Interactive False Discovery Rate Calculator
Use one of the three calculators below depending on what data you have: observed outcomes, expected outcomes, or a list of p-values for the Benjamini-Hochberg (BH) procedure.
1) Observed FDR from outcomes
Use this when you already know how many discoveries were false positives.
2) Expected FDR from study assumptions
Useful for planning. Inputs: number of tests, null proportion, significance level, and power.
3) Benjamini-Hochberg (BH) FDR control
Paste p-values separated by commas, spaces, or line breaks. This returns rejected tests and BH-adjusted p-values (q-values).
What is the false discovery rate (FDR)?
The false discovery rate is the expected proportion of false positives among all declared significant results. In multiple testing, this is often a better target than trying to eliminate every false positive, because strict methods can destroy statistical power.
In plain language: if your FDR is 5%, then among your “discoveries,” about 5% are expected to be false alarms (on average).
Core formulas
Observed FDR
If you already know outcomes:
FDR = V / R
- V = false discoveries (false positives)
- R = total discoveries (all rejected null hypotheses)
If R = 0 (no findings), FDR is usually reported as 0 by convention.
Expected FDR (planning approximation)
For rough study planning with m tests, null proportion π₀, type I error α, and power:
- Expected false positives: m × π₀ × α
- Expected true positives: m × (1 − π₀) × power
- Expected FDR: FP / (FP + TP)
Why FDR matters in real analysis
In genomics, neuroimaging, A/B testing, and high-dimensional machine learning, analysts often run hundreds or thousands of statistical tests. If you use a naive p < 0.05 threshold for each test, false positives accumulate quickly.
FDR procedures (especially Benjamini-Hochberg) provide a practical compromise:
- More discoveries than ultra-conservative family-wise methods (like Bonferroni)
- Controlled average false-positive proportion among reported results
- Better balance between finding signal and limiting noise
How the Benjamini-Hochberg procedure works
- Sort p-values from smallest to largest.
- For rank i out of m, compute BH critical value: (i/m) × q, where q is your target FDR (e.g., 0.05).
- Find the largest rank where p(i) ≤ (i/m) × q.
- Reject all hypotheses up to that rank.
The calculator above also computes BH-adjusted p-values (often called q-values in software output), which let you compare each test directly to your target FDR level.
FDR vs related concepts
FDR vs Family-Wise Error Rate (FWER)
FWER controls the chance of making any false positive at all. FDR controls the fraction of false positives among discoveries. FWER is stricter; FDR is often more powerful.
FDR vs p-value
A p-value is test-specific evidence against one null hypothesis. FDR is a multi-test error-control framework across a whole set of hypotheses.
Practical interpretation tips
- FDR control does not guarantee every individual significant result is true.
- The chosen q-level (0.05, 0.10, etc.) should match domain risk tolerance.
- Report your correction method and software settings transparently.
- When possible, validate top findings in independent data.
Common mistakes to avoid
- Applying uncorrected p-values after running many tests.
- Confusing FDR with the probability that a specific result is false.
- Ignoring dependence structure when using advanced procedures.
- Cherry-picking only corrected-significant results without effect sizes and confidence intervals.
Quick FAQ
What is a good FDR threshold?
0.05 is common, but 0.10 is often used in exploratory work. Confirmatory settings may choose stricter levels.
Can FDR be used outside biology?
Yes. It is useful in any field involving many simultaneous tests: marketing experiments, economics, social science, and model diagnostics.
If no tests are significant, what is FDR?
Conventionally 0, since there are no discoveries to be false.