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).
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.
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.