Kendall's Tau-b

kendall_tau_b() computes Kendall's Tau-b for a two-way contingency table of ordinal variables.

Usage

kendall_tau_b(
  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: tau-b = 0 (Wald z-test).

Details

Kendall's Tau-b is computed as \(\tau_b = (C - D) / \sqrt{(n_0 - n_1)(n_0 - n_2)}\), where \(n_0 = n(n-1)/2\), \(n_1\) is the number of pairs tied on the row variable, and \(n_2\) is the number tied on the column variable. Tau-b corrects for ties and is appropriate for square tables. Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

See also

kendall_tau_c(), gamma_gk(), somers_d(), assoc_measures()

Examples

tab <- table(sochealth$education, sochealth$self_rated_health)
kendall_tau_b(tab)
#> [1] 0.2045524