Goodman-Kruskal Gamma

gamma_gk() computes the Goodman-Kruskal Gamma statistic for a two-way contingency table of ordinal variables.

Usage

gamma_gk(
  x,
  detail = FALSE,
  conf_level = 0.95,
  digits = 3L,
  .include_se = FALSE
)

Arguments

x

A contingency table (of class table).

detail

Logical. If FALSE (default), return the estimate as a numeric scalar. If TRUE, return a named numeric vector including confidence interval and p-value.

conf_level

A number between 0 and 1 giving the confidence level (default 0.95). Only used when detail = TRUE. Set to NULL to omit the confidence interval.

digits

Number of decimal places used when printing the result (default 3). Only affects the detail = TRUE output.

.include_se

Internal parameter; do not use.

Value

Same structure as cramer_v(): a scalar when detail = FALSE, a named vector when detail = TRUE. The p-value tests H0: gamma = 0 (Wald z-test).

Details

Gamma is computed as \(\gamma = (C - D) / (C + D)\), where \(C\) and \(D\) are the numbers of concordant and discordant pairs. It ignores tied pairs, making it appropriate for ordinal variables with many ties. Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

See also

kendall_tau_b(), kendall_tau_c(), somers_d(), assoc_measures()

Examples

tab <- table(sochealth$education, sochealth$self_rated_health)
gamma_gk(tab)
#> [1] 0.3104791
gamma_gk(tab, detail = TRUE)
#> Estimate  CI lower  CI upper        p
#>    0.310     0.238     0.383  < 0.001