Intraclass Correlation
The intraclass correlation (or the intraclass correlation coefficient, abbreviated 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. Another prominent application is the assessment of consistency or reproducibility of quantitative measurements made by different observers measuring the same quantity.
The intraclass correlation can be regarded within the framework of analysis of variance (ANOVA), and more recently it has been regarded in the framework of a random effect model. Most of the estimators can be defined in terms of the random effects model in:
where
Relationship to Pearson's Correlation Coefficient
One key difference between the two statistics is that in the ICC, the data are centered and scaled using a pooled mean and standard deviation; whereas in the Pearson correlation, each variable is centered and scaled by its own mean and standard deviation. This pooled scaling for the ICC makes sense because all measurements are of the same quantity (albeit on units in different groups). For example, in a paired data set where each "pair" is a single measurement made for each of two units (e.g., weighing each twin in a pair of identical twins) rather than two different measurements for a single unit (e.g., measuring height and weight for each individual), the ICC is a more natural measure of association than Pearson's correlation.
An important property of the Pearson correlation is that it is invariant to application of separate linear transformations to the two variables being compared. Thus, if we are correlating
Concordance Correlation Coefficient
The concordance correlation coefficient measures the agreement between two variables (e.g., to evaluate reproducibility or for inter-rater reliability). The formula is written as:
where
Relation to Other Measures of Correlation
Whereas Pearson's correlation coefficient is immune to whether the biased or unbiased version for estimation of the variance is used, the concordance correlation coefficient is not.
The concordance correlation coefficient is nearly identical to some of the measures called intraclass correlations. Comparisons of the concordance correlation coefficient with an "ordinary" intraclass correlation on different data sets will find only small differences between the two correlations.