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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).
Somers’ D takes values between when all pairs of the variables disagree and when all pairs of the variables agree. Somers’ D is named after Robert H. Somers, who proposed it in 1962. [1] Somers’ D plays a central role in rank statistics and is the parameter behind many nonparametric methods. [2]
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]
All points in the gray area are concordant and all points in the white area are discordant with respect to point (,). With = points, there are a total of () = possible point pairs. In this example there are 395 concordant point pairs and 40 discordant point pairs, leading to a Kendall rank correlation coefficient of 0.816.
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.
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So, a high value in the numerator means that most pairs are concordant, indicating that the two rankings are consistent. Note that a tied pair is not regarded as concordant or discordant. If there is a large number of ties, the total number of pairs (in the denominator of the expression of ) should be adjusted accordingly."