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

The form of the concordance correlation coefficient ${\displaystyle \rho _{c}}$ as

where ${\displaystyle \mu _{x}}$ and ${\displaystyle \mu _{y}}$ are the means for the two variables and ${\displaystyle \sigma _{x}^{2}}$ and ${\displaystyle \sigma _{y}^{2}}$ are the corresponding variances. ${\displaystyle \rho }$ is the Pearson's correlation coefficient between the two variables.

This follows from its definition as

When the concordance correlation coefficient is computed on a ${\displaystyle N}$-length data set (i.e., ${\displaystyle N}$ paired data values ${\displaystyle (x_{n},y_{n})}$, for ${\displaystyle n=1,...,N}$), the form is

where the mean is computed as

and the variance

and the covariance