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Kendall's Tau-b

Source: R/assoc.R
kendall_tau_b.Rd

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)

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-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. 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.

The asymptotic standard error is the Brown and Benedetti (1977) ASE1, as printed by SPSS / PSPP CROSSTABS. It deliberately diverges from DescTools::KendallTauB(), whose implementation mis-scales one margin term of the gradient; see cramer_v() for full references.

References

Kendall, M. G. (1938). A new measure of rank correlation. Biometrika, 30(1-2), 81-93. doi:10.2307/2332226

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

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

Examples

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