Which problem does Bonferroni correction address?

Which problem does Bonferroni correction address?

• A. Heteroscedasticity
• B. Multiple comparisons inflating Type I error
• C. Non-normality
• D. Autocorrelation

Answer: (B)

Bonferroni correction targets the problem that arises when you perform many statistical tests at once: the chance of getting a false positive increases with each additional test. It keeps the overall chance of making any Type I error across all tests from rising too high by making each individual test stricter. Practically, you either divide the overall alpha by the number of tests or multiply each p-value by the number of tests and compare to the original alpha. This preserves the familywise error rate near the desired level. For example, if you run twenty tests with an overall alpha of 0.05, without adjustment you’d expect about 1 false positive on average. With Bonferroni, each test uses alpha = 0.05/20 = 0.0025, so only very strong signals pass. The trade-off is reduced power to detect real effects when many tests are involved. Other issues—heteroscedasticity (unequal variances), non-normality, and autocorrelation (dependence over time)—are addressed by other methods (robust standard errors, nonparametric tests, time-series models, etc.). Bonferroni specifically targets the inflation of Type I error across multiple comparisons.

Bonferroni correction targets the problem that arises when you perform many statistical tests at once: the chance of getting a false positive increases with each additional test. It keeps the overall chance of making any Type I error across all tests from rising too high by making each individual test stricter. Practically, you either divide the overall alpha by the number of tests or multiply each p-value by the number of tests and compare to the original alpha. This preserves the familywise error rate near the desired level.

For example, if you run twenty tests with an overall alpha of 0.05, without adjustment you’d expect about 1 false positive on average. With Bonferroni, each test uses alpha = 0.05/20 = 0.0025, so only very strong signals pass. The trade-off is reduced power to detect real effects when many tests are involved.

Other issues—heteroscedasticity (unequal variances), non-normality, and autocorrelation (dependence over time)—are addressed by other methods (robust standard errors, nonparametric tests, time-series models, etc.). Bonferroni specifically targets the inflation of Type I error across multiple comparisons.