Skip to main content

INTRACLASS CORRELATION CALCULATOR

Intraclass correlation (ICC) calculator with 95% confidence intervals.

Measure inter-rater or test-retest reliability for numeric ratings. You get all six Shrout and Fleiss ICC forms with confidence intervals and F tests, help choosing the right one, and an APA sentence.

RATINGS

Rows = subjects, columns = raters

SHROUT & FLEISS

For test-retest reliability, put each occasion (time 1, time 2) in its own column.

WHO ARE THE RATERS?
WHAT COUNTS AS AGREEMENT?
WILL YOU USE ONE RATER OR THE AVERAGE?

METHOD

Intraclass correlation: which ICC to use, interpretation, and reporting

Which ICC should I report?

  • Different raters rate each subject → ICC(1)
  • Raters are a random sample and you need the same scores → ICC(2), absolute agreement
  • These are the only raters you care about → ICC(3); choose consistency if only the ranking matters
  • Use the ',1' single-rater form if one rater will be used in practice, the ',k' form if you will use the average
  • Test-retest reliability → usually ICC(2,1) absolute agreement

Formulas (two-way ANOVA mean squares)

ICC(2,1) = (MSR − MSE) ÷ [MSR + (k−1)MSE + k(MSC − MSE)/n] ICC(3,1) = (MSR − MSE) ÷ [MSR + (k−1)MSE]

MSR is the between-subjects mean square, MSC the between-raters mean square, MSE the residual, n the number of subjects and k the number of raters.

Worked example (Shrout & Fleiss, 1979)

Four judges rated six targets. ICC(3,1) = .71 (moderate) but ICC(2,1) = .29 (poor): the judges ranked targets similarly but used very different parts of the scale. That is why the choice between consistency and absolute agreement matters.

ICC, Cohen's kappa, or Cronbach's alpha?

  • Numeric ratings from two or more raters → ICC
  • Category ratings from two raters → Cohen's kappa
  • Internal consistency of questionnaire items → Cronbach's alpha (equivalent to ICC(3,k) consistency)

How to report it (APA style)

“Inter-rater reliability was assessed with a two-way random-effects, absolute-agreement, single-rater ICC. Reliability was poor, ICC(2,1) = .29, 95% CI [.02, .76].” Koo and Li (2016) recommend naming the model, type, and unit, and reporting the 95% CI.

References

  • Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420–428.
  • McGraw, K. O., & Wong, S. P. (1996). Forming inferences about some intraclass correlation coefficients. Psychological Methods, 1(1), 30–46.
  • 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.