% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/assoc.R
\name{phi}
\alias{phi}
\title{Phi coefficient}
\usage{
phi(x, detail = FALSE, conf_level = 0.95, digits = 3L, .include_se = FALSE)
}
\arguments{
\item{x}{A contingency table (of class \code{table}).}

\item{detail}{Logical. If \code{FALSE} (default), return the estimate
as a numeric scalar. If \code{TRUE}, return a named numeric vector
including confidence interval and p-value.}

\item{conf_level}{A number between 0 and 1 giving the confidence
level (default \code{0.95}). Only used when \code{detail = TRUE}. Set
to \code{NULL} to omit the confidence interval.}

\item{digits}{Number of decimal places used when printing the
result (default \code{3}). Only affects the \code{detail = TRUE} output.}

\item{.include_se}{Internal parameter; do not use.}
}
\value{
Same structure as \code{\link[=cramer_v]{cramer_v()}}: a scalar when
\code{detail = FALSE}, a named vector when \code{detail = TRUE}.
The p-value tests the null hypothesis of no association
(Pearson chi-squared test).
}
\description{
\code{phi()} computes the phi coefficient for a 2x2 contingency table.
}
\details{
The phi coefficient is \eqn{\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 \code{\link[=cramer_v]{cramer_v()}} for full references.
}
\examples{
tab <- table(sochealth$smoking, sochealth$sex)
phi(tab)
phi(tab, detail = TRUE)

}
\seealso{
\code{\link[=cramer_v]{cramer_v()}}, \code{\link[=yule_q]{yule_q()}}, \code{\link[=assoc_measures]{assoc_measures()}}
}
