Phi coefficient

phi() computes the phi coefficient for a 2x2 contingency table.

Usage

phi(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

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).

Details

The phi coefficient is \(\phi = \sqrt{\chi^2 / n}\). It is equivalent to Cramer's V for 2x2 tables and equals the absolute value of the Pearson correlation between the two binary variables – spicy returns only the magnitude (always non-negative), matching the DescTools (Signorell et al., 2024) and SPSS conventions. To recover the signed direction of the 2x2 association, compute the Pearson correlation directly (e.g. cor(x, y) after coding both variables 0/1).

The confidence interval uses the Fisher z-transformation on \(\phi\); see cramer_v() for the formula and full references.

See also

cramer_v(), yule_q(), assoc_measures()

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

Examples

tab <- table(sochealth$smoking, sochealth$sex)
phi(tab)
#> [1] 0.0107495
phi(tab, detail = TRUE)
#> Estimate  CI lower  CI upper     p
#>    0.011     0.000     0.068  .713