Goodman and Kruskal's tau

The proportional reduction in the error of predicting the column category from the row (tau_col_given_row) and the reverse (Hedderich, Sachs & Reynarowych 2023, eqs 3.9-3.10): tau_C|R = (n sum_ij n_ij^2 / n_i. - sum_j n_.j^2) / (n^2 - sum_j n_.j^2).

Usage

gktau(table)

Arguments

table

An r x c matrix of counts.

Value

Named list: tau_col_given_row, tau_row_given_col, n.

References

Goodman, L. A. & Kruskal, W. H. (1954). JASA 49, 732-764.

Examples

gktau(matrix(c(10, 30, 5, 0, 20, 30, 5, 0, 0), 3, byrow = TRUE))
#> $tau_col_given_row
#> [1] 0.2359963
#> 
#> $tau_row_given_col
#> [1] 0.2800349
#> 
#> $n
#> [1] 100
#>