Testing Thousands of Genes at Once: False Discovery Rate and What q Means
With twenty thousand tests, a five percent error rate on each one is meaningless. This stop separates family-wise error control from false discovery rate control and reads a q-value for exactly what it claims.
What a learner can do afterwards
- Contrast Bonferroni with a false discovery rate procedure applied to the same p-value list
- State what a q-value of 0.05 asserts about a list of genes rather than about one gene
- Explain how pre-filtering or an independent covariate changes the number of discoveries
1 · Read
When you scan the genome you run thousands of tests, one for each gene, and per test error control collapses. A 5 percent false alarm rate on each test produces about 1,000 chance false alarms across 20,000 tests. Five percent per gene sounds strict until you multiply it by twenty thousand genes.
The older answer is family wise error control: cap the chance of even one false alarm across the whole list. Bonferroni is the classic version, and it divides your error budget by the test count. With 20,000 genes, only p below 0.0000025 counts, since 0.05 divided by 20,000 is 0.0000025. Real signals drown under a bar that strict.
False discovery rate control asks a gentler question: among the genes you call hits, what fraction may be false? A q value of 0.05 claims that about 5 percent of the whole list at or below that cutoff are expected false discoveries, not 5 percent for one gene. When scanning thousands of genes, guarding against any single false alarm buries real signals, so controlling the fraction in the list beats Bonferroni.
You can raise honest discoveries without loosening standards. Pre filtering drops untrustworthy genes before testing, and an independent covariate adds outside evidence for ranking. Both shrink the effective test count, so real signals clear the bar more often while the error promise holds.
Divide the budget for zero false alarms, or control the false fraction when you can afford a few.
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.