Intraclass correlation coefficient
2025-09-04
Last updated: 2025-09-04
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| Rmd | 1edea74 | Dave Tang | 2025-09-04 | Intraclass correlation coefficient |
Introduction
In statistics, the intraclass correlation, or the intraclass correlation coefficient (ICC), is a descriptive statistic that can be used when quantitative measurements are made on units that are organized into groups. It describes how strongly units in the same group resemble each other. While it is viewed as a type of correlation, unlike most other correlation measures, it operates on data structured as groups rather than data structured as paired observations.
Setup
Install {irr}.
install.packages("irr")Example
The icc() function:
Computes single score or average score ICCs as an index of interrater reliability of quantitative data. Additionally, F-test and confidence interval are computed.
Takes:
ratings- \(n \times m\) matrix or dataframe, \(n\) subjects \(m\) raters.model- a character string specifying if a “oneway” model (default) with row effects random, or a “twoway” model with column and row effects random should be applied. You can specify just the initial letter.type- a character string specifying if “consistency” (default) or “agreement” between raters should be estimated. If a “oneway” model is used, only “consistency” could be computed. You can specify just the initial letter.unit- a character string specifying the unit of analysis: Must be one of “single” (default) or “average”. You can specify just the initial letter.
data(anxiety)
head(anxiety) rater1 rater2 rater3
1 3 3 2
2 3 6 1
3 3 4 4
4 4 6 4
5 5 2 3
6 5 4 2icc(anxiety, model="twoway", type="agreement") Single Score Intraclass Correlation
Model: twoway
Type : agreement
Subjects = 20
Raters = 3
ICC(A,1) = 0.198
F-Test, H0: r0 = 0 ; H1: r0 > 0
F(19,39.7) = 1.83 , p = 0.0543
95%-Confidence Interval for ICC Population Values:
-0.039 < ICC < 0.494Another example from the documentation; high consistency.
set.seed(1984)
r1 <- round(rnorm(20, 10, 4))
r2 <- round(r1 + 10 + rnorm(20, 0, 2))
r3 <- round(r1 + 20 + rnorm(20, 0, 2))
boxplot(data.frame(r1 = r1, r2 = r2, r3 = r3))
icc(cbind(r1, r2, r3), "twoway") Single Score Intraclass Correlation
Model: twoway
Type : consistency
Subjects = 20
Raters = 3
ICC(C,1) = 0.892
F-Test, H0: r0 = 0 ; H1: r0 > 0
F(19,38) = 25.8 , p = 4.25e-16
95%-Confidence Interval for ICC Population Values:
0.789 < ICC < 0.952Low agreement.
icc(cbind(r1, r2, r3), "twoway", "agreement")
sessionInfo()R version 4.5.0 (2025-04-11)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 24.04.2 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.26.so; LAPACK version 3.12.0
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time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] irr_0.84.1 lpSolve_5.6.23 lubridate_1.9.4 forcats_1.0.0
[5] stringr_1.5.1 dplyr_1.1.4 purrr_1.0.4 readr_2.1.5
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