---
title: "Confidence interval for a proportion (Wilson)"
method_id: SM.EST.CI.PROP.CIPROP
family: Estimation
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/confidence_interval_proportion.md
source: Clarus method library
---

# Confidence interval for a proportion (Wilson)

> A classical statistical method in the Clarus library (Estimation 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:** Wilson score interval; Wilson confidence interval for a binomial proportion; score interval for a rate.

## When to use it

Use this method when your goal is to:
- estimate a single proportion
- report confidence interval for a rate or percentage

## Data it expects

- **dependent:** 1 binary (success/failure)
- **independent:** none
- **pairing:** single_sample

## Assumptions Clarus checks

- **sufficient count** (gate: proportion_normal_approx; severity: info; on violation: warn_only)
- **independent bernoulli trials** (severity: warning; on violation: warn_only)

## Effect size reported

- **proportion** (Wilson (1927))

## Honest limitations

- A confidence interval expresses uncertainty about the population proportion; a single interval either does or does not contain the true value — the confidence level refers to the long-run procedure.
- The interval assumes independent observations from one population; clustered or repeated-measures data make the true interval wider than reported.
- Results generalize only to the population that was actually sampled.
- The Wilson interval is asymmetric near 0% and 100% by design — this is correct behaviour, not an error.

## Primary sources

- Wilson, E. B. (1927). Probable inference, the law of succession, and statistical inference. Journal of the American Statistical Association, 22(158), 209-212. https://doi.org/10.1080/01621459.1927.10502953
- Brown, L. D., Cai, T. T., & DasGupta, A. (2001). Interval estimation for a binomial proportion. Statistical Science, 16(2), 101-133. https://doi.org/10.1214/ss/1009213286
- Agresti, A., & Coull, B. A. (1998). Approximate is better than 'exact' for interval estimation of binomial proportions. The American Statistician, 52(2), 119-126. https://doi.org/10.1080/00031305.1998.10480550
- Agresti, A. (2013). Categorical Data Analysis (3rd ed.). Wiley.

## 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, "Confidence interval for a proportion (Wilson)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/confidence_interval_proportion.md

**APA**

Clarus. (2026). Confidence interval for a proportion (Wilson) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/confidence_interval_proportion.md

**BibTeX**

```bibtex
@misc{clarus-confidence-interval-proportion,
  author       = {Clarus},
  title        = {Confidence interval for a proportion (Wilson)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/confidence_interval_proportion.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.EST.CI.PROP.CIPROP · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library