MAGIC criteria¶
A five-part framework for evaluating whether a statistical argument is compelling through magnitude, articulation, generality, interestingness and credibility.
Core Idea¶
Robert Abelson’s criteria assess the argumentative force of an empirical claim rather than provide a mechanical significance test, and each dimension requires domain-specific judgment. An analyst states the effect size and pattern precisely, evaluates transfer beyond the immediate study, asks whether the result changes important beliefs and weighs design and evidence credibility before presenting the inference. 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¶
MAGIC criteria belongs to statistical argumentation and is useful where the analyst can specify the typed statistical argumentation carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, then evaluate the claim and intended audience, measured magnitude, articulated pattern, population and context of generality, prior beliefs and interestingness, design and inferential credibility, tradeoffs among dimensions and supporting evidence are explicit. The scope is broad within that domain but bounded by the need for the claim and intended audience, measured magnitude, articulated pattern, population and context of generality, prior beliefs and interestingness, design and inferential credibility, tradeoffs among dimensions and supporting evidence are explicit.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the claim and intended audience, measured magnitude, articulated pattern, population and context of generality, prior beliefs and interestingness, design and inferential credibility, tradeoffs among dimensions and supporting evidence 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 MAGIC criteria. MAGIC criteria 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 argumentation 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 claim and intended audience, measured magnitude, articulated pattern, population and context of generality, prior beliefs and interestingness, design and inferential credibility, tradeoffs among dimensions and supporting evidence are explicit independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of statistical argumentation because they reuse the typed statistical argumentation carrier, including objects, relations, parameters, conventions, evidence, boundaries, and comparison targets, An analyst states the effect size and pattern precisely, evaluates transfer beyond the immediate study, asks whether the result changes important beliefs and weighs design and evidence credibility before presenting the inference., and type the carrier, state every parameter and convention in the definition, test that the claim and intended audience, measured magnitude, articulated pattern, population and context of generality, prior beliefs and interestingness, design and inferential credibility, tradeoffs among dimensions and supporting evidence are explicit, compare the nearest accepted identity, and report counterexamples, uncertainty, and limiting cases.
Relationships to Other Abstractions¶
Current abstraction MAGIC criteria Domain-specific
Parents (1) — more general patterns this builds on
-
MAGIC criteria is a kind of Evaluation Prime
The proposed strict upward parent is
prime:evaluation.
Hierarchy path (1) — routes to 1 parentless root
- MAGIC criteria → Evaluation → Comparison → Self Checking
Neighborhood in Abstraction Space¶
MAGIC criteria sits in a crowded region of the domain-specific corpus (28th percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.
Family — Epistemic Measurement & Causal Reasoning (19 abstractions)
Nearest neighbors
- Appeal to consequences — 0.93
- Persuasive definition — 0.91
- Testing hypotheses suggested by the data — 0.91
- Sequential analysis — 0.90
- Nuisance parameter — 0.90
Computed from structural-signature embeddings · 2026-09-08