Exact sign test

When to consider it

• Test whether positive and negative differences are equally likely, using the exact sign test.

Assumptions and scope

• For paired data, calculate x minus y for each pair and enter those differences with reference 0.
• Independent observations/pairs; zeros are counted and omitted. A continuous median interpretation needs no point mass at the reference.

Direction only; discards difference magnitudes.

Required inputs

• Observations or differences — Numeric observations; preserve the row and column structure described above.
• Reference location — Enter the method parameter described above.

Review missing values and data coding before running. Sample inputs are synthetic teaching examples.

Implementation

Exact two-sided binomial test of signs relative to a reference. Enter one-sample values, or precomputed within-pair differences with reference 0. Zeros are counted and omitted. Independent observations/pairs required; a continuous median interpretation needs no point mass at the reference. Synthetic example: 40 independent simulated changes in outcome units; no patient records.

• scipy 1.15.3: scipy.stats.binomtest

These are pinned library versions; saved results record the versions actually used at runtime.

Library references

• SciPy statistical methods
• statsmodels models and statistical tests
• scikit-learn clustering
• lifelines survival comparisons