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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 \(E[V/\max(R,1)]\). 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. 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. 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

Local relationship map for False Discovery RateParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.False Discovery RateDOMAINPrime abstraction: Type I & Type II Errors — is a decomposition ofType I & TypeII ErrorsPRIMEDomain-specific abstraction: Benjamini–Hochberg Procedure — presupposesBenjamini–Hochb…DOMAIN

Current abstraction False Discovery Rate Domain-specific

Parents (1) — more general patterns this builds on

  • 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.

Children (1) — more specific cases that build on this

  • Benjamini–Hochberg Procedure Domain-specific presupposes False Discovery Rate

    Benjamini Hochberg Procedure presupposes False Discovery Rate.

Hierarchy paths (6) — routes to 6 parentless roots

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.

Notes

(Canonical first draft from the adjudicated missing-node gate. Queued for Claude house-style re-authoring and independent citation review; no citations have been fabricated.)