Anderson–Darling test¶
Test a sample’s agreement with a specified continuous distribution by integrating squared empirical-CDF deviations with extra weight in the tails.
Core Idea¶
The Anderson–Darling statistic is a Cramér–von Mises-type goodness-of-fit measure weighted by [F(x)(1−F(x))]^{-1}, emphasizing tail departures. Data are transformed through the null CDF, ordered, and compared with uniform order-statistic expectations; logarithmic tail terms accumulate discrepancies into A². 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.
The load-bearing residual is not the broad topic of statistics. It is the Anderson–Darling tail-weighted statistic and distribution-specific calibration. That residual remains recognizable when examples, notation, scale, or implementation change, but it disappears if Kolmogorov–Smirnov critical values are reused, fitted parameters are ignored, discrete data use continuous tables without adjustment, or a p-value is treated as fit magnitude.
Scope of Application¶
Anderson–Darling test belongs to statistics and is useful where the analyst can specify an ordered sample, a fully specified or fitted continuous null cumulative distribution, and the transformed empirical distribution, then evaluate the declared tail-weighted empirical-versus-null CDF statistic and matching null calibration determine the test. The scope is broad within that domain but bounded by the need for the declared tail-weighted empirical-versus-null CDF statistic and matching null calibration determine the test. The entry records a descriptive analytical identity; practical use requires the governing domain's evidence, standards, and safety obligations.
Clarity¶
The abstraction clarifies a crowded vocabulary by making the declared tail-weighted empirical-versus-null CDF statistic and matching null calibration determine the test the center of the account. A claim should name the carrier, the governing operation or relation, the applicable assumptions, and the recognition test. A bare label is insufficient because the name Anderson–Darling test can be used for a formal identity, an implementation, or a neighboring result unless carrier and convention are stated.
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 Anderson–Darling test. Anderson–Darling test 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: an ordered sample, a fully specified or fitted continuous null cumulative distribution, and the transformed empirical distribution. Reject examples whose alleged carrier belongs to a different problem. 2. Lock the constitutive rule. Express the declared tail-weighted empirical-versus-null CDF statistic and matching null calibration determine the test independently of one notation or implementation.
Knowledge Transfer¶
Knowledge transfers strongly among subfields of statistics because they reuse an ordered sample, a fully specified or fitted continuous null cumulative distribution, and the transformed empirical distribution, Data are transformed through the null CDF, ordered, and compared with uniform order-statistic expectations; logarithmic tail terms accumulate discrepancies into A²., and state whether parameters are known or estimated, use the correct finite-sample calibration, handle ties and censoring, inspect effect size and plots, and avoid accepting the null from nonsignificance. A theorem, diagnostic, or modeling warning can travel when those roles remain literal.
Relationships to Other Abstractions¶
Current abstraction Anderson–Darling test Domain-specific
Parents (1) — more general patterns this builds on
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Anderson–Darling test is a kind of Hypothesis Testing (Null vs. Alternative) Prime
The proposed strict upward parent is
prime:hypothesis_testing_null_vs_alternative.
Hierarchy paths (5) — routes to 5 parentless roots
- Anderson–Darling test → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Inductive Reasoning
- Anderson–Darling test → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Uncertainty
- Anderson–Darling test → Hypothesis Testing (Null vs. Alternative) → Verification → Evaluation → Comparison → Self Checking
- Anderson–Darling test → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Set and Membership
- Anderson–Darling test → Hypothesis Testing (Null vs. Alternative) → Statistical Inference → Probability → Measure → Aggregation → Micro Macro Linkage
Neighborhood in Abstraction Space¶
Anderson–Darling test sits in a moderately populated region (55th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Statistical Dispersion & Testing (44 abstractions)
Nearest neighbors
- Z-test — 0.89
- Portmanteau test — 0.88
- Logrank test — 0.88
- Exact test — 0.87
- Normality test — 0.87
Computed from structural-signature embeddings · 2026-09-08