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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]
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence
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]
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."
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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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.