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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]
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]
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.
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.
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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."