Intraclass correlation

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. 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. The intraclass correlation is commonly used to quantify the degree to which individuals with a fixed degree of relatedness (e.g. full siblings) resemble each other in terms of a quantitative trait (see heritability). Another prominent application is the assessment of consistency or reproducibility of quantitative measurements made by different observers measuring the same quantity. The earliest work on intraclass correlations focused on the case of paired measurements, and the first intraclass correlation (ICC) statistics to be proposed were modifications of the interclass correlation (Pearson correlation). Consider a data set consisting of N paired data values (xn,1, xn,2), for n = 1, ..., N. The intraclass correlation r originally proposed by Ronald Fisher is