The False Discovery Rate (FDR) Calculator helps you estimate the likelihood of false positives among your statistically significant results. It is widely use in scientific studies where many hypotheses are test at the same time—like in gene expression studies, psychological surveys, or data science models. Instead of strictly controlling the chance of any false positives (which can be too harsh in large tests), FDR focuses on limiting the rate of errors, making it practical and widely accepted in research today.
This tool falls under the Statistical Testing and Analysis Calculators category.
formula of False Discovery Rate Calculator
Basic Formula for FDR:
FDR = False Positives / (False Positives + True Positives)
Where:
- False Positives (FP): Number of tests incorrectly declared significant
- True Positives (TP): Number of correctly identified significant results
FDR as a Percentage:
FDR (%) = [FP / (FP + TP)] × 100
Benjamini–Hochberg Procedure (for multiple hypothesis testing):
If you test m hypotheses and get sorted p-values: p₁ ≤ p₂ ≤ ... ≤ pₘ, and q is your FDR threshold (like 0.05), find the largest k where:
pₖ ≤ (k / m) × q
Then reject all p-values less than or equal to pₖ.
This method balances discovery with control over false positives when you're testing many variables at once.
Reference Table: Common Scenarios
| True Positives (TP) | False Positives (FP) | FDR (Decimal) | FDR (%) |
|---|---|---|---|
| 90 | 10 | 0.10 | 10% |
| 50 | 25 | 0.33 | 33% |
| 100 | 5 | 0.047 | 4.7% |
| 75 | 15 | 0.167 | 16.7% |
| 60 | 40 | 0.40 | 40% |
This table helps researchers and analysts quickly assess the expected error rate under different discovery conditions.
Example of False Discovery Rate Calculator
Let’s say you conducted a study and identified:
- 80 results as statistically significant
- Of those, 60 are confirmed true positives
- 20 are later found to be false positives
Using the FDR formula:
FDR = 20 / (20 + 60) = 0.25 or 25%
This means that 1 in 4 of your significant results may be a false finding.
Using Benjamini–Hochberg:
Suppose you test 100 hypotheses with a significance threshold of q = 0.05 and sort the p-values. You find that the 12th smallest p-value (p₁₂) is 0.045.
Check: Is 0.045 ≤ (12 / 100) × 0.05 = 0.006?
No. So this p-value fails the FDR condition.
Let’s say the 3rd p-value (p₃) is 0.001 and (3/100) × 0.05 = 0.0015. Since 0.001 ≤ 0.0015, you can reject the first 3 hypotheses as statistically significant with FDR under 5%.
Most Common FAQs
FDR is used when you're okay with a small proportion of false discoveries, especially in large-scale tests like genetic studies. FWER controls even one error, which may be too strict.
Yes. FDR can help during feature selection or when testing multiple model parameters, where multiple comparisons are involved.
The original method is built around p-values, but other statistical metrics like q-values or posterior probabilities can adapt the concept for different models.