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Pearson's contingency coefficient

Source: R/assoc.R
contingency_coef.Rd

contingency_coef() computes Pearson's contingency coefficient C for a two-way contingency table.

Usage

contingency_coef(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 the null hypothesis of no association (Pearson chi-squared test). CI values are NA because no standard asymptotic SE exists for C.

Details

The contingency coefficient is \(C = \sqrt{\chi^2 / (\chi^2 + n)}\). It ranges from 0 (independence) to a maximum that depends on the table dimensions. No standard asymptotic standard error exists, so the confidence interval is not computed.

References

Liebetrau, A. M. (1983). Measures of Association. Sage.

See also

cramer_v(), assoc_measures()

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

Examples

tab <- table(sochealth$smoking, sochealth$education)
contingency_coef(tab)
#> [1] 0.1344361