Intraclass Correlation Coefficient (ICC) Calculator

This calculator computes the Intraclass Correlation Coefficient (ICC), a measure of reliability or agreement for continuous measurements. ICC is commonly used to assess inter-rater reliability, test-retest reliability, and measurement consistency.

Enter ANOVA summary statistics

Enter the Mean Square Between (MSB) and Mean Square Within (MSW) from a one-way or two-way ANOVA. These values can be obtained from statistical software output.

Mean Square Between (MSB) Between-subjects variance
Mean Square Within (MSW) Within-subjects variance (error)
Number of Raters/Measurements (k) How many raters or repeated measurements
Number of Subjects (n) Number of subjects or items rated

Formula

ICC(2,1) — Two-Way Random Effects, Single Measures

\( ICC = \frac{MS_B - MS_W}{MS_B + (k-1) \cdot MS_W} \)

where \( MS_B \) is the mean square between subjects, \( MS_W \) is the mean square within subjects, and \( k \) is the number of raters.

Interpreting ICC Values

Based on Koo & Li (2016) guidelines:

  • ICC < 0.50 — Poor reliability
  • 0.50 ≤ ICC < 0.75 — Moderate reliability
  • 0.75 ≤ ICC < 0.90 — Good reliability
  • ICC ≥ 0.90 — Excellent reliability

Always report the 95% confidence interval alongside the point estimate.

Types of ICC

There are multiple forms of ICC depending on the study design:

  • ICC(1,1) — One-way random effects, single measures
  • ICC(2,1) — Two-way random effects, single measures, absolute agreement (most common)
  • ICC(3,1) — Two-way mixed effects, single measures, consistency
  • ICC(2,k) — Two-way random effects, average measures

Choose the appropriate form based on whether raters are fixed or random, and whether you need absolute agreement or consistency.

When to Use ICC

ICC is appropriate for:

  • Continuous or ordinal measurements with multiple levels
  • Assessing reliability between two or more raters
  • Test-retest reliability studies
  • Comparing measurement methods

For categorical data, use Cohen's kappa instead.

Assumptions & Limitations

  • Assumes normally distributed data
  • Sensitive to range restriction (low variability reduces ICC)
  • Requires balanced designs (same number of raters per subject)
  • Confidence intervals require F-distribution assumptions
  • Different ICC forms can give different results for the same data

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