FDR Calculator (Benjamini-Hochberg)
Paste your p-values and get Benjamini-Hochberg, Bonferroni, and Benjamini-Yekutieli adjusted values, matching R's p.adjust exactly. See how many tests remain significant at any false discovery rate threshold.
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3 of 10 tests significant at FDR ≤ 0.05
| Test | Raw p | Adjusted p | Significant |
|---|---|---|---|
| TP53 | 1.00e-4 | 1.00e-3 | yes |
| BRCA1 | 9.00e-4 | 4.50e-3 | yes |
| EGFR | 8.00e-3 | 2.67e-2 | yes |
| MYC | 2.10e-2 | 5.25e-2 | no |
| KRAS | 3.90e-2 | 6.00e-2 | no |
| PTEN | 4.10e-2 | 6.00e-2 | no |
| CDK4 | 4.20e-2 | 6.00e-2 | no |
| RB1 | 6.00e-2 | 7.50e-2 | no |
| MDM2 | 7.40e-2 | 8.22e-2 | no |
| AKT1 | 2.05e-1 | 2.05e-1 | no |
Why Multiple Testing Breaks Raw P-values
When you test one hypothesis at a p-value cutoff of 0.05, you accept a 5% chance of a false positive. When you test twenty thousand genes at the same cutoff, you expect roughly a thousand false positives even if nothing is truly changing. This is the multiple comparisons problem, and it is why an unadjusted list of significant genes from a high-throughput experiment is untrustworthy.
The older fix, family-wise error rate control via Bonferroni, protects against even a single false positive by shrinking every p-value by the number of tests. That is appropriate when any false positive is costly, but in exploratory genomics it is so conservative that it discards most real signal. Benjamini and Hochberg (1995) reframed the goal: instead of preventing any false positive, control the expected proportion of false positives among the discoveries, the false discovery rate.
The Benjamini-Hochberg procedure is a step-up test: rank the p-values and find the largest one that still falls under a rank-scaled threshold. The adjusted value this tool reports is the equivalent transformation, and it matches R's p.adjust with method BH to the decimal. Under arbitrary dependence between tests, the Benjamini-Yekutieli variant adds a harmonic correction factor, which is also provided here.
FDR correction is the last step of a differential-expression analysis, applied after per-gene testing. It pairs naturally with the volcano plot generator, which plots fold change against significance and draws the FDR threshold, and the log2 fold change calculator for the effect-size axis. For the full pipeline from raw counts to a corrected, annotated gene list, the bioinformatics analysis service delivers reproducible results.
A Worked Example: Correcting Eight P-values
Suppose eight tests return the raw p-values below. Benjamini-Hochberg ranks them, scales each by m / rank (here m = 8), then enforces monotonicity from the largest downward so an adjusted value is never smaller than the one below it. Notice that the third-ranked p-value of 0.039 is not significant at a false discovery rate of 0.05 even though its raw value is well under 0.05, because too few smaller tests support it. This is the exact arithmetic the calculator runs, and it matches R's p.adjust.
| Rank | Raw p | p × m / rank | Adjusted p (BH) | Significant at 0.05 |
|---|---|---|---|---|
| 1 | 0.001 | 0.008 | 0.008 | yes |
| 2 | 0.008 | 0.032 | 0.032 | yes |
| 3 | 0.039 | 0.104 | 0.067 | no |
| 4 | 0.041 | 0.082 | 0.067 | no |
| 5 | 0.042 | 0.067 | 0.067 | no |
| 6 | 0.060 | 0.080 | 0.080 | no |
| 7 | 0.074 | 0.085 | 0.085 | no |
| 8 | 0.205 | 0.205 | 0.205 | no |
Common Mistakes When Controlling the False Discovery Rate
- Filtering on the raw p-value, then reporting an FDR. The correction must be applied to the complete set of tests. Dropping the non-significant genes first and adjusting only the survivors understates the true false discovery rate.
- Correcting an already-filtered list. If your differential-expression tool output is pre-filtered by fold change, the p-value set is no longer the full family, and the adjustment is biased. Correct on all tested genes.
- Confusing the adjusted p-value with the probability a hit is false. An FDR of 0.05 means about 5% of the whole significant set is expected to be false, not that any single gene has a 5% chance of being wrong.
- Using Bonferroni at genome scale. Controlling the family-wise error rate across twenty thousand genes is so conservative that it discards most real signal; the false discovery rate is the appropriate target for discovery work.
How to Use This Calculator
Paste your p-values
One per line, optionally with a gene or test label first. Values between 0 and 1.
Choose a method
Benjamini-Hochberg for FDR, Bonferroni for family-wise error, or Benjamini-Yekutieli for dependence.
