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

# Paired-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:** dependent-samples t-test; repeated-measures t-test; matched-pairs t-test; within-subjects t-test.

## Hypotheses

- **Null (H0):** mu_diff = 0
- **Alternative (H1):** mu_diff != 0

## When to use it

Use this method when your goal is to:
- compare two related measurements
- compare pre post within subjects
- compare matched pairs

## Data it expects

- **dependent:** 1 continuous
- **independent:** 1 within-subject factor/2 levels
- **pairing:** paired

## Assumptions Clarus checks

- **normality of differences** (gate: shapiro_wilk; severity: warning; on violation: reroute)
- **independence of pairs** (severity: design; on violation: warn_only)

## Effect size reported

- **cohen d**: cohen_d_paired = mean(difference) / sd(difference) (Cohen (1988))

## Honest limitations

- This test evaluates the WITHIN-unit change; it says nothing about between-group differences.
- A pre/post change is not causal unless the intervention between measurements was randomly assigned in a controlled design — maturation, history, practice, and regression-to-the-mean can all produce a change.
- With many pairs, a trivially small mean change can be statistically significant — always read Cohen's d and the raw mean difference.
- Assess normality on the paired DIFFERENCES, not on the two raw measurement columns.
- Results generalize only to the sampled population and to the specific interval between the two measurements.

## Primary sources

- Student (1908). The probable error of a mean. Biometrika, 6(1), 1-25. https://doi.org/10.1093/biomet/6.1.1
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Field, A. (2013). Discovering Statistics Using IBM SPSS (4th ed.). Sage. Ch.9.
- Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
- Howell, D. C. (2013). Statistical Methods for Psychology (8th ed.). Wadsworth.

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

**APA**

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

**BibTeX**

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