ICC Calculator — Intraclass Correlation Coefficient

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How this is calculated

The ICC framework described by Shrout & Fleiss (1979) applies a one-way random-effects ANOVA to a reliability study where n subjects are each measured k times (or by k raters). The ANOVA partitions total variance into between-subjects variance (captured in MSB — mean square between subjects) and within-subjects variance (MSW — mean square within subjects, also called the error term). When subjects genuinely differ from each other, MSB is large; when measurements are noisy or raters disagree, MSW is large. The ICC is the ratio of true subject variance to total observed variance, bounded between −1 and +1 (though negative values are practically meaningless and indicate anti-agreement).

ICC(1,1) is the single-measurement reliability — the expected correlation between any one rater's score and a latent true score. ICC(1,k) is the reliability of the average of k raters, which is always higher than ICC(1,1) by the Spearman-Brown formula. Select (1,1) if you will use a single rater in practice; select (1,k) if you will always average k raters. Koo & Mae (2016) recommend < 0.5 as poor, 0.5–0.75 moderate, 0.75–0.90 good, > 0.90 excellent for clinical measurements.

The Standard Error of Measurement (SEM = √MSW) quantifies the typical measurement error in the original unit. The Minimum Detectable Change at 95% confidence (MDC₉₅ = 1.96 × √2 × SEM) is the smallest real-score change distinguishable from measurement error — commonly reported in rehabilitation and physiotherapy research.