Benjamini–Hochberg procedure

Sort m p values from smallest to largest and compare rank i with threshold i·q/m. Find the largest rank whose p value does not exceed its threshold; reject that and all smaller p values. For four tests and q=0.05, thresholds are 0.0125, 0.025, 0.0375 and 0.05. Define the test family scientifically in advance to avoid manipulating results through later selection. Define the test family and dependence structure. FDR is the expected false share among rejections, not the probability that one finding is false. Report q level and the full number of hypotheses tested.

FDR targets the expected false share among rejected null hypotheses over repeated studies or procedures. It is not the probability that a particular significant finding is false. Thus q=0.05 does not mean each discovery has a 95% chance of being true. It is a group-level error criterion and should be interpreted alongside effect sizes, uncertainty and independent validation. Define the test family and dependence structure. FDR is the expected false share among rejections, not the probability that one finding is false. Report q level and the full number of hypotheses tested.

The classical Benjamini–Hochberg guarantee holds for independent tests and certain positive dependence structures. In genomic data, tests are often correlated because markers are linked or traits measured jointly. The standard method may miss nominal control under arbitrary dependence. Check the test structure and analysis goal; more conservative procedures or resampling may fit complex dependence better. The number m must include every test in the defined family. Define the test family and dependence structure. FDR is the expected false share among rejections, not the probability that one finding is false. Report q level and the full number of hypotheses tested.

Reproduce the example calculation: For p values 0.004, 0.018, 0.04, 0.20 with m=4 and q=0.05, thresholds are 0.0125, 0.025, 0.0375, 0.05. Benjamini–Hochberg procedure uses p(i) ≤ (i/m)·q. In plain terms, the Benjamini–Hochberg procedure controls the expected false discovery rate within a family of tests. Unit check: p values, q and FDR are fractions 0…1 · i and m are integer ranks/counts. Standard guarantee under independent tests; dependence and definition of the tested family matter. Values are comparable only when their definitions, denominators and periods match. Record these details next to the result so the reference group is clear. If the direction is implausible, check data preparation and the calculation basis before discussing biological causes.

A key limit of Benjamini–Hochberg procedure is this: Standard guarantee under independent tests; dependence and definition of the tested family matter. Do not use the metric without its reference; it is useful for Multiple-testing correction in genomics, omics and parallel biological hypothesis tests. The Benjamini–Hochberg procedure controls the expected false discovery rate within a family of tests. When comparing populations or experiments, check whether definitions, denominators and observation periods match. If the assumption is implausible, the result shows only what the simplified model calculates from its inputs; it is not a reliable estimate for the target population. State this limitation in the report, and do not infer a causal effect from the formula alone.