Šidák cutoff for 10 tests at a 10% family level

Question

You run 10 independent tests and are willing to tolerate a 10% family-wise error rate. Bonferroni would use 0.10/10 = 0.01 per test. Compute the exact Šidák per-test cutoff for this 10% budget.

Accepted Answer

The exact requirement. With m independent tests at per-test level \alpha', the family-wise error is 1 - (1-\alpha')^m. Setting this equal to the chosen budget \alpha = 0.10 and solving: \alpha' = 1 - (1-\alpha)^{1/m} = 1 - (0.90)^{1/10}. Compute. (0.90)^{1/10} \approx 0.98952, so \alpha' \approx 1 - 0.98952 = 0.0105. Compare. Bonferroni gives 0.10/10 = 0.01. Šidák's 0.0105 is slightly more generous. Note the family budget in the base is now 0.90 (that is 1 - 0.10), because the target family-wise rate is 10%, not 5%. The formula adapts automatically to whatever budget you choose. Perspective. …

Šidák cutoff for 10 tests at a 10% family level

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