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Cramer's V

Source: R/assoc.R
cramer_v.Rd

cramer_v() computes Cramer's V for a two-way contingency table, measuring the strength of association between two categorical variables.

Usage

cramer_v(
  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

When detail = FALSE: a single numeric value (the estimate). When detail = TRUE and conf_level is non-NULL: c(estimate, ci_lower, ci_upper, p_value). When detail = TRUE and conf_level = NULL: c(estimate, p_value). The p-value tests the null hypothesis of no association (Pearson chi-squared test).

Details

Cramer's V is computed as \(V = \sqrt{\chi^2 / (n \cdot (k - 1))}\), where \(\chi^2\) is the Pearson chi-squared statistic, \(n\) is the total count, and \(k = \min(r, c)\). The point estimate matches the DescTools (Signorell et al., 2024) and SPSS implementations. The confidence interval uses the Fisher z-transformation on \(V\) (\(\tanh(\mathrm{atanh}(V) \pm z_{\alpha/2} / \sqrt{n - 3})\)), which differs from the noncentral chi-squared or bootstrap CIs reported by DescTools::CramerV().

References

Agresti, A. (2002). Categorical Data Analysis (2nd ed.). Wiley.

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

Signorell, A. et al. (2024). DescTools: Tools for Descriptive Statistics. R package.

See also

phi(), contingency_coef(), assoc_measures()

Other association measures: assoc_measures(), contingency_coef(), 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)
cramer_v(tab)
#> [1] 0.1356677
cramer_v(tab, detail = TRUE)
#> Estimate  CI lower  CI upper      p
#>    0.136     0.079     0.191  <.001
cramer_v(tab, detail = TRUE, conf_level = NULL)
#> Estimate      p
#>    0.136  <.001