% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/chi2.stat.R
\name{chi2.stat}
\alias{chi2.stat}
\title{Chi-squared test statistic for contingency tables}
\usage{
chi2.stat(tab)
}
\arguments{
\item{tab}{A \code{K x C} matrix (contingency table) of counts. See details.}
}
\value{
The calculated value of the chi-squared statistic.
}
\description{
Calculates the chi-squared test statistic for a two-way contingency table.
}
\details{
Suppose that \code{tab} consists of counts from \eqn{K} populations (rows) in \eqn{C} categories.  The chi-squared test statistic is computed as
\deqn{
  \sum_{i=1}^K \sum_{j=1}^C (E_{ij} - O_{ij})^2/E_{ij},
}{
  \sum_ij (E_ij - O_ij)^2/E_ij,
}
where \eqn{O_{ij}}{O_ij} is the observed number of counts in the \eqn{i}th row and \eqn{j}th column of \code{tab}, and \eqn{E_{ij}}{E_ij} is the expected number of counts under \eqn{H_0} that the populations have indentical proportions in each category:
\deqn{
  E_{ij} = \frac 1 N \sum_{i=1}^K O_{ij} \times \sum_{j=1}^C O_{ij}.
}{
  E_ij = \sum_i O_ij * \sum_j O_ij / N,
}
where \eqn{N} is the total number of counts in \code{tab}.
}
\examples{
# simple contingency table
ctab <- rbind(pop1 = c(5, 3, 0, 3),
                pop2 = c(4, 10, 2, 5))
colnames(ctab) <- LETTERS[1:4]
ctab
chi2.stat(ctab) # chi^2 test statistic
}