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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).
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.
Twins are concordant when both have or both lack a given trait. [ 1 ] The ideal example of concordance is that of identical twins , because the genome is the same, an equivalence that helps in discovering causation via deconfounding , regarding genetic effects versus epigenetic and environmental effects ( nature versus nurture ).
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.
Concordant coastline, in geology, where beds, or layers, of differing rock types form ridges that run parallel to the coast; Concordant pair, in statistics; Concordance (publishing), a list of words used in a body of work, with their immediate contexts
N s, the number of pairs of cases ranked in the same order on both variables (number of concordant pairs), N d, the number of pairs of cases ranked in reversed order on both variables (number of reversed pairs), where "ties" (cases where either of the two variables in the pair are equal) are dropped. Then
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."
For a group of twins in which at least one member of each pair is affected, probandwise concordance is a measure of the proportion of twins who have the illness who have an affected twin and can be calculated with the formula of 2C/(2C+D), in which C is the number of concordant pairs and D is the number of discordant pairs.