How does the Benjamini-Hochberg procedure work?
hardAnswer
- Controls the FDR (expected fraction of false positives among rejections) at level q.
- Steps: (1) Sort p-values p_(1) ≤ ... ≤ p_(m).
- (2) Find largest k such that p_(k) ≤ (k/m) * q.
- (3) Reject all H_(i) with i ≤ k.
- Much more powerful than Bonferroni for large m — accepts a small fraction of false positives to detect many true effects.
- Standard in genomics, feature selection, high-dim testing.
Check yourself — multiple choice
- Same as Bonferroni
- Sort p-values; reject up to largest k where p_(k) ≤ k·q/m → controls FDR at q; much better power than Bonferroni for large m
- Random
- Only for one test
BH: p_(k) ≤ k·q/m rule → controls FDR at q; standard for high-dim.
#hypothesis-testing#multiple-testing
Practise Statistics Fundamentals
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