Rodger's method¶
A post-hoc multiple-comparison framework selecting orthogonal contrasts while controlling the expected proportion of false rejection decisions.
Core Idea¶
The method’s decision-based error criterion differs from familywise error and false discovery rate, and interpretation depends on contrast selection and the omnibus experimental model. Candidate contrasts are ranked or constructed after inspection, a fixed rejection allowance based on degrees of freedom determines how many can be declared and selected orthogonal contrasts partition interpretable treatment variation. The abstraction is therefore identified by a declared carrier, a transformation or constraint over that carrier, and an invariant that tells an analyst whether the named structure is genuinely present.
Scope of Application¶
Rodger's method belongs to statistics and is useful where the analyst can specify the typed statistics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the fitted ANOVA and treatment means, error term and degrees of freedom, candidate contrast coefficients, orthogonality, decision-based error parameter, selection algorithm, test statistics, rejected contrasts and interpretation against conventional multiplicity controls are explicit. The scope is broad within that domain but bounded by the need for the fitted ANOVA and treatment means, error term and degrees of freedom, candidate contrast coefficients, orthogonality, decision-based error parameter, selection algorithm, test statistics, rejected contrasts and interpretation against conventional multiplicity controls are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the fitted ANOVA and treatment means, error term and degrees of freedom, candidate contrast coefficients, orthogonality, decision-based error parameter, selection algorithm, test statistics, rejected contrasts and interpretation against conventional multiplicity controls are explicit the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test.
Manages Complexity¶
Without the abstraction, an analyst must reason directly over many local details: the carrier roles, admissibility assumptions, competing conventions, derived invariants, boundary cases, and proof or validation obligations specific to Rodger's method. Rodger's method compresses them into the roles in the structural signature. That compression permits comparison across instances without erasing the variables that determine validity. It also exposes which details may be varied safely and which are constitutive.
Abstract Reasoning¶
- Identify the carrier. State what the elements, states, objects, or observations are: the typed statistics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the fitted ANOVA and treatment means, error term and degrees of freedom, candidate contrast coefficients, orthogonality, decision-based error parameter, selection algorithm, test statistics, rejected contrasts and interpretation against conventional multiplicity controls are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of statistics because they reuse the typed statistics carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Candidate contrasts are ranked or constructed after inspection, a fixed rejection allowance based on degrees of freedom determines how many can be declared and selected orthogonal contrasts partition interpretable treatment variation., and type the carrier, state every parameter and convention in the definition, test that the fitted ANOVA and treatment means, error term and degrees of freedom, candidate contrast coefficients, orthogonality, decision-based error parameter, selection algorithm, test statistics, rejected contrasts and interpretation against conventional multiplicity controls are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Rodger's method Domain-specific
Parents (1) — more general patterns this builds on
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Rodger's method is a kind of Multiple Comparisons Correction Prime
The proposed strict upward parent is
prime:multiple_comparisons_correction.
Hierarchy paths (6) — routes to 6 parentless roots
- Rodger's method → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Inductive Reasoning
- Rodger's method → Multiple Comparisons Correction → Type I & Type II Errors → Trade-offs → Constraint
- Rodger's method → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Uncertainty
- Rodger's method → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Verification → Evaluation → Comparison → Self Checking
- Rodger's method → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Set and Membership
- Rodger's method → Multiple Comparisons Correction → Type I & Type II Errors → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Rodger's method sits in a moderately populated region (49th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Robust Decomposition & Sensitivity Analysis (5 abstractions)
Nearest neighbors
- Brown–Forsythe test — 0.90
- Nuisance parameter — 0.89
- Correspondence analysis — 0.88
- Two-way analysis of variance — 0.88
- Studentization — 0.88
Computed from structural-signature embeddings · 2026-09-08