Concordant and Discordant Pairs
This function counts concordant and discordant pairs for two variables x, y with at least ordinal scale, aggregated in a 2way table. This is the base for many association measures like Goodman Kruskal's gamma, but also all tau measures.
ConDisPairs(x)
x |
a 2-dimensional table. The column and the row order must be the logical one. |
The code is so far implemented in R (O(n^2)) and therefore slow for large sample sizes (>5000).
An O(n log(n)) implementation is available as (so far) undocumented function DescTools:::.DoCount(x, y, wts) returning only concorant and discordant pairs (not including standard errors to be used for calculating confidence intervals).
a list with the number of concordant pairs, the number of discordant pairs and the matrix
Andri Signorell <andri@signorell.net>
Agresti, A. (2002) Categorical Data Analysis. John Wiley & Sons, pp. 57-59.
Goodman, L. A., & Kruskal, W. H. (1954) Measures of association for cross classifications. Journal of the American Statistical Association, 49, 732-764.
Goodman, L. A., & Kruskal, W. H. (1963) Measures of association for cross classifications III: Approximate sampling theory. Journal of the American Statistical Association, 58, 310-364.
Association measures: KendallTauA (tau-a), cor (method="kendall") for tau-b, StuartTauC (tau-c), SomersDeltaLambda, GoodmanKruskalTau (tau), UncertCoef, MutInf
tab <- as.table(rbind(c(26,26,23,18,9),c(6,7,9,14,23))) ConDisPairs(tab)
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