---
title: "Intraclass correlation coefficient (ICC)"
method_id: SM.RLB.AGR.RATER.ICC
family: Reliability
version: 1.1.0
date_modified: 2026-06-18
canonical: https://clarus.ofrencber.com/library/intraclass_correlation.md
source: Clarus method library
---

# Intraclass correlation coefficient (ICC)

> A classical statistical method in the Clarus library (Reliability 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:** ICC; interrater reliability; ICC(1,1); ICC(2,1); ICC(3,1); ICC(1,k); ICC(2,k); ICC(3,k); Shrout-Fleiss ICC.

## Hypotheses

- **Null (H0):** ICC = 0 (no consistency beyond chance: between-target variance does not exceed error variance)
- **Alternative (H1):** ICC > 0 (targets account for variance beyond rater error)

## When to use it

Use this method when your goal is to:
- quantify rater agreement
- quantify test retest reliability
- estimate measurement consistency

## Data it expects

- **dependent:** 1 continuous rating
- **structure:** n targets x k raters (long or wide)
- **pairing:** fully crossed (each target rated by every rater) for two-way models

## Assumptions Clarus checks

- **rating continuity** (severity: error; on violation: reroute)
- **residual normality** (gate: shapiro_wilk; severity: warning; on violation: warn_only)
- **fully crossed design** (severity: warning; on violation: reroute)

## Effect size reported

- **icc** (Shrout & Fleiss (1979); Koo & Li (2016))

## Honest limitations

- ICC is meaningless without stating the model (1/2/3) and form (single vs average measures) — the same data yield very different ICCs.
- ICC measures consistency/agreement, not validity: raters can agree and all be wrong.
- Few targets produce very wide confidence intervals; grade reliability on the CI lower bound, not the point estimate.
- Two-way ICCs assume a fully crossed design; with raters that differ across targets use the one-way model (ICC1).
- A negative ICC reflects error exceeding between-target variance and is interpreted as effectively zero reliability.
- Results generalize only to the rater and target population sampled.

## Primary sources

- Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420-428. https://doi.org/10.1037/0033-2909.86.2.420
- McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1(1), 30-46. https://doi.org/10.1037/1082-989X.1.1.30
- Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of Chiropractic Medicine, 15(2), 155-163. https://doi.org/10.1016/j.jcm.2016.02.012
- Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16(3), 297-334. https://doi.org/10.1007/BF02310555

## 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, "Intraclass correlation coefficient (ICC)", version 1.1.0, Clarus method library, 2026. https://clarus.ofrencber.com/library/intraclass_correlation.md

**APA**

Clarus. (2026). Intraclass correlation coefficient (ICC) (Version 1.1.0) [Statistical method, Clarus method library]. Retrieved from https://clarus.ofrencber.com/library/intraclass_correlation.md

**BibTeX**

```bibtex
@misc{clarus-intraclass-correlation,
  author       = {Clarus},
  title        = {Intraclass correlation coefficient (ICC)},
  howpublished = {Clarus method library},
  version      = {1.1.0},
  year         = {2026},
  url          = {https://clarus.ofrencber.com/library/intraclass_correlation.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.RLB.AGR.RATER.ICC · VERSION 1.1.0 · UPDATED 2026-06-18 · SOURCE Clarus method library