\name{chisq.test}
\alias{chisq.test}
\title{Pearson's Chi-squared Test for Count Data}
\description{
  \code{chisq.test} performs chi-squared tests on contingency tables.
}
\usage{
chisq.test(x, y = NULL, correct = TRUE,
           p = rep(1/length(x), length(x)),
           simulate.p.value = FALSE, B = 2000)
}
\arguments{
  \item{x}{a vector or matrix.}
  \item{y}{a vector; ignored if \code{x} is a matrix.}
  \item{correct}{a logical indicating whether to apply continuity
    correction when computing the test statistic.}
  \item{p}{a vector of probabilities of the same length of \code{x}.}
  \item{simulate.p.value}{a logical indicating whether to compute
    p-values by Monte Carlo simulation.}
  \item{B}{an integer specifying the number of replicates used in the
    Monte Carlo simulation.}
}
\details{
  If \code{x} is a matrix with one row or column, or if \code{x} is a
  vector and \code{y} is not given, \code{x} is treated as a
  one-dimensional contingency table.  In this case, the hypothesis
  tested is whether the population probabilities equal those in
  \code{p}, or are all equal if \code{p} is not given.

  If \code{x} is a matrix with at least two rows and columns, it is
  taken as a two-dimensional contingency table, and hence its entries
  should be nonnegative integers.  Otherwise, \code{x} and \code{y} must
  be vectors or factors of the same length; incomplete cases are
  removed, the objects are coerced into factor objects, and the
  contingency table is computed from these.  Then, Pearson's chi-squared
  test of the null that the joint distribution of the cell counts in a
  2-dimensional contingency table is the product of the row and column
  marginals is performed.  If \code{simulate.p.value} is \code{FALSE},
  the p-value is computed from the asymptotic chi-squared distribution
  of the test statistic; continuity correction is only used in the
  2-by-2 case if \code{correct} is \code{TRUE}.  Otherwise, if
  \code{simulate.p.value} is \code{TRUE}, the p-value is computed by
  Monte Carlo simulation with \code{B} replicates.  This is done by
  random sampling from the set of all contingency tables with given
  marginals, and works only if the marginals are positive.  (A C
  translation of the algorithm of Patefield (1981) is used.)
}
\value{
  A list with class \code{"htest"} containing the following
  components:
  \item{statistic}{the value the chi-squared test statistic.}
  \item{parameter}{the degrees of freedom of the approximate
    chi-squared distribution of the test statistic, \code{NA} if the
    p-value is computed by Monte Carlo simulation.}
  \item{p.value}{the p-value for the test.}
  \item{method}{a character string indicating the type of test
    performed, and whether Monte Carlo simulation or continuity
    correction was used.}
  \item{data.name}{a character string giving the name(s) of the data.}
  \item{observed}{the observed counts.}
  \item{expected}{the expected counts under the null hypothesis.}
  \item{residuals}{the Pearson residuals, \code{(observed - expected)
      / sqrt(expected)}.}
}
\references{
  Patefield, W. M. (1981)
  Algorithm AS159.  An efficient method of generating r x c tables
  with given row and column totals.
  \emph{Applied Statistics} \bold{30}, 91--97.
} 
\examples{
data(InsectSprays)              # Not really a good example
chisq.test(InsectSprays$count > 7, InsectSprays$spray)
                                # Prints test summary
chisq.test(InsectSprays$count > 7, InsectSprays$spray)$obs
                                # Counts observed
chisq.test(InsectSprays$count > 7, InsectSprays$spray)$exp
                                # Counts expected under the null

## Effect of simulating p-values
x <- matrix(c(12, 5, 7, 7), nc = 2)
chisq.test(x)$p.value           # 0.4233
chisq.test(x, simulate.p.value = TRUE, B = 10000)$p.value
                                # around 0.29!

## Testing for population probabilities
## Case A. Tabulated data
x <- c(A = 20, B = 15, C = 25)
chisq.test(x)
chisq.test(as.table(x))		# the same
## Case B. Raw data
x <- trunc(5 * runif(100))
chisq.test(table(x))            # NOT 'chisq.test(x)'!
}
\keyword{htest}
\keyword{distribution}
