---
title: "Sign test (paired)"
method_id: SM.DIF.NPA.2DEP.SIGN
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/sign_test.md
source: Clarus method library
---

# Sign test (paired)

> A classical statistical method in the Clarus library (Difference family).
> Clarus selects, assumption-checks and runs this method on your data with a
> deterministic rule engine and real numerical libraries (scipy / statsmodels);
> it never generates numbers, citations or results.

**Also known as:** paired sign test; binomial sign test; median sign test.

## Hypotheses

- **Null (H0):** P(condition2 > condition1) = P(condition2 < condition1) = 0.5 (median of within-pair differences = 0)
- **Alternative (H1):** P(condition2 > condition1) != 0.5 (median of within-pair differences != 0)

## When to use it

Use this method when your goal is to:
- compare two related measurements
- test paired median shift
- paired difference minimal assumptions

## Data it expects

- **dependent:** 2 paired measurements (ordinal or higher; only the SIGN of each within-pair difference is used)
- **independent:** 1 within-subjects factor / 2 related conditions
- **pairing:** paired (repeated/matched)

## Assumptions Clarus checks

- **paired independence** (severity: critical; on violation: warn_only)
- **ordinal comparability** (severity: warning; on violation: warn_only)

## Effect size reported

- **proportion** (Proportion of non-tied pairs in the positive direction = n_positive / n_effective; 0.5 indicates no directional tendency.)

## Honest limitations

- The sign test uses only the DIRECTION of each pair's change, not its size; if magnitudes are meaningful, the Wilcoxon signed-rank test is more powerful.
- Tied pairs (no change) are dropped, which lowers the effective sample size and can substantially reduce power.
- With few changing pairs the exact p-value is coarse and may be unable to reach significance at any alpha.
- A significant result indicates a directional tendency in the paired changes; it is not causal unless the pairing arose from random assignment.
- Conclusions concern the median/direction of change, not the mean.

## Primary sources

- Arbuthnott, J. (1710). An argument for Divine Providence, taken from the constant regularity observed in the births of both sexes. Philosophical Transactions, 27, 186-190. https://doi.org/10.1098/rstl.1710.0011
- Conover, W. J. (1999). Practical Nonparametric Statistics (3rd ed.), Ch.3. Wiley.
- Sprent, P., & Smeeton, N. C. (2007). Applied Nonparametric Statistical Methods (4th ed.), Ch.3. Chapman & Hall/CRC.
- Siegel, S., & Castellan, N. J. (1988). Nonparametric Statistics for the Behavioral Sciences (2nd ed.). McGraw-Hill.

## How to cite this

To cite this Clarus method page (the page itself — for the method's own primary sources, see above):

**Plain text**

Clarus, "Sign test (paired)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/sign_test.md

**APA**

Clarus. (2026). Sign test (paired) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/sign_test.md

**BibTeX**

```bibtex
@misc{clarus-sign-test,
  author       = {Clarus},
  title        = {Sign test (paired)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/sign_test.md}
}
```

_No DOI is minted for Clarus method pages yet; this citation uses the canonical URL, version and date. Cite the primary sources above for the method's scientific provenance._

---

METHOD SM.DIF.NPA.2DEP.SIGN · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library