Bonferroni Correction¶
Control the family-wise probability of any false rejection across m tests by comparing each p-value with alpha/m, or equivalently multiplying each p-value by m, without requiring independence.
Core Idea¶
Bonferroni correction controls the probability of one or more false rejections across a fixed family of \(m\) hypothesis tests by testing each hypothesis at \(\alpha/m\), or equivalently by multiplying each raw p-value by \(m\) and truncating at one. Its guarantee does not require test independence. The procedure requires a declared test family, a family-wise error budget, a finite count \(m\), and a uniform division of that budget across family members. Its conservatism is the price of a simple, dependence-robust union-bound guarantee.
Scope of Application¶
The recipe runs unchanged in genomics, physics, medicine, and online experiments, but each use imports the same statistical-testing apparatus. Its reach is broad application of a statistical method, not substrate removal.
Clarity¶
It is one procedure within Multiple Comparisons Correction, not an alias for that family. False Discovery Rate is a criterion about the proportion of false discoveries; Benjamini–Hochberg is a different procedure targeting that criterion. Look-Elsewhere problems can require an effective rather than literal count of opportunities.
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. Dividing alpha by the number of observations rather than the number of tested claims is not Bonferroni correction.
Knowledge Transfer¶
The recipe runs unchanged in genomics, physics, medicine, and online experiments, but each use imports the same statistical-testing apparatus. Its reach is broad application of a statistical method, not substrate removal.
Example¶
A case qualifies only when the definition and every load-bearing role remain present. Dividing alpha by the number of observations rather than the number of tested claims is not Bonferroni correction.
Relationships to Other Abstractions¶
Current abstraction Bonferroni Correction Domain-specific
Parents (1) — more general patterns this builds on
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Bonferroni Correction is a kind of Multiple Comparisons Correction Prime
Bonferroni Correction is a strict specialization of Multiple Comparisons Correction.
Hierarchy paths (6) — routes to 6 parentless roots
- Bonferroni Correction → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Inductive Reasoning
- Bonferroni Correction → Multiple Comparisons Correction → Type I & Type II Errors → Trade-offs → Constraint
- Bonferroni Correction → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Uncertainty
- Bonferroni Correction → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Verification → Evaluation → Comparison → Self Checking
- Bonferroni Correction → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Set and Membership
- Bonferroni Correction → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Aggregation → Micro Macro Linkage
Not to Be Confused With¶
It is one procedure within Multiple Comparisons Correction, not an alias for that family. False Discovery Rate is a criterion about the proportion of false discoveries; Benjamini–Hochberg is a different procedure targeting that criterion. Look-Elsewhere problems can require an effective rather than literal count of opportunities.
Notes¶
(Canonical first draft; queued for Claude house-style re-authoring and citation review.)