Concordant pair

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

$\sgn (X_2 - X_1)\ = \sgn (Y_2 - Y_1)\$

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

$\sgn (X_2 - X_1)\ = - \sgn (Y_2 - Y_1)\$

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

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

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