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In [[statistics]], a ''' concordant pair''' is a pair of a two-variable ([[Multivariate_statistics|bivariate]]) observation data-set {'''X'''<sub>''1''</sub>,'''Y'''<sub>''1''</sub>} and {'''X'''<sub>''2''</sub>,'''Y'''<sub>''2''</sub>}, where: | |||
:<math> \sgn (X_2 - X_1)\ = \sgn (Y_2 - Y_1)\ </math> | |||
Correspondingly, a ''' discordant pair''' is a pair, as defined above, where | |||
:<math> \sgn (X_2 - X_1)\ = - \sgn (Y_2 - Y_1)\ </math> | |||
and the [[sign function]], often represented as '''sgn''', is defined as: | |||
:<math> \sgn x = \left\{ \begin{matrix} | |||
-1 & : & x < 0 \\ | |||
0 & : & x = 0 \\ | |||
1 & : & x > 0 \end{matrix} \right. </math> | |||
==See also== | |||
* [[Kendall tau distance]] | |||
* [[Spearman's rank correlation coefficient]] | |||
* [[Rank correlation]] | |||
* [[sign function]] | |||
==References== | |||
*[http://www.utdallas.edu/~herve/Abdi-KendallCorrelation2007-pretty.pdf Kendall rank correlation.] | |||
* Kendall, M. (1948) ''Rank Correlation Methods'', Charles Griffin & Company Limited | |||
* Kendall, M. (1938) "A New Measure of Rank Correlation", Biometrica, 30, 81-89. | |||
==External links== | |||
* [http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Kendall.html MacTutor: David George Kendall] | |||
* [http://janus.lib.cam.ac.uk/db/node.xsp?id=EAD%2FGBR%2F0014%2FKNDL Janus: The Papers of Professor David Kendall] | |||
[[Category:Non-parametric statistics]] | |||
[[Category:Statistical terminology]] | |||
Revision as of 00:16, 29 October 2013
In statistics, a concordant pair is a pair of a two-variable (bivariate) observation data-set {X1,Y1} and {X2,Y2}, where:
Correspondingly, a discordant pair is a pair, as defined above, where
and the sign function, often represented as sgn, is defined as:
See also
References
- Kendall rank correlation.
- Kendall, M. (1948) Rank Correlation Methods, Charles Griffin & Company Limited
- Kendall, M. (1938) "A New Measure of Rank Correlation", Biometrica, 30, 81-89.