Benjamini-Hochberg Procedure
Visualize rank-based false-discovery control across a family of hypotheses.
Free theory articleVisualize rank-based false-discovery control across a family of hypotheses.
Concept & interpretation
A family of five p-values can produce several rejections. BH controls the expected false-discovery proportion under valid null p-values and suitable independence or positive-dependence assumptions. It cannot reveal which decisions in one fixed list are false.
Compare targets, ties and zero
Open the Benjamini-Hochberg experiment. The control q is a probability from zero to 0.20; for example 0.05 means a five-percent target.
- Set P-value set to Default, Target q to 0.05 and Method to BH. Only ID 1 is rejected.
- Set q to 0.10. IDs 1, 2 and 3 are rejected. Switch Method to Bonferroni: only ID 1 remains rejected.
- Select Ties, q = 0.04 and BH. Rank 3 passes although ranks 1 and 2 fail their own thresholds; all three tied IDs are rejected. Each adjusted p-value is 1/30.
- Select Zero and q = 0. Equality at zero rejects ID 1. Select Default while keeping q = 0: no IDs are rejected.