False Discovery Rate¶
The expected proportion of false rejections among all rejected hypotheses, conventionally V/max(R,1), used as an at-scale error criterion that accepts a controlled fraction of false discoveries in exchange for power.
Core Idea¶
False discovery rate is the expected proportion of false rejections among all rejected hypotheses, conventionally \(E[V/\max(R,1)]\)[1]. It is an error criterion for discovery at scale: it permits a controlled fraction of false positives in exchange for greater ability to find real effects.
The canonical identity is narrower than the phrase’s everyday use. It requires a family of decisions, a set of rejections \(R\), an unobserved subset of false rejections \(V\), and an expectation over the discovery process. The zero-rejection convention prevents an undefined ratio.
Structural Signature¶
- It requires a family of decisions, a set of rejections \(R\), an unobserved subset of false rejections \(V\), and an expectation over the discovery process. The zero-rejection convention prevents an undefined ratio.
What It Is Not¶
FDR is not an adjustment algorithm. Benjamini–Hochberg, Benjamini–Yekutieli, q-values, and knockoff methods are different procedures that can target it[2]. Family-wise error rate instead controls the chance of any false rejection and answers a stricter question.
- FDR is not an adjustment algorithm. Benjamini–Hochberg, Benjamini–Yekutieli, q-values, and knockoff methods are different procedures that can target it. Family-wise error rate instead controls the chance of any false rejection and answers a stricter question.
Scope of Application¶
FDR is used in many empirical fields, but its roles remain those of statistical multiple testing everywhere[3]. Applications travel; the formal criterion stays within an imported inference substrate.
A shared label or downstream consequence is insufficient; the load-bearing roles must survive.
Clarity¶
False Discovery Rate separates a specific relation from neighboring ideas that can produce similar observations. FDR is not an adjustment algorithm. Benjamini–Hochberg, Benjamini–Yekutieli, q-values, and knockoff methods are different procedures that can target it. Family-wise error rate instead controls the chance of any false rejection and answers a stricter question.
Manages Complexity¶
The abstraction compresses recurring cases into one inspectable model. An analyst can track the structural roles, compare mechanisms, and locate exactly which missing commitment invalidates an analogy.
Abstract Reasoning¶
Identify the candidate roles, test the defining relation, then challenge the nearest boundary case. Saying “ten percent of published findings are false” is not an FDR statement unless the discovery rule and expectation over repeated realizations are specified.
Knowledge Transfer¶
FDR is used in many empirical fields, but its roles remain those of statistical multiple testing everywhere. Applications travel; the formal criterion stays within an imported inference substrate. Transfer is warranted only when the same causal, formal, or relational work survives.
Examples¶
Qualifying pattern. False discovery rate is the expected proportion of false rejections among all rejected hypotheses, conventionally \(E[V/\max(R,1)]\). It is an error criterion for discovery at scale: it permits a controlled fraction of false positives in exchange for greater ability to find real effects.
Boundary case. Saying “ten percent of published findings are false” is not an FDR statement unless the discovery rule and expectation over repeated realizations are specified.
Structural Tensions¶
T1 — Reach versus identity inflation. Broad use is valuable only while every defining role survives.
T2 — Observation versus mechanism. Similar outcomes can arise from neighboring mechanisms, so classification follows the relation and its counterfactual rather than appearance.
Structural Core vs. Domain Accent¶
FDR is used in many empirical fields, but its roles remain those of statistical multiple testing everywhere. Applications travel; the formal criterion stays within an imported inference substrate. The transferable residue is thinner than the named mechanism, whose domain vocabulary and causal apparatus remain constitutive.
Relationships to Other Abstractions¶
Current abstraction False Discovery Rate Domain-specific
Parents (1) — more general patterns this builds on
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False Discovery Rate is a decomposition of Type I & Type II Errors Prime
Removing the child’s frame leaves the reusable structure named by Type I Type Ii Errors.The child’s domain vocabulary can be removed while the parent’s roles remain, so the relation records portable structural cargo rather than taxonomic identity.
Children (1) — more specific cases that build on this
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Benjamini–Hochberg Procedure Domain-specific presupposes False Discovery Rate
Benjamini Hochberg Procedure presupposes False Discovery Rate.The parent can occur independently, but without it the child mechanism is undefined, establishing prerequisite dependence.
Hierarchy paths (6) — routes to 6 parentless roots
- False Discovery Rate → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Inductive Reasoning
- False Discovery Rate → Type I & Type II Errors → Trade-offs → Constraint
- False Discovery Rate → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Uncertainty
- False Discovery Rate → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Verification → Evaluation → Comparison → Self Checking
- False Discovery Rate → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Set and Membership
- False Discovery Rate → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
False Discovery Rate sits in a sparse region of the domain-specific corpus (99th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Unclustered & Miscellaneous (1565 abstractions)
Nearest neighbors
- Family-Wise Error Rate — 0.78
- Fourier–Motzkin Elimination — 0.75
- Set splitting problem — 0.73
- Bonferroni Correction — 0.73
- Benjamini–Hochberg Procedure — 0.73
Computed from structural-signature embeddings · 2026-09-08
Not to Be Confused With¶
FDR is not an adjustment algorithm. Benjamini–Hochberg, Benjamini–Yekutieli, q-values, and knockoff methods are different procedures that can target it. Family-wise error rate instead controls the chance of any false rejection and answers a stricter question.
- FDR is not an adjustment algorithm. Benjamini–Hochberg, Benjamini–Yekutieli, q-values, and knockoff methods are different procedures that can target it. Family-wise error rate instead controls the chance of any false rejection and answers a stricter question.
References¶
[1] Benjamini, Yoav and Hochberg, Yosef. “Controlling the False Discovery Rate”. Journal of the Royal Statistical Society: Series B (Methodological), 1995. Benjamini & Hochberg (1995) define FDR as E[Q], Q=V/R with Q:=0 when R=0 – precisely the E[V/max(R,1)] convention stated here. registry ↩
[2] Barber and Candès. “Controlling the false discovery rate via knockoffs”. The Annals of Statistics, 2015. Barber & Candes (2015) name BH and BY as prior FDR-control procedures and cite Storey (2002) as related work before introducing knockoffs, but the paper does not use the term 'q-values' or assert 'FDR is not an adjustment algorithm' as an explicit proposition. registry ↩
[3] Benjamini. “Discovering the False Discovery Rate”. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2010. Benjamini (2010) documents FDR's spread across many empirical fields but does not itself assert the article's added claim that its role remains multiple-testing 'everywhere.'. registry ↩