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In statistics, a concordant pair is a pair of observations, each on two variables, (X 1,Y 1) and (X 2,Y 2), having the property that = (), where "sgn" refers to whether a number is positive, zero, or negative (its sign).
The concordance correlation coefficient is nearly identical to some of the measures called intra-class correlations.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. [2]
Note that Kendall's tau is symmetric in X and Y, whereas Somers’ D is asymmetric in X and Y. As (,) quantifies the number of pairs with unequal X values, Somers’ D is the difference between the number of concordant and discordant pairs, divided by the number of pairs with X values in the pair being unequal.
The Tau-b statistic, unlike Tau-a, makes adjustments for ties. This Tau-b was first described by Kendall in 1945 under the name Tau-w [12] as an extension of the original Tau statistic supporting ties. Values of Tau-b range from −1 (100% negative association, or perfect disagreement) to +1 (100% positive association, or perfect agreement).
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In statistics, Goodman and Kruskal's gamma is a measure of rank correlation, i.e., the similarity of the orderings of the data when ranked by each of the quantities.It measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level.