Concordant pair

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In statistics, a concordant pair is a pair of a two-variable (bivariate) observation data-set X₁,Y₁} and {X₂,Y₂}, where:

$\operatorname {sgn}(X_{2}-X_{1})\ =\operatorname {sgn}(Y_{2}-Y_{1})\$

Correspondingly, a discordant pair is a pair, as defined above, where

$\operatorname {sgn}(X_{2}-X_{1})\ =-\operatorname {sgn}(Y_{2}-Y_{1})\$

and the sign function, often represented as sgn, is defined as:

$\operatorname {sgn} x=\left\{{\begin{matrix}-1&:&x<0\\0&:&x=0\\1&:&x>0\end{matrix}}\right.$

See also

• Kendall tau distance
• Spearman's rank correlation coefficient
• Rank correlation
• sign function

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.

External links

• MacTutor: David George Kendall
• Janus: The Papers of Professor David Kendall

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