---
title: "One-proportion z-test"
method_id: SM.DIF.PRP.1SAM.ZPROP
family: Difference
version: 1.2.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/one_proportion_z_test.md
source: Clarus method library
---

# One-proportion z-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-proportion z-test; one-sample proportion test; normal-approximation test for a proportion; z-test for a proportion.

## Hypotheses

- **Null (H0):** p_{dependent} = {p0}
- **Alternative (H1):** p_{dependent} != {p0}

## When to use it

Use this method when your goal is to:
- compare one proportion to reference

## Data it expects

- **dependent:** 1 binary/dichotomous
- **independent:** none
- **pairing:** single_sample_vs_constant

## Assumptions Clarus checks

- **normal approximation validity** (gate: proportion_normal_approx; severity: warning; on violation: reroute)
- **independence of observations** (severity: warning; on violation: warn_only)
- **random sampling** (severity: warning; on violation: warn_only)

## Effect size reported

- **cohen h** (Cohen (1988))

## Honest limitations

- Large n can pair statistical significance with a trivially small departure from p0 — read Cohen's h and the confidence interval.
- A one-proportion z-test is observational; a difference from the reference proportion cannot support a causal claim.
- The normal-approximation z-test is unreliable when n*p0 or n*(1-p0) is below 10; the exact binomial test should be used instead.
- Results generalize only to the population from which the sample was drawn, and assume the reference value p0 is meaningful.
- If p >= alpha, this is absence of evidence for a difference, not evidence that the population proportion equals p0.

## Primary sources

- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum. (Cohen's h, Ch.6).
- Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. JASA, 22(158), 209-212. https://doi.org/10.1080/01621459.1927.10502953
- Agresti, A. (2018). Statistical Methods for the Social Sciences (5th ed.). Pearson, Ch.5.
- Moore, McCabe & Craig (2017). Introduction to the Practice of Statistics (9th ed.). W.H. Freeman, Ch.8.

## 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-proportion z-test", version 1.2.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/one_proportion_z_test.md

**APA**

Clarus. (2026). One-proportion z-test (Version 1.2.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/one_proportion_z_test.md

**BibTeX**

```bibtex
@misc{clarus-one-proportion-z-test,
  author       = {Clarus},
  title        = {One-proportion z-test},
  howpublished = {Clarus method library},
  version      = {1.2.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/one_proportion_z_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.PRP.1SAM.ZPROP · VERSION 1.2.0 · UPDATED 2026-06-18 · SOURCE Clarus method library