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)

Arguments

x

a 2-dimensional table. The column and the row order must be the logical one.

Details

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).

Value

a list with the number of concordant pairs, the number of discordant pairs and the matrix

References

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.

Author

Andri Signorell <andri@signorell.net>

See also

Association measures:
KendallTauA (tau-a), cor (method="kendall") for tau-b, StuartTauC (tau-c), SomersDelta
Lambda, GoodmanKruskalTau (tau), UncertCoef, MutInf

Examples

tab <- as.table(rbind(c(26,26,23,18,9),c(6,7,9,14,23)))
ConDisPairs(tab)
#> $pi.c
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]   53   46   37   23    0
#> [2,]    0   26   52   75   93
#> 
#> $pi.d
#>      [,1] [,2] [,3] [,4] [,5]
#> [1,]    0    6   13   22   36
#> [2,]   76   50   27    9    0
#> 
#> $C
#> [1] 3839
#> 
#> $D
#> [1] 1175
#>