Bonferroni t-tests are used to do what in multiple comparisons?

• A. Reduce the risk of Type I error by adjusting the critical value of t
• B. Increase the power of the test regardless of familywise error
• C. Replace the use of ANOVA entirely
• D. Adjust for heteroscedasticity

Answer: (A)

When you run several t-tests, the chance of a false positive grows with each additional comparison. Bonferroni t-tests address this by making each individual test more stringent, so the overall probability of any false positive across all comparisons stays at your chosen level.

In practice, you divide the overall alpha by the number of comparisons k. You then compare each test’s p-value to this smaller threshold (or equivalently use a t-critical value that corresponds to alpha/k). This adjustment ensures that the familywise error rate—the chance of at least one Type I error across all tests—remains at or below the desired alpha.

Keep in mind this approach is conservative: tightening the criteria for each test can reduce statistical power, especially when many comparisons are made or effects are small. Bonferroni is commonly used after an ANOVA has shown a significant effect to identify which specific groups differ, rather than replacing ANOVA. It doesn’t address heteroscedasticity; that would require other methods designed for unequal variances.