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. 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.
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.
Clarity¶
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 turns a scattered family of cases into one role-based test: identify the required elements, test their relation, and reject the classification when a constitutive commitment is missing.
Abstract Reasoning¶
Use the structural signature rather than the label, then challenge the nearest counterexample. 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.
Example¶
A case qualifies only when the definition and every load-bearing role remain present. Saying “ten percent of published findings are false” is not an FDR statement unless the discovery rule and expectation over repeated realizations are specified.
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.
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.
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
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.
Notes¶
(Canonical first draft; queued for Claude house-style re-authoring and citation review.)