Cramer's V

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 confidence interval uses the Fisher z-transformation. Standard error formulas follow the DescTools implementations (Signorell et al., 2024).

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()

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  < 0.001
cramer_v(tab, detail = TRUE, conf_level = NULL)
#> Estimate        p
#>    0.136  < 0.001