Which post-hoc method controls familywise error rate typically after ANOVA?

• A. Tukey or Bonferroni adjustments.
• B. Pearson correlation.
• C. Kruskal-Wallis test.
• D. Mann-Whitney test.

Answer: (D)

When you have a significant ANOVA and want to know which specific group means differ, you use post-hoc adjustments that keep the overall probability of a false positive across all comparisons under control. Two common approaches are Tukey’s HSD and the Bonferroni adjustment. Tukey’s method is designed for all pairwise comparisons among group means and provides adjusted inferences that maintain the familywise error rate, usually under the assumption of equal variances. Bonferroni is a simpler, more general approach that tightens the criterion for each test by dividing the overall alpha by the number of comparisons, which is straightforward but can be quite conservative when many groups are involved.

The other options aren’t post-hoc methods for this purpose. Pearson correlation measures the strength of a linear relationship between two variables. Kruskal-Wallis is a nonparametric test that detects differences among three or more groups but doesn’t specify which groups differ. Mann-Whitney compares two independent groups and likewise isn’t used for adjusting multiple comparisons after an ANOVA.