Goodman-Kruskal's Tau

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. 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()

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  0.022