Set the threshold
Set the target FDR or alpha, and the tool marks which tests stay significant after correction.
Read and export
Read the adjusted values and the significant count, then export the table as a CSV.
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Frequently Asked Questions
What is the false discovery rate?
The false discovery rate (FDR) is the expected proportion of false positives among the results you declare significant. If you call 100 genes significant at an FDR of 0.05, you expect about 5 of them to be false positives. Controlling the FDR is the standard approach in genomics and other high-throughput settings because it tolerates a small, known fraction of false discoveries in exchange for far greater power than family-wise error control.
What is the difference between FDR and p-value?
A raw p-value is the probability of a result at least as extreme under the null hypothesis for a single test, with no adjustment for how many tests you ran. An FDR-adjusted p-value, sometimes called a q-value, accounts for multiple testing: it is the smallest FDR at which that test would be called significant. When you test thousands of genes, raw p-values below 0.05 include many false positives, which is exactly what the adjustment corrects.
How do you calculate the false discovery rate?
The standard method is the Benjamini-Hochberg procedure (1995): rank the p-values from smallest to largest, then compare each to a threshold that scales with its rank, so the i-th smallest p-value is compared to (i / m) times the target rate, where m is the number of tests. The largest p-value that passes, and all smaller ones, are declared significant. The adjusted value reported by this tool is the equivalent step-up transformation, which matches R's p.adjust with method BH. Paste or import your p-values and it computes the whole column for you.
How do you correct for the false discovery rate?
You apply a multiple-testing correction to the whole set of p-values before deciding which are significant. Benjamini-Hochberg is the usual choice because it controls the expected fraction of false positives while keeping good power; Bonferroni is stricter and controls the chance of any false positive; and Benjamini-Yekutieli is used when the tests are arbitrarily dependent. This tool applies all three so you can compare, and marks which tests survive at your chosen threshold.
What is the difference between FDR and Bonferroni correction?
Bonferroni controls the family-wise error rate, the probability of even a single false positive, by multiplying each p-value by the number of tests. It is simple but very conservative and loses power when you run thousands of tests. Benjamini-Hochberg instead controls the expected fraction of false positives among discoveries, which is a more appropriate and far more powerful goal for exploratory genomics. This tool computes both so you can compare.
What is a good false discovery rate?
An FDR of 0.05 is the common default, meaning up to 5% of your declared discoveries are expected to be false. Genome-wide studies often accept 0.05 or 0.10 depending on whether the results are hypothesis-generating or confirmatory, and some screening contexts go looser. The right value is a trade-off: a stricter FDR yields fewer but more reliable hits, while a looser one recovers more true positives at the cost of more false ones.
Is a p-value of 0.001 highly significant?
For a single test, a p-value of 0.001 is strong evidence against the null hypothesis. But in a high-throughput setting it can be unremarkable: if you test 20,000 genes, roughly 20 will reach p < 0.001 by chance alone even when nothing is truly changing. That is why significance in genomics is judged on the adjusted p-value, not the raw one. A raw p of 0.001 may or may not survive a false discovery rate of 0.05 depending on how many other tests are at least as extreme, which is exactly what this calculator resolves.
What is a q-value?
A q-value is the false discovery rate analogue of a p-value: it is the minimum false discovery rate at which a given test is called significant. Storey's q-value (2002) additionally estimates the proportion of true null hypotheses to gain power, whereas the Benjamini-Hochberg adjusted p-value assumes that proportion is one. The adjusted p-values from this tool are Benjamini-Hochberg values; they are conservative q-values.
Related Analysis Tools
To visualize fold change against corrected significance, the volcano plot generator draws the FDR threshold, and the log2 fold change calculator computes the effect-size axis. To convert a test statistic into a p-value first, use the p-value calculator. For a complete differential-expression analysis, the bioinformatics analysis service takes it from raw counts to a corrected gene list.
Reviewed by
Dr. Sarah Mitchell
Dr. Sarah Mitchell holds a PhD in Biostatistics from Johns Hopkins Bloomberg School of Public Health and has over 15 years of experience in systematic review methodology and meta-analysis. She has authored or co-authored 40+ peer-reviewed publications in journals including the Journal of Clinical Epidemiology, BMC Medical Research Methodology, and Research Synthesis Methods. A former Cochrane Review Group statistician and current editorial board member of Systematic Reviews, Dr. Mitchell has supervised 200+ evidence synthesis projects across clinical medicine, public health, and social sciences. She reviews all Research Gold tools to ensure statistical accuracy and compliance with Cochrane Handbook and PRISMA 2020 standards.
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