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Goodman-Kruskal Gamma

Source: R/assoc.R
gamma_gk.Rd

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)

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 single number strictly between 0 and 1 giving the confidence level (default 0.95). Only used when detail = TRUE. Set to NULL to omit the confidence interval. Any other value – including percentages such as 95 – raises a classed error (spicy_invalid_input).

digits

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

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. When the asymptotic standard error is zero (e.g. a perfect association), the Wald z-test is undefined and the p-value is NA, matching the other measures in the family. Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

References

Goodman, L. A., & Kruskal, W. H. (1954). Measures of association for cross classifications. Journal of the American Statistical Association, 49(268), 732-764. doi:10.2307/2281536

Brown, M. B., & Benedetti, J. K. (1977). Sampling behavior of tests for correlation in two-way contingency tables. Journal of the American Statistical Association, 72(358), 309-315. doi:10.1080/01621459.1977.10480995

See also

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

Other association measures: assoc_measures(), contingency_coef(), cramer_v(), goodman_kruskal_tau(), kendall_tau_b(), kendall_tau_c(), lambda_gk(), phi(), somers_d(), uncertainty_coef(), yule_q()

Examples

tab <- table(sochealth$education, sochealth$self_rated_health)
gamma_gk(tab)
#> [1] 0.3104791
gamma_gk(tab, detail = TRUE)
#> Estimate     SE  CI lower  CI upper      p
#>    0.310  0.037     0.238     0.383  <.001