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Lawrence Lin has the form of the concordance correlation coefficient 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 different between implementations.
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 differencies between the two correlations, in one case on the third decimal.
- ↑ 1.0 1.1 1.2 Lawrence I-Kuei Lin (March 1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics 45 (1): 255–268.
- ↑ 2.0 2.1 Carol A. E. Nickerson (December 1997). A Note on "A Concordance Correlation Coefficient to Evaluate Reproducibility. Biometrics 53 (4): 1503–1507.
- ↑ Reinhold Müller & Petra Büttner (December 1994). A critical discussion of intraclass correlation coefficients. Statistics in Medicine 13 (23-24): 2465–2476.
- ↑ Klaus Krippendorff (1970). "Bivariate agreement coefficients for reliability of data" E. F. Borgatta Sociological Methodology, 139–150, San Francisco: Jossey-Bass.
- ↑ Lawrence I-Kuei Lin (March 2000). A Note on the Concordance Correlation Coefficient. Biometrics 56: 324–325.
- ↑ Nicholas Lange, Stephen C. Strother, J. R. Anderson, Finn Årup Nielsen, Andrew P. Holmes, Thomas Kolenda, Robert L. Savoy and Lars Kai Hansen (September 1999). Plurality and resemblance in fMRI data analysis. NeuroImage 10 (3 Part 1): 282–303.