---
title: "Independent-samples t-test"
method_id: SM.DIF.PAR.2IND.TTEST
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/independent_t_test.md
source: Clarus method library
---

# Independent-samples t-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:** Student's t-test; two-sample t-test; unpaired t-test.

## Hypotheses

- **Null (H0):** mu_{g1} = mu_{g2}
- **Alternative (H1):** mu_{g1} != mu_{g2}

## When to use it

Use this method when your goal is to:
- compare two independent groups
- test mean difference between two groups

## Data it expects

- **dependent:** 1 continuous
- **independent:** 1 nominal/2 levels
- **pairing:** independent

## Assumptions Clarus checks

- **normality** (gate: shapiro_wilk; severity: warning; on violation: reroute)
- **variance homogeneity** (gate: levene; severity: warning; on violation: correct)
- **independence** (severity: critical; on violation: warn_only)

## Effect size reported

- **cohen d** (Cohen (1988))

## Honest limitations

- With a large sample, statistical significance can accompany a trivially small difference — always read Cohen's d alongside the p-value.
- A significant difference between groups is not evidence of causation unless participants were randomly assigned to the groups.
- Results generalize only to the population from which the sample was drawn.
- If p >= alpha, this is absence of evidence, not evidence of absence; the confidence interval and minimum detectable effect describe what the study could realistically rule out.

## Primary sources

- Student (1908). The probable error of a mean. Biometrika, 6(1), 1-25. https://doi.org/10.2307/2331554
- Welch, B. L. (1947). The generalization of 'Student's' problem when several different population variances are involved. Biometrika, 34(1-2), 28-35. https://doi.org/10.1093/biomet/34.1-2.28
- Levene, H. (1960). Robust tests for equality of variances. In Contributions to Probability and Statistics (pp. 278-292). Stanford University Press.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Hedges, L. V. (1981). Distribution theory for Glass's estimator of effect size and related estimators. Journal of Educational Statistics, 6(2), 107-128. https://doi.org/10.3102/10769986006002107
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.). Sage.

## 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, "Independent-samples t-test", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/independent_t_test.md

**APA**

Clarus. (2026). Independent-samples t-test (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/independent_t_test.md

**BibTeX**

```bibtex
@misc{clarus-independent-t-test,
  author       = {Clarus},
  title        = {Independent-samples t-test},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/independent_t_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.PAR.2IND.TTEST · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library