Goodman-Kruskal Gamma from a Contingency Table

Computes the Goodman-Kruskal gamma coefficient for an ordinal contingency table. This is an internal helper function.

Usage

gk_gamma(tab)

Arguments

tab

A matrix or table representing a contingency table with rows and columns in ordinal order.

Value

A scalar: the gamma coefficient in \([-1, 1]\).

Details

Gamma is defined as \((C - D) / (C + D)\), where \(C\) is the number of concordant pairs and \(D\) is the number of discordant pairs. Uses cumulative suffix sums for \(O(nr \times nc)\) complexity.

References

Goodman, L. A. & Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49(268), 732–764.