If ANOVA is significant, which statement is an accurate interpretation?

If ANOVA is significant, which statement is an accurate interpretation?

• A. All group means are different.
• B. At least one pair of group means differs.
• C. All group variances are different.
• D. The groups have non-normal distributions.

Answer: (B)

ANOVA compares the means across several groups to see if they are all the same or if at least one differs. The result being significant means the variation among the group means is larger than what we’d expect from random sampling if all the means were truly equal. That leads to the conclusion that at least one pair of group means differs, though it doesn’t specify which pairs or how many. To know exactly which groups differ, you’d typically run post hoc tests or planned contrasts. The other ideas aren’t what the test directly addresses: a significant ANOVA doesn’t imply that all group variances are different, nor that the group distributions are non-normal. ANOVA relies on assumptions about residual normality and equal variances, but a significant result speaks to differences in means, not to variances or distribution shapes.

ANOVA compares the means across several groups to see if they are all the same or if at least one differs. The result being significant means the variation among the group means is larger than what we’d expect from random sampling if all the means were truly equal. That leads to the conclusion that at least one pair of group means differs, though it doesn’t specify which pairs or how many. To know exactly which groups differ, you’d typically run post hoc tests or planned contrasts.

The other ideas aren’t what the test directly addresses: a significant ANOVA doesn’t imply that all group variances are different, nor that the group distributions are non-normal. ANOVA relies on assumptions about residual normality and equal variances, but a significant result speaks to differences in means, not to variances or distribution shapes.