor about testing equality of variances or normality of residuals, which are addressed by other tests and diagnostics.

In a one-way ANOVA, the F-statistic measures whether the group means are all the same by comparing how much the data vary between groups to how much they vary within groups. It’s calculated as the mean square between groups divided by the mean square within groups. If all group means are equal, most variation comes from random fluctuation within groups, so the between-group variation is small and the F value is close to 1. If at least one group mean differs, the between-group variation increases, making the F statistic larger and providing evidence that not all means are equal. This is the test of the overall effect: is there some difference among the group means?

It’s worth noting that a large F tells you that at least one mean differs, but it doesn’t specify which groups differ—that requires post hoc comparisons. The F-statistic here is not about a linear relationship, nor about testing equality of variances or normality of residuals, which are addressed by other tests and diagnostics.