What is the probability of making a Type I error in any family of tests when the null hypothesis is true in each case?

• A. Fixed coefficient
• B. Fisher's exact test
• C. Familywise error rate
• D. Factor transformation matrix, ∧

Answer: (C)

This is about the familywise error rate. When you perform multiple hypothesis tests and the null hypothesis is true for every test, the chance of making at least one Type I error (falsely rejecting a true null) across the whole set of tests is called the familywise error rate (FWER).

If you have m tests and each test uses the same per-test significance level alpha, and the tests are independent, the probability of no false rejections is (1 − alpha)^m, so the probability of at least one false rejection is 1 − (1 − alpha)^m. This is the FWER. In practice we often aim to control the FWER at a desired level (like 0.05) by adjusting the per-test alphas (Bonferroni, Holm, etc.).

The other terms listed aren’t about controlling error rates across a family of tests: a fixed coefficient is a parameter concept, Fisher's exact test is a specific test for 2x2 contingency tables, and a factor transformation matrix relates to factor analysis. The correct concept here is the familywise error rate.