---
title: "Cochran's Q test"
method_id: SM.DIF.CAT.KDEP.COCHRANQ
family: Difference
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/cochran_q.md
source: Clarus method library
---

# Cochran's Q 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:** Cochran Q; Cochran's Q for related proportions; k-sample extension of McNemar's test.

## Hypotheses

- **Null (H0):** p_1 = p_2 = ... = p_k (the success proportion is equal across all conditions)
- **Alternative (H1):** At least one condition's success proportion differs from the others

## When to use it

Use this method when your goal is to:
- compare proportions across 3plus related conditions
- compare binary outcome repeated measures

## Data it expects

- **dependent:** 1 binary/dichotomous (0/1)
- **independent:** 1 within-subjects factor / 3+ related conditions
- **pairing:** repeated_measures

## Assumptions Clarus checks

- **binary outcome** (severity: error; on violation: reroute)
- **related blocks** (severity: error; on violation: reroute)
- **adequate sample** (gate: expected_frequency; severity: warning; on violation: warn_only)

## Effect size reported

- **kendall w** (Serlin, Marascuilo & Busk (1982) [W definition, NOT a magnitude-band anchor])

## Honest limitations

- Cochran's Q only tells you that the conditions differ somewhere; it does not say which pairs differ — use the Bonferroni-corrected pairwise McNemar follow-ups for that.
- The p-value rests on a chi-square approximation that can be unreliable with few subjects; treat small-sample p-values as approximate.
- Subjects who answered identically across all conditions contribute nothing to the statistic — a dataset dominated by such rows has little power.
- A difference across conditions is not causal unless the conditions were assigned by random assignment within subjects.
- Results generalize only to the sampled population and the specific conditions tested.

## Primary sources

- Cochran, W. G. (1950). The comparison of percentages in matched samples. Biometrika, 37(3-4), 256-266. https://doi.org/10.1093/biomet/37.3-4.256
- Tate, M. W., & Brown, S. M. (1970). Note on the Cochran Q test. Journal of the American Statistical Association, 65(329), 155-160. https://doi.org/10.1080/01621459.1970.10481070
- Sheskin, D. J. (2011). Handbook of Parametric and Nonparametric Statistical Procedures (5th ed.). Chapman & Hall/CRC. (Test 26: Cochran Q).
- Serlin, R. C., Marascuilo, L. A., & Busk, P. L. (1982). Tukey-like contrasts and effect sizes for related binary data. (Kendall's W from Q).

## 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, "Cochran's Q test", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/cochran_q.md

**APA**

Clarus. (2026). Cochran's Q test (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/cochran_q.md

**BibTeX**

```bibtex
@misc{clarus-cochran-q,
  author       = {Clarus},
  title        = {Cochran's Q test},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/cochran_q.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.CAT.KDEP.COCHRANQ · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library