Concordance correlation coefficient
Encyclopedia
In statistics
, the concordance correlation coefficient measures the agreement between two variables, e.g., to evaluate reproducibility
or for inter-rater reliability
.
as
where
and 
are the mean
s for the two variables and
and 
are the corresponding variance
s.
is the correlation coefficient between the two variables.
This follows from its definition as
When the concordance correlation coefficient is computed on a N-length data set (i.e., two vectors of length N) the form is
where the mean is computed as
and the variance
and the covariance
Whereas the ordinary correlation coefficient
(Pearson's) is immune to whether the biased or unbiased versions for estimation of the variance is used, the concordance correlation coefficient is not. In the original article Lin suggested the 1/N normalization,
while in another article Nickerson appears to have used the 1/(N-1),
i.e., the concordance correlation coefficient may be computed slightly differently between implementations.
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.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the concordance correlation coefficient measures the agreement between two variables, e.g., to evaluate reproducibility
Reproducibility
Reproducibility is the ability of an experiment or study to be accurately reproduced, or replicated, by someone else working independently...
or for inter-rater reliability
Inter-rater reliability
In statistics, inter-rater reliability, inter-rater agreement, or concordance is the degree of agreement among raters. It gives a score of how much homogeneity, or consensus, there is in the ratings given by judges. It is useful in refining the tools given to human judges, for example by...
.
Definition
Lawrence Lin has the form of the concordance correlation coefficient aswhere
and are the meanMean
In statistics, mean has two related meanings:* the arithmetic mean .* the expected value of a random variable, which is also called the population mean....
s for the two variables and
and are the corresponding varianceVariance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
s.
is the correlation coefficient between the two variables.This follows from its definition as
When the concordance correlation coefficient is computed on a N-length data set (i.e., two vectors of length N) the form is
where the mean is computed as
and the variance
and the covariance
Whereas the ordinary correlation coefficient
Pearson product-moment correlation coefficient
In statistics, the Pearson product-moment correlation coefficient is a measure of the correlation between two variables X and Y, giving a value between +1 and −1 inclusive...
(Pearson's) is immune to whether the biased or unbiased versions for estimation of the variance is used, the concordance correlation coefficient is not. In the original article Lin suggested the 1/N normalization,
while in another article Nickerson appears to have used the 1/(N-1),
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, and 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 Krippendorffin 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
Functional magnetic resonance imaging
Functional magnetic resonance imaging or functional MRI is a type of specialized MRI scan used to measure the hemodynamic response related to neural activity in the brain or spinal cord of humans or other animals. It is one of the most recently developed forms of neuroimaging...
brain scans.