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Goodman-Kruskal's Tau

Source: R/assoc.R
goodman_kruskal_tau.Rd

goodman_kruskal_tau() computes Goodman-Kruskal's Tau, a proportional reduction in error (PRE) measure for nominal variables.

Usage

goodman_kruskal_tau(
  x,
  direction = c("row", "column"),
  detail = FALSE,
  conf_level = 0.95,
  digits = 3L,
  .include_se = FALSE
)

Arguments

x

A contingency table (of class table).

direction

Direction of prediction: "row" (default, column predicts row) or "column" (row predicts column).

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: tau = 0 (Wald z-test).

Details

Unlike lambda_gk(), Goodman-Kruskal's Tau uses all cell frequencies rather than only the modal categories, making it more sensitive to association patterns where lambda may be zero. Goodman-Kruskal's Tau is intrinsically directional and has no canonical symmetric form (unlike lambda_gk() or uncertainty_coef()); only "row" and "column" are supported.

Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

See also

lambda_gk(), uncertainty_coef(), assoc_measures()

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

Examples

tab <- table(sochealth$smoking, sochealth$education)
goodman_kruskal_tau(tab)
#> [1] 0.01840572
goodman_kruskal_tau(tab, direction = "column", detail = TRUE)
#> Estimate  CI lower  CI upper     p
#>    0.008     0.001     0.014  .022