---
title: "Confidence interval for a mean"
method_id: SM.EST.CI.MEAN.CIMEAN
family: Estimation
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/confidence_interval_mean.md
source: Clarus method library
---

# Confidence interval for a mean

> 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:** t-interval for the mean; confidence interval for the population mean; one-sample mean estimate with CI.

## When to use it

Use this method when your goal is to:
- estimate population mean with uncertainty

## Data it expects

- **dependent:** 1 continuous
- **independent:** none
- **pairing:** single_sample

## Assumptions Clarus checks

- **normality or large n** (gate: shapiro_wilk; severity: warning; on violation: warn_only)
- **independence of observations** (severity: warning; on violation: warn_only)

## Honest limitations

- A 95% confidence interval means the procedure captures the true population mean 95% of the time across repeated samples; it does NOT mean there is a 95% probability the true mean lies in THIS specific interval.
- With a small and clearly non-normal sample the interval's real coverage can differ from the stated level; consider a larger sample or a bootstrap/nonparametric interval.
- The interval describes the mean of the population the sample was drawn from; it does not generalize beyond that population and implies no causal claim.
- A wide interval signals an imprecise estimate, not the absence of an effect; narrow it by increasing n (see required_n).

## Primary sources

- Student (1908). The probable error of a mean. Biometrika, 6(1), 1-25. https://doi.org/10.2307/2331554
- Neyman, J. (1937). Outline of a theory of statistical estimation based on the classical theory of probability. Philosophical Transactions of the Royal Society A, 236(767), 333-380. https://doi.org/10.1098/rsta.1937.0005
- Moore, McCabe & Craig (2017). Introduction to the Practice of Statistics (9th ed.). W.H. Freeman, Ch.7.
- Cumming, G. (2014). The New Statistics: Why and How. Psychological Science, 25(1), 7-29. https://doi.org/10.1177/0956797613504966

## 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 mean", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/confidence_interval_mean.md

**APA**

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

**BibTeX**

```bibtex
@misc{clarus-confidence-interval-mean,
  author       = {Clarus},
  title        = {Confidence interval for a mean},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/confidence_interval_mean.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.MEAN.CIMEAN · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library