--- title: "Testing thousands of genes at once: false discovery rate and what q means" description: "Testing thousands of genes requires error control across tests. This stop compares family-wise error and false discovery rate, interprets q-values under stated conventions, and explains conditions for" canonical: https://lightmysky.com/learn/science/testing-thousands-of-genes-at-once-false-discovery-rate-and-what-q-means-mt_mIQ27rphrC source: https://lightmysky.com/learn/science/testing-thousands-of-genes-at-once-false-discovery-rate-and-what-q-means-mt_mIQ27rphrC.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Testing thousands of genes at once: false discovery rate and what q means Testing thousands of genes requires error control across tests. This stop compares family-wise error and false discovery rate, interprets q-values under stated conventions, and explains conditions for valid filtering and covariate weighting. Subject: Science · Area: Genetics & Evolution · Ages 23 to 24 Page: https://lightmysky.com/learn/science/testing-thousands-of-genes-at-once-false-discovery-rate-and-what-q-means-mt_mIQ27rphrC ## Ready when they can - Contrast Bonferroni with a false discovery rate procedure applied to the same p-value list - Interpret a q-value of 0.05 as an estimated list-level error threshold under a stated definition, not one gene's null probability - Explain how valid filtering or covariate weighting can change discoveries without guaranteeing an increase ## Lesson: One test is easy, twenty thousand are not A gene test can report a p-value. Under a true null, a valid p-value has probability at most t of being <= t. Rejecting a true null is a false positive. If 4,000 true nulls each have exact Type I error probability 0.05, expect 200 false positives. If their rates are only bounded by 0.05, expect at most 200. Sum over true nulls, not all tests; this expectation does not require independence. Family-wise error is the probability of at least one false positive in the tested family. Bonferroni rejects when p <= alpha/m, where m is the total test count. With 5,000 tests and alpha = 0.05, use 0.00001. For valid p-values, the family-wise error is at most alpha even with dependent tests. This can reduce power, but it neither rules out true discoveries nor guarantees zero false positives. *(drawing: Bonferroni bounds a probability of any false positive. It does not promise an error-free result.)* Let R count all rejections and V count false rejections. The false discovery proportion is V/R when R > 0, and zero when R = 0. FDR is its expectation over repeated studies. FDR control at 0.05 bounds this expectation by 5%, not the false fraction in every observed list. It can allow more discoveries than family-wise control when some nulls are false. Benjamini-Hochberg (BH) sorts m p-values from smallest to largest. Find the largest rank k with p(k) <= k*alpha/m, then reject every rank through k. If none qualifies, reject none. Standard BH controls FDR for valid p-values under independence or suitable positive dependence, not arbitrary dependence. Bonferroni instead compares every p-value with the fixed threshold alpha/m. *(drawing: Both procedures use the same four p-values. BH rejects through rank 3; Bonferroni uses 0.0125 for every test.)* Positive FDR, or pFDR, is the expected false discovery proportion conditional on making at least one rejection. FDR also includes studies with no rejections, whose proportion is zero. The two targets can differ, especially when discoveries are rare. Neither target is the probability that one particular gene's null hypothesis is true. Here a Storey-style q-value estimates the lowest pFDR over p-value cutoffs that include the gene. Selecting q <= 0.05 targets a conditional expected false fraction of at most 5%, subject to estimation and model assumptions. It does not guarantee the observed fraction. Some software uses q-value to mean a BH-adjusted p-value, which targets FDR instead. Check the reported method and definition. Filtering removes tests before correction. Null p-values must remain valid after selection, and the procedure's dependence assumptions must still hold. A filter independent of null p-values can help preserve validity. Covariate weighting may keep all tests but allocate different thresholds. Its covariate and weight learning need safeguards against reusing the same null p-value signal. Neither approach guarantees more discoveries. **Recap.** Bonferroni bounds the chance of any false positive. FDR bounds an expected false fraction. Check a q-value's definition and assumptions; filtering and weighting need valid safeguards. *Original lesson, questions and flashcards about multiple-testing error control, written for this learning dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Differential Expression from Counts: Dispersion, Fit and Shrinkage](https://lightmysky.com/learn/science/differential-expression-from-counts-dispersion-fit-and-shrinkage-mt_nEV9547kSN) ## Optional connections - [Errors, Power and the Design of a Test](https://lightmysky.com/learn/mathematics/errors-power-and-the-design-of-a-test-mt_D7ZXbvSD0l) ## Opens up - [From a gene list to biology: enrichment tests and their backgrounds](https://lightmysky.com/learn/science/from-a-gene-list-to-biology-enrichment-tests-and-their-backgrounds-mt_M9eHEXq6iA)