Sign test¶
Test a paired-difference or one-sample median null by reducing non-tied observations to positive and negative signs and evaluating the positive count against its exact binomial distribution under a declared null probability, usually one half.
Core Idea¶
The sign test discards magnitude and counts the signs of independent nonzero differences; under the usual continuous null of no directional tendency or median difference zero, the positive count \(W\) has distribution \(\operatorname{Binomial}(m,1/2)\) after ties are omitted. each non-tied pair contributes one Bernoulli outcome determined only by direction; under the null, exchangeability or the median condition gives equal positive and negative probabilities, so an unusually imbalanced count supplies evidence against the null through calibrated binomial tails.
Scope of Application¶
Sign test applies when the analyst can specify independent paired differences or independent one-sample deviations from a declared median value, observed on at least an ordinal scale and establish that observations are independent across units, within-unit comparisons are meaningfully ordered, the null fixes sign probability, ties follow a declared rule, and the rejection probability is computed from the resulting sign-count distribution. This is descriptive statistical reference content, not an instruction to select a test without study-design, sampling, missingness, multiplicity, and domain-effect considerations.
Clarity¶
A clear claim names the carrier, governing rule, assumptions, and recognition test. This matters because sign test can refer to paired differences or a one-sample median formulation, and software packages can implement different two-sided exact p-value conventions. The disciplined statement is that the object counts as Sign test exactly when observations are independent across units, within-unit comparisons are meaningfully ordered, the null fixes sign probability, ties follow a declared rule, and the rejection probability is computed from the resulting sign-count distribution
Manages Complexity¶
The abstraction compresses paired sign test, one-sample median sign test, one- and two-sided forms, exact and normal-approximate calibration, randomized and conservative discrete tests, and tie-aware extensions into a stable carrier, rule, invariant, and failure boundary. It makes comparison tractable while retaining the variables that control validity.
Abstract Reasoning¶
- Type the carrier. Establish independent paired differences or independent one-sample deviations from a declared median value, observed on at least an ordinal scale and reject examples from a different problem.
- Lock the rule. Express that observations are independent across units, within-unit comparisons are meaningfully ordered, the null fixes sign probability, ties follow a declared rule, and the rejection probability is computed from the resulting sign-count distribution independently of one notation or implementation.
Knowledge Transfer¶
Transfer within statistics is strong when new cases preserve the same carrier, mechanism, and diagnostic. The move from For ten paired measurements with eight positive and two negative differences and no ties, the two-sided exact sign-test p-value under a fair-sign null is twice the smaller binomial tail, with the discrete convention stated. to For a one-sample median test, subtract the hypothesized median from each observation, omit exact ties under the classical continuous rule, and test whether positive signs occur with probability one half. demonstrates that continuity.
Relationships to Other Abstractions¶
Current abstraction Sign test Domain-specific
Parents (1) — outgoing typed relations
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Sign test is a kind of Hypothesis Testing (Null vs. Alternative) Prime
The sign test literally compares a calibrated null with a directional or two-sided alternative and uses a statistic to decide whether evidence crosses a rejection rule; sign reduction and binomial calibration supply the specialization.
Hierarchy paths (4) — routes to 4 parentless roots
- Sign test → is a kind of Hypothesis Testing (Null vs. Alternative) → is a kind of Statistical Inference → is a kind of Inductive Reasoning
- Sign test → is a kind of Hypothesis Testing (Null vs. Alternative) → is a kind of Statistical Inference → presupposes Uncertainty
- Sign test → is a kind of Hypothesis Testing (Null vs. Alternative) → is a kind of Verification → is a kind of Evaluation → presupposes Comparison
- Sign test → is a kind of Hypothesis Testing (Null vs. Alternative) → is a kind of Statistical Inference → presupposes Probability → is a kind of Measure → presupposes Set and Membership
Neighborhood in Abstraction Space¶
Sign test sits in a moderately populated region (50th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Descriptive Statistics & Correlation Measures (40 abstractions)
Nearest neighbors
- Kendall rank correlation coefficient — 0.88
- Nemenyi test — 0.86
- Paired difference test — 0.85
- Exchangeable random variables — 0.85
- Logrank test — 0.85
Computed from structural-signature embeddings · 2026-10-25