Testing hypotheses suggested by the data¶
The invalid reuse of the same observations both to select a hypothesis and to test it as though the test had been specified independently.
Core Idea¶
Exploratory hypothesis generation is legitimate when labeled, the bias arises from unaccounted selection, and valid selective-inference adjustments or independent replication can restore calibrated error control without forbidding data-driven discovery. Searching many patterns selects one with an unusually favorable statistic; a conventional test that ignores this selection compares it with the wrong null distribution, producing exaggerated evidence unless selection is modeled or evaluation data are held out. 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¶
Testing hypotheses suggested by the data belongs to statistical inference and is useful where the analyst can specify the typed statistical inference carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the dataset and analysis population, exploratory search space and analyst degrees of freedom, selected hypothesis, selection criterion, test statistic and null model, reuse of observations, nominal and actual error rates, multiplicity or selective-inference adjustment, preregistration sample splitting or replication remedy and reporting of exploratory status are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the dataset and analysis population, exploratory search space and analyst degrees of freedom, selected hypothesis, selection criterion, test statistic and null model, reuse of observations, nominal and actual error rates, multiplicity or selective-inference adjustment, preregistration sample splitting or replication remedy and reporting of exploratory status 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 Testing hypotheses suggested by the data. Testing hypotheses suggested by the data 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 statistical inference 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 dataset and analysis population, exploratory search space and analyst degrees of freedom, selected hypothesis, selection criterion, test statistic and null model, reuse of observations, nominal and actual error rates, multiplicity or selective-inference adjustment, preregistration sample splitting or replication remedy and reporting of exploratory status are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of statistical inference because they reuse the typed statistical inference carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, Searching many patterns selects one with an unusually favorable statistic; a conventional test that ignores this selection compares it with the wrong null distribution, producing exaggerated evidence unless selection is modeled or evaluation data are held out., and type the carrier, state every parameter and convention in the definition, test that the dataset and analysis population, exploratory search space and analyst degrees of freedom, selected hypothesis, selection criterion, test statistic and null model, reuse of observations, nominal and actual error rates, multiplicity or selective-inference adjustment, preregistration sample splitting or replication remedy and reporting of exploratory status are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction Testing hypotheses suggested by the data Domain-specific
Parents (1) — more general patterns this builds on
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Testing hypotheses suggested by the data is a kind of Verification Prime
The proposed strict upward parent is
prime:verification.
Hierarchy path (1) — routes to 1 parentless root
- Testing hypotheses suggested by the data → Verification → Evaluation → Comparison → Self Checking
Neighborhood in Abstraction Space¶
Testing hypotheses suggested by the data sits in a crowded region of the domain-specific corpus (2nd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Statistical Estimation & Hypothesis Testing (35 abstractions)
Nearest neighbors
- Standard error — 0.95
- Score test — 0.95
- Pivotal quantity — 0.94
- Normality test — 0.94
- Generalized p-value — 0.94
Computed from structural-signature embeddings · 2026-09-08