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Kendall's Tau-c (Stuart's Tau-c)

Source: R/assoc.R
kendall_tau_c.Rd

kendall_tau_c() computes Stuart's Tau-c (also known as Kendall's Tau-c) for a two-way contingency table of ordinal variables.

Usage

kendall_tau_c(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: tau-c = 0 (Wald z-test).

Details

Stuart's Tau-c is computed as \(\tau_c = 2m(C - D) / (n^2(m - 1))\), where \(m = \min(r, c)\). It is designed for rectangular tables; the estimate is bounded by \([-1, 1]\) only when the table is square, and may fall outside that range otherwise. 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. When one variable is constant (all observations in a single row or column), there are no untied pairs and the statistic degenerates to a meaningless 0: the function returns NA with a spicy_undefined_stat warning, like its siblings, matching the SPSS / PSPP behavior of reporting no value. Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

References

Stuart, A. (1953). The estimation and comparison of strengths of association in contingency tables. Biometrika, 40(1-2), 105-110. doi:10.2307/2333101

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

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

Examples

tab <- table(sochealth$education, sochealth$self_rated_health)
kendall_tau_c(tab)
#> [1] 0.1996409