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 Pearson correlation between the two binary variables. The confidence interval uses the Fisher z-transformation. Standard error formulas follow the DescTools implementations (Signorell et al., 2024); see cramer_v() for full references.

See also

cramer_v(), yule_q(), assoc_measures()

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  0.713