The Šidák correction is what kind of adjustment?

The Šidák correction is what kind of adjustment?

• A. More conservative than Bonferroni correction
• B. A method to adjust p-values using permutation
• C. A slightly less conservative variant of a Bonferroni correction
• D. A correction for heteroscedasticity in regression

Answer: (C)

The idea here is how to control the chance of making a false positive when you run many statistical tests. The Šidák correction computes a per-test significance level that makes the overall familywise error rate (the probability of at least one Type I error across all tests) equal to the desired alpha, but it does so using the independence assumption. Specifically, if you want the familywise error rate to be alpha and you perform m tests, the Šidák adjustment sets the per-test threshold to alpha' = 1 − (1 − alpha)^(1/m). This comes from the idea that the probability that none of the tests yields a false positive is (1 − alpha')^m, which should equal 1 − alpha. Solving for alpha' gives the formula above. Because 1 − (1 − alpha)^(1/m) is slightly larger than alpha/m for typical values of alpha and m, the Šidák correction is slightly less conservative than Bonferroni, meaning it allows a bit more room for each individual test while still controlling the overall error rate, assuming the tests are independent. In contrast, Bonferroni uses a fixed per-test threshold of alpha/m, which is simpler but more conservative. The difference is usually small, but it means Šidák is a bit more powerful when the independence assumption holds. It’s not about permutation p-values or correcting heteroscedasticity in regression.

The idea here is how to control the chance of making a false positive when you run many statistical tests. The Šidák correction computes a per-test significance level that makes the overall familywise error rate (the probability of at least one Type I error across all tests) equal to the desired alpha, but it does so using the independence assumption.

Specifically, if you want the familywise error rate to be alpha and you perform m tests, the Šidák adjustment sets the per-test threshold to alpha' = 1 − (1 − alpha)^(1/m). This comes from the idea that the probability that none of the tests yields a false positive is (1 − alpha')^m, which should equal 1 − alpha. Solving for alpha' gives the formula above. Because 1 − (1 − alpha)^(1/m) is slightly larger than alpha/m for typical values of alpha and m, the Šidák correction is slightly less conservative than Bonferroni, meaning it allows a bit more room for each individual test while still controlling the overall error rate, assuming the tests are independent.

In contrast, Bonferroni uses a fixed per-test threshold of alpha/m, which is simpler but more conservative. The difference is usually small, but it means Šidák is a bit more powerful when the independence assumption holds. It’s not about permutation p-values or correcting heteroscedasticity in regression.