Benjamini-Hochberg Procedure (FDR Control)
Benjamini-Hochberg False Discovery Rate Procedure · Also known as: BH procedure, FDR control, false discovery rate procedure, Benjamini-Hochberg düzeltmesi
The Benjamini-Hochberg (BH) procedure, introduced by Yoav Benjamini and Yosef Hochberg in 1995, controls the false discovery rate (FDR) — the expected proportion of false positives among all rejected hypotheses — rather than the probability of any false positive. By tolerating a controlled fraction of false discoveries, it delivers far greater power than family-wise error rate methods such as Bonferroni or Holm, which is why it has become the standard tool for large-scale simultaneous testing in genomics, neuroimaging, and other high-throughput fields.
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When to use it
Use the BH procedure when you perform many simultaneous tests and the cost of a few false positives among your discoveries is acceptable, so long as their proportion is controlled — the typical situation in exploratory, high-throughput analysis. It is the field standard for genome-wide expression and association studies, mass-spectrometry proteomics, voxel-wise neuroimaging, and large survey or A/B-test screens. It assumes independence or positive dependence among the tests for the original 1995 guarantee; under unknown or negative dependence, switch to the more conservative Benjamini-Yekutieli variant. When even a single false positive would be unacceptable — confirmatory trials, regulatory endpoints — control the family-wise error rate with Holm or Bonferroni instead.
Strengths & limitations
- Far greater power than FWER methods when the number of tests is large, recovering many true effects that Bonferroni would miss.
- Controls an interpretable and often more relevant quantity — the expected fraction of false discoveries among rejections.
- Simple step-up computation on ordered p-values, with a widely implemented adjusted-p-value form.
- The 1995 guarantee holds under independence and positive dependence, covering many realistic correlation structures.
- Permits some false discoveries by design, so it is inappropriate when any single false positive is unacceptable.
- The original proof assumes independence or positive regression dependence; arbitrary dependence needs the more conservative Benjamini-Yekutieli correction.
- FDR is an expectation, so in any single experiment the realised proportion of false discoveries can exceed q.
- When the proportion of true nulls is high, the effective control level q·(m₀/m) is conservative, leaving some power on the table.
Frequently asked
What is the difference between FDR and FWER?
The family-wise error rate (FWER) is the probability of making at least one false rejection across the whole family of tests. The false discovery rate (FDR) is the expected proportion of false rejections among the hypotheses you actually reject. FDR is the less stringent criterion, which is why BH is far more powerful than Bonferroni or Holm when many tests are performed.
Does the BH procedure require independent tests?
The original 1995 proof guarantees FDR control under independence or positive regression dependence, which covers many practical cases. For arbitrary or negative dependence, use the Benjamini-Yekutieli (2001) variant, which multiplies the threshold by a harmonic-sum correction factor at the cost of some power.
If I control FDR at 5%, are exactly 5% of my discoveries false?
No. FDR is an expectation over repeated experiments; in any single analysis the realised proportion of false discoveries can be above or below q. Controlling FDR at 5% means that on average no more than 5% of declared discoveries are false.
Should I ever use Bonferroni or Holm instead?
Yes — when even one false positive is costly, such as in confirmatory clinical trials or regulatory decisions. There you want to bound the chance of any false claim (FWER), which calls for Holm or Bonferroni rather than the FDR-controlling BH procedure.
Sources
- Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal Statistical Society: Series B, 57(1), 289–300. DOI: 10.1111/j.2517-6161.1995.tb02031.x ↗
- Benjamini, Y., & Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29(4), 1165–1188. DOI: 10.1214/aos/1013699998 ↗
How to cite this page
ScholarGate. (2026, June 2). Benjamini-Hochberg False Discovery Rate Procedure. ScholarGate. https://scholargate.app/en/statistics/benjamini-hochberg-procedure
Which method?
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- Multiple Linear RegressionStatistics↔ compare