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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]
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.
The analysis is conducted on pairs, defined as a member of one group compared to a member of the other group. For example, the fastest runner in the study is a member of four pairs: (1,5), (1,7), (1,8), and (1,9). All four of these pairs support the hypothesis, because in each pair the runner from Group A is faster than the runner from Group B.
With <math>n=30<\math> points, there are a total of <math>\binom{30}{2} = 435<\math> 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.
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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.
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