Šidák cutoff for 4 independent tests

Question

You run 4 independent tests and want the family-wise error rate held at 5%. Bonferroni would use 0.05/4 = 0.0125 per test. Compute the exact Šidák per-test cutoff, and compare it to Bonferroni.

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The exact requirement. With m independent tests at per-test level \alpha', all stay quiet with probability (1-\alpha')^m, so the family-wise error is 1 - (1-\alpha')^m. Setting this to 5% and solving: \alpha' = 1 - (1-\alpha)^{1/m} = 1 - (0.95)^{1/4}. Compute. (0.95)^{1/4} \approx 0.98726, so \alpha' \approx 1 - 0.98726 = 0.0127. Compare. Bonferroni gives 0.05/4 = 0.0125. Šidák's 0.0127 is slightly larger, a touch more permissive and thus a touch more powerful. Šidák is exact for independent tests; Bonferroni is a conservative bound that ignores independence. Perspective. The difference (0.01…

Šidák cutoff for 4 independent tests

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