If a one-way ANOVA yields a significant F-statistic, what does this imply about the group means?

If a one-way ANOVA yields a significant F-statistic, what does this imply about the group means?

• A. At least one group mean differs from the others.
• B. All group means are equal.
• C. The within-group variance is zero.
• D. The between-group variance is zero.

Answer: (A)

In a one-way ANOVA, you compare how much the group means differ from each other to how much observations vary within each group. A significant F-statistic means the variability between the group means is large relative to the variability within groups, so at least one group mean differs from the others. It doesn’t tell you which groups differ or how many, so follow-up post-hoc tests are usually needed to pinpoint the differences. If all group means were equal, the between-group variability would be small and the F statistic would not be significant. The statements about within-group or between-group variances being zero aren’t implied by a significant F in general and aren’t the takeaway of the result.

In a one-way ANOVA, you compare how much the group means differ from each other to how much observations vary within each group. A significant F-statistic means the variability between the group means is large relative to the variability within groups, so at least one group mean differs from the others. It doesn’t tell you which groups differ or how many, so follow-up post-hoc tests are usually needed to pinpoint the differences.

If all group means were equal, the between-group variability would be small and the F statistic would not be significant. The statements about within-group or between-group variances being zero aren’t implied by a significant F in general and aren’t the takeaway of the result.