False Discovery Rate Calculator
Solve false discovery rate problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.
Formula
BH threshold(i) = (i / m) ร ฮฑ | Adjusted p(i) = min(p(i) ร m / i, 1)
The Benjamini-Hochberg procedure sorts p-values, calculates rank-based thresholds, and finds the largest rank where the p-value falls below its threshold. All hypotheses up to that rank are rejected. Adjusted p-values (q-values) represent the minimum FDR for significance.
Worked Examples
Example 1: Genomics Study with 10 Tests
Problem: A researcher tests 10 genes for differential expression and obtains p-values: 0.001, 0.008, 0.039, 0.041, 0.042, 0.06, 0.10, 0.25, 0.50, 0.80. Apply BH correction at FDR = 0.05.
Solution: Sort p-values and calculate BH thresholds:\nRank 1: p=0.001, threshold=0.005 โ Significant\nRank 2: p=0.008, threshold=0.010 โ Significant\nRank 3: p=0.039, threshold=0.015 โ Not significant\nRank 4: p=0.041, threshold=0.020 โ Not significant\nLargest significant rank: 2\nBonferroni would require p < 0.005 (only 1 discovery)
Result: 2 discoveries at FDR 0.05 vs 1 with Bonferroni | BH is more powerful
Example 2: A/B Testing Multiple Variants
Problem: An A/B test platform runs 5 tests with p-values: 0.01, 0.03, 0.04, 0.15, 0.60. Determine which are significant at FDR = 0.10.
Solution: Sort and apply BH procedure at alpha=0.10:\nRank 1: p=0.01, threshold=0.02 โ Significant (q=0.05)\nRank 2: p=0.03, threshold=0.04 โ Significant (q=0.075)\nRank 3: p=0.04, threshold=0.06 โ Significant (q=0.067)\nRank 4: p=0.15, threshold=0.08 โ Not significant\nRank 5: p=0.60, threshold=0.10 โ Not significant
Result: 3 significant variants at FDR 0.10 | Expected false discoveries: 0.3
Frequently Asked Questions
What is the False Discovery Rate (FDR) and why is it important?
The False Discovery Rate is the expected proportion of false positives among all rejected hypotheses in multiple testing scenarios. When you perform many statistical tests simultaneously, like testing thousands of genes for differential expression or running hundreds of A/B test variants, the probability of obtaining false positives by chance alone increases dramatically. At a significance level of 0.05, testing 1,000 hypotheses would yield approximately 50 false positives even if none of the effects are real. FDR control provides a principled way to manage this multiple comparisons problem while retaining more statistical power than ultra-conservative methods like Bonferroni correction, making it essential in genomics, neuroimaging, and large-scale A/B testing.
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No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
What formula does False Discovery Rate Calculator use?
The formula used is described in the Formula section on this page. It is based on widely accepted standards in the relevant field. If you need a specific reference or citation, the References section provides links to authoritative sources.
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