Benjamini–Hochberg example
The fifteen p values used to illustrate the step-up procedure.
Source: Benjamini and Hochberg (1995) · Neuhaus et al. (1992)False Discovery Rate Calculator
FigranPaste your p values for FDR correction with Benjamini–Hochberg or other adjustments, keeping your IDs.
- Thousands of p values
- BH, Bonferroni, Holm and more
- CSV and figures
Leave blank to use the number of non-missing p values. Set a larger total when only part of the tests is pasted.
Results
Calculating…
Adjusted values
| Row | Status | ID | p |
|---|
Values are rounded to four decimal places; decisions and CSV exports use full precision.
Methods sentence
False discovery rate examples
Load an example to see adjusted p values and a diagnostic figure.
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Simulated · 12 regionsHow to adjust p values
Use this adjusted p value calculator in four steps.
1Paste or import
Paste p values or import a CSV or Excel table.
2Choose columns
Select the p-value column and an optional ID column.
3Choose methods
Select corrections and set your threshold.
4Export
Download the adjusted table or figure.
Bonferroni correction vs Benjamini–Hochberg
Bonferroni adjustment and Benjamini–Hochberg both correct for multiple testing, but they control different error rates.
Bonferroni and Holm–Bonferroni control the family-wise error rate under arbitrary dependence. Benjamini–Hochberg controls the false discovery rate under independence and certain positive dependence. Choose a method based on the error rate and assumptions appropriate for your study.
Bonferroni per-test α: 0.005
| Method | Error rate | Dependence assumptions |
|---|---|---|
| Bonferroni / Holm | FWER | Arbitrary dependence |
| Hochberg / Hommel | FWER | Independence or certain positive dependence |
| Šídák / Holm-Šídák | FWER | Independent tests |
| Benjamini–Hochberg (BH) | FDR | Independence or certain positive dependence |
| Benjamini-Yekutieli | FDR | Arbitrary dependence |
| Storey q-value | Estimated q-value | Depends on the estimator and data |
The comparison below uses the 15 p values in the default example.
Benjamini–Hochberg (BH)4 discoveries
Bonferroni3 discoveries
References: R p.adjust documentation · Benjamini and Hochberg (1995) · Neuhaus et al. (1992)
How Benjamini–Hochberg works
The Benjamini–Hochberg procedure controls the false discovery rate (FDR). Sort p values and compare each to its rank multiplied by the chosen threshold, divided by the total number of tests. All values up to the largest passing rank are discoveries. Adjusted values are made monotone from the largest rank backward.
| Rank | P value | BH threshold | Status |
|---|---|---|---|
| 1 | 0.0001 | 0.0033 | Passes |
| 2 | 0.0004 | 0.0067 | Passes |
| 3 | 0.0019 | 0.0100 | Passes |
| 4 | 0.0095 | 0.0133 | Passes |
| 5 | 0.0201 | 0.0167 | Does not pass |
Reading the p-value histogram
A roughly uniform histogram can be consistent with null tests; an excess near zero can indicate signal. An excess near one or an unusual shape may reflect model or data issues. A histogram alone does not establish validity.
False discovery rate FAQ
What is the false discovery rate?
The false discovery rate is the expected proportion of false positives among rejected hypotheses.
How is FDR different from FWER?
FDR concerns the expected false proportion among discoveries; FWER is the probability of at least one false positive.
What are adjusted p values and q values?
An adjusted p value can be compared with a chosen error threshold. A q value estimates the minimum FDR threshold at which a test is called significant; definitions depend on the method.
Which method should I choose?
Choose according to the error rate and dependence assumptions appropriate to your study. BH targets FDR under independence or certain positive dependence, while BY is valid under arbitrary dependence; Holm controls FWER under arbitrary dependence. Weighted methods and gatekeeping are not provided.
Bonferroni vs Tukey post hoc test: which should I use?
Tukey's HSD compares every pair of group means after an ANOVA and is usually less conservative than Bonferroni for all pairwise comparisons; Bonferroni works for any set of tests, including a few planned comparisons. Select Bonferroni to multiply each p value by the total number of tests, capped at one. In SPSS One-Way ANOVA, choose Analyze → Compare Means → One-Way ANOVA → Post Hoc → Bonferroni. SPSS Bonferroni post hoc values are already adjusted; do not adjust them again. This tool does not run ANOVA from raw groups.
How many tests should I include?
Include the full family of tests defined by your analysis, including nonsignificant results. If only some values are pasted, enter the full total in Total tests.
Is this the same as A/B testing FDR?
No. This calculator adjusts a family of p values; project-level A/B FDR tools may instead estimate false discoveries from experiment counts and other assumptions.
Why do my values differ from DESeq2's padj?
DESeq2 uses independent filtering by default and adjusts only the genes that pass its filter, leaving filtered genes with NA in padj. All-zero counts or outliers can also lead to missing values. The six p.adjust methods here match R for the same non-missing p values and total test count.
Are my data uploaded?
No. Calculation and file processing run in your browser. The session draft stays in browser session storage.