\Header{chisq.test}{Pearson's Chi-squared Test for Count Data}
\keyword{htest}{chisq.test}
\keyword{distribution}{chisq.test}
\begin{Description}\relax
\code{chisq.test} performs chi-squared tests on contingency tables.
\end{Description}
\begin{Usage}
\begin{verbatim}
chisq.test(x, y = NULL, correct = TRUE,
           p = rep(1/length(x), length(x)),
           simulate.p.value = FALSE, B = 2000)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x}] a vector or matrix.
\item[\code{y}] a vector; ignored if \code{x} is a matrix.
\item[\code{correct}] a logical indicating whether to apply continuity
correction when computing the test statistic.
\item[\code{p}] a vector of probabilities of the same length of \code{x}.
\item[\code{simulate.p.value}] a logical indicating whether to compute
p-values by Monte Carlo simulation.
\item[\code{B}] an integer specifying the number of replicates used in the
Monte Carlo simulation.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
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.)
\end{Details}
\begin{Value}
A list with class \code{"htest"} containing the following
components:
\begin{ldescription}
\item[\code{statistic}] the value the chi-squared test statistic.
\item[\code{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[\code{p.value}] the p-value for the test.
\item[\code{method}] a character string indicating the type of test
performed, and whether Monte Carlo simulation or continuity
correction was used.
\item[\code{data.name}] a character string giving