---
title: "One-sample Wilcoxon signed-rank test"
method_id: SM.DIF.NPA.1SAM.WSR
family: Difference
version: 1.0.0
date_modified: 2026-06-21
canonical: https://clarus.ofrencber.com/library/one_sample_wilcoxon.md
source: Clarus method library
---

# One-sample Wilcoxon signed-rank test

> 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:** single-sample Wilcoxon signed-rank test; Wilcoxon signed-rank test against mu0; one-sample signed-rank test; nonparametric one-sample location test.

## Hypotheses

- **Null (H0):** The distribution of the differences d = {dependent} - mu0 is symmetric about zero (the sample is symmetric about mu0; median of {dependent} = mu0; no systematic shift away from {mu0}).
- **Alternative (H1):** The distribution of the differences d = {dependent} - mu0 is NOT centred at zero (the sample is not symmetric about mu0; the median/location of {dependent} differs from {mu0}).

## When to use it

Use this method when your goal is to:
- compare one median to reference
- test symmetry about a reference value

## Data it expects

- **dependent:** 1 ordinal or continuous (rank-able)
- **independent:** none
- **pairing:** single_sample_vs_constant

## Assumptions Clarus checks

- **symmetry about mu0** (severity: warning; on violation: warn_only)
- **ordinal differences** (severity: critical; on violation: warn_only)
- **independence of observations** (severity: design; on violation: warn_only)

## Effect size reported

- **rank biserial** (Kerby (2014); King, Rosopa & Minium — one-sample rank-biserial r_rb = (W_plus - W_minus) / sum_of_ranks (equivalently 1 - 2T/[n(n+1)/2]), computed on the differences d = value - mu0.)

## Honest limitations

- This test evaluates whether a single sample is symmetric about (its median equals) the reference value mu0; it says nothing about between-group differences.
- Observations equal to mu0 are dropped, which lowers the effective sample size — report how many observations actually contributed.
- If the differences from mu0 are markedly asymmetric, the result reflects a shift in the whole distribution (stochastic dominance) relative to mu0, not specifically a median change.
- With very few non-zero observations the exact test cannot reach significance even for a large effect, so a non-significant p-value is inconclusive rather than evidence that the median equals mu0.
- A one-sample signed-rank test is observational; a difference from the reference value cannot support a causal claim.
- Results generalize only to the population from which the sample was drawn, and assume mu0 is meaningful on the same scale.

## Primary sources

- Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83. https://doi.org/10.2307/3001968
- Kerby, D. S. (2014). The simple difference formula: An approach to teaching nonparametric correlation. Comprehensive Psychology, 3, 11.IT.3.1. https://doi.org/10.2466/11.IT.3.1
- Hollander, M., Wolfe, D. A., & Chicken, E. (2014). Nonparametric Statistical Methods (3rd ed.). Wiley.
- Field, A. (2013). Discovering Statistics Using IBM SPSS (4th ed.). Sage. Ch.6.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum. (r effect-size bands.)

## 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, "One-sample Wilcoxon signed-rank test", version 1.0.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/one_sample_wilcoxon.md

**APA**

Clarus. (2026). One-sample Wilcoxon signed-rank test (Version 1.0.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/one_sample_wilcoxon.md

**BibTeX**

```bibtex
@misc{clarus-one-sample-wilcoxon,
  author       = {Clarus},
  title        = {One-sample Wilcoxon signed-rank test},
  howpublished = {Clarus method library},
  version      = {1.0.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/one_sample_wilcoxon.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.1SAM.WSR · VERSION 1.0.0 · UPDATED 2026-06-21 · SOURCE Clarus method library