A researcher conducting multiple comparisons across 20 outcomes uses alpha = 0.05 for each test without correction. The probability of committing at least one Type I error across all 20 tests is approximately:
- A 64% ✓
- B 5%
- C 36%
- D 64% only if all null hypotheses are true
Correct answer: A. 64%
Explanation
The family-wise error rate (FWER) when performing k independent tests, each at alpha = 0.05, is 1 - (1 - 0.05)^k. For 20 tests: 1 - (0.95)^20 = 1 - 0.358 ≈ 0.64, or about 64%. This is the probability of at least one false positive when all null hypotheses are true. Corrections like the Bonferroni correction (divide alpha by number of tests: 0.05/20 = 0.0025) control FWER. The Benjamini-Hochberg procedure controls the false discovery rate (FDR), which is less conservative and preferred for exploratory studies.
Reference: Park's Textbook of Preventive and Social Medicine, 27th ed.
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