---
title: "Kendall's tau rank correlation"
method_id: SM.REL.COR.BIV.KENDALL
family: Relationship
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/kendall_tau.md
source: Clarus method library
---

# Kendall's tau rank correlation

> A classical statistical method in the Clarus library (Relationship 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:** Kendall tau; Kendall's tau-b; Kendall rank correlation coefficient; tau.

## Hypotheses

- **Null (H0):** tau = 0 (the two variables are independent; concordant and discordant pairs are equally likely in the population)
- **Alternative (H1):** tau != 0 (a monotonic association exists; one direction of ordering predominates)

## When to use it

Use this method when your goal is to:
- measure monotonic association between two ordinal or ranked variables
- rank correlation robust to ties and small n

## Data it expects

- **dependent:** not_applicable (symmetric bivariate relationship)
- **independent:** 2 ordinal-or-continuous variables, paired
- **pairing:** paired (each case carries both measures)
- **favorable_when:** ordinal data, many tied ranks, or small n where Spearman's variance approximation is unstable

## Assumptions Clarus checks

- **monotonicity meaningful** (severity: warning; on violation: warn_only)
- **paired observations independent** (severity: critical; on violation: warn_only)

## Effect size reported

- **correlation r** (Derived from Cohen (1988) r-bands via the arcsin bridge tau=(2/pi)*arcsin(r); NOT a Cohen tau threshold (Omer audit D029, ruling b').)

## Honest limitations

- Correlation does NOT imply causation — an unmeasured third variable may drive both rankings.
- Kendall's tau measures only MONOTONIC ordering; a non-monotonic (e.g. U-shaped) relationship can yield tau near 0.
- tau is on a different scale from Pearson/Spearman r and is usually smaller in magnitude for the same data — do not compare the numbers directly.
- With very large n a negligible tau can still be statistically significant.
- No confidence interval and no power/MDE are reported here; absence of significance is not evidence of no association.
- Results generalize only to the sampled population.

## Primary sources

- Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1-2), 81-93. https://doi.org/10.1093/biomet/30.1-2.81
- Kendall, M. G., & Gibbons, J. D. (1990). Rank Correlation Methods (5th ed.). Edward Arnold.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.).
- Field, A. (2013). Discovering Statistics Using IBM SPSS Statistics (4th ed.), Ch.7.

## 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, "Kendall's tau rank correlation", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/kendall_tau.md

**APA**

Clarus. (2026). Kendall's tau rank correlation (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/kendall_tau.md

**BibTeX**

```bibtex
@misc{clarus-kendall-tau,
  author       = {Clarus},
  title        = {Kendall's tau rank correlation},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/kendall_tau.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.REL.COR.BIV.KENDALL · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library