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.

## 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>

## 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
#>
```