In statistics, the concordance correlation coefficient measures the agreement between two variables, e.g., to evaluate reproducibility or for inter-rater reliability.

Definition

as

are the means are the corresponding variances is Pearson's correlation coefficient between the two variables.

This follows from its definition, as:

), the form is

where the mean is computed as

and the variance

and the covariance

Whereas the ordinary correlation coefficient normalization,, i.e., the concordance correlation coefficient may be computed slightly differently between implementations.

Relation to other measures of correlation

The concordance correlation coefficient is nearly identical to some of the measures called intra-class correlations. Comparisons of the concordance correlation coefficient with an "ordinary" intraclass correlation on different data sets found only small differences between the two correlations, in one case on the third decimal. It has also been stated that the ideas for concordance correlation coefficient "are quite similar to results already published by Krippendorff in 1970".

In the original article Lin suggested a form for multiple classes (not just 2). Over ten years later a correction to this form was issued.

One example of the use of the concordance correlation coefficient is in a comparison of analysis method for functional magnetic resonance imaging brain scans.

References

For a small Excel and VBA implementation by Peter Urbani see here