FreedomIntelligence name: bio-experimental-design-multiple-testing description: Applies multiple testing correction methods including FDR, Bonferroni, and q-value for genomics data. Use when filtering differential expression results, setting significance thresholds, or choosing between correction methods for different study designs. tool_type: r primary_tool: qvalue measurable_outcome: Execute skill workflow successfully with valid output within 15 minutes. allowed-tools: - read_file - run_shell_command
Multiple Testing Correction
The Problem
Testing 20,000 genes at p < 0.05 yields ~1,000 false positives by chance. Correction is essential.
Common Methods
Bonferroni (Most Conservative)
# Strict family-wise error rate control
p_adj <- p.adjust(pvalues, method = 'bonferroni')
# Threshold: alpha / n_tests
# Use for: small gene sets, confirmatory studies
Benjamini-Hochberg FDR (Standard)
# Controls false discovery rate
p_adj <- p.adjust(pvalues, method = 'BH')
# Most common for genomics
# FDR 0.05 = expect 5% of significant results to be false
q-value (Recommended for Large-Scale)
library(qvalue)
qobj <- qvalue(pvalues)
qvalues <- qobj$qvalues
pi0 <- qobj$pi0 # Estimated proportion of true nulls
# q-value directly estimates FDR for each gene
# More powerful than BH when many true positives exist
Method Selection Guide
| Scenario | Recommended Method | Threshold |
|---|---|---|
| Genome-wide DE | BH or q-value | FDR < 0.05 |
| Candidate genes | Bonferroni | p < 0.05/n |
| Exploratory | BH | FDR < 0.10 |
| Validation study | Bonferroni | p < 0.05/n |
| GWAS | Bonferroni | p < 5e-8 |
Python Equivalent
from statsmodels.stats.multitest import multipletests
# Benjamini-Hochberg
rejected, pvals_corrected, _, _ = multipletests(pvalues, method='fdr_bh')
# Bonferroni
rejected, pvals_corrected, _, _ = multipletests(pvalues, method='bonferroni')
Interpreting Results
- FDR 0.05: Among genes called significant, ~5% are false positives
- FDR 0.01: More stringent, fewer false positives but more false negatives
- padj vs qvalue: Both estimate FDR; q-value is slightly more powerful
Related Skills
- differential-expression/de-results - Applying corrections to DE output
- population-genetics/association-testing - GWAS significance thresholds
- pathway-analysis/go-enrichment - Correcting enrichment p-values