The problem. Test one hypothesis at p < 0.05 and you accept a 5% chance of a false positive. Test 20,000 genes at once and you’d expect a thousand false positives by chance alone. The old fix — Bonferroni, controlling the chance of any false positive — is so conservative on genome-scale data that it throws away nearly every real signal.

The idea. Benjamini and Hochberg reframe the goal. Instead of controlling the probability of a single false positive (family-wise error), control the expected proportion of false positives among the things you call significant — the false discovery rate. Their procedure is almost trivially simple: rank the p-values, and find the largest one that still clears a step-up threshold. You tolerate some false positives, but you know roughly what fraction, and you keep far more real discoveries.

Why it matters. This is the statistical backbone of my RNA-seq work. DESeq2 reports BH-adjusted p-values; every volcano plot I’ve made draws its significance line here. FDR is the honest answer to “how much of this list do I believe?” — and getting multiple testing right is table stakes for any pipeline I’d defend.

Verdict. Foundational and elegantly practical — one of those rare stats papers whose method you can do by hand and whose logic reshaped a whole field. Its assumptions (independence or particular dependence structures) matter, which is why later variants exist, but BH remains the default for good reason.