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Intraclass Correlation (ICC) Calculator

Describes how strongly units in the same group resemble each other.

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ICC

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Overview

The Intraclass Correlation (ICC) is a statistical measure used in psychometrics to evaluate the reliability of ratings or measurements within grouped data. It quantifies the proportion of total variance that is explained by the differences between subjects, effectively distinguishing true score variance from measurement error.

Symbols

Variables

ICC = ICC, MS_B = MS Between, MS_W = MS Within, k = Num Raters

ICC
MS Between
MS Within
Num Raters

Apply it well

When To Use

When to use: Apply the ICC when assessing inter-rater reliability among multiple observers or when dealing with clustered data where observations are not independent. It is specifically used for continuous or interval-level data where you must account for both the correlation and the absolute level of agreement between scores.

Why it matters: In clinical psychology and research, high ICC values ensure that diagnostic tools provide consistent results regardless of who administers the test. This reliability is critical for the validity of psychological assessments, as it minimizes the risk of misdiagnosis due to observer bias or measurement noise.

One free problem

Practice Problem

A psychology study measures the anxiety levels of 3 siblings (k = 3) across several families. If the Mean Square Between-groups (msb) is 15.0 and the Mean Square Within-groups (msw) is 5.0, calculate the Intraclass Correlation (icc).

MS Between15
MS Within5
Num Raters3

Solve for:

Hint: Subtract msw from msb for the numerator, then divide by the sum of msb and (k - 1) times msw.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Psychometric Theory by Jum C. Nunnally and Ira H. Bernstein
  2. Applied Psychometrics: The Statistical Foundations of Psychological Measurement by Robert J. Gregory
  3. Wikipedia: Intraclass correlation
  4. Intraclass correlation (Wikipedia article)
  5. Statistical Methods for Rates and Proportions by Joseph L. Fleiss, Bruce Levin, and Myunghee Cho Paik
  6. Shrout, P. E., & Fleiss, J. L. (1979). Intraclass correlations: Uses in assessing rater reliability. Psychological Bulletin, 86(2), 420-428.
  7. Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research.
  8. Streiner, D. L., Norman, G. R., & Cairney, N. (2015). Health Measurement Scales: A Practical Guide to Their Development and Use (5th ed.).