How does the Bonferroni correction affect the per-test alpha level?

How does the Bonferroni correction affect the per-test alpha level?

• A. It increases alpha
• B. It does not change alpha
• C. It decreases alpha, making significance harder to achieve
• D. It randomizes alpha

Answer: (C)

The Bonferroni correction lowers the threshold for each individual test to keep the overall chance of a false positive across all tests under control. You start with the desired family-wise alpha (the overall false-positive rate you’re willing to accept) and divide it by the number of tests. The result is a smaller per-test alpha, so a test has to show a stronger signal to be deemed significant. For example, with an overall alpha of 0.05 and 10 tests, each test would need p ≤ 0.005 to be significant. This makes significance harder to achieve, though it reduces the risk of any false positives across the set. It does not increase alpha, it does not leave alpha unchanged, and it does not randomize alpha.

The Bonferroni correction lowers the threshold for each individual test to keep the overall chance of a false positive across all tests under control. You start with the desired family-wise alpha (the overall false-positive rate you’re willing to accept) and divide it by the number of tests. The result is a smaller per-test alpha, so a test has to show a stronger signal to be deemed significant. For example, with an overall alpha of 0.05 and 10 tests, each test would need p ≤ 0.005 to be significant. This makes significance harder to achieve, though it reduces the risk of any false positives across the set. It does not increase alpha, it does not leave alpha unchanged, and it does not randomize alpha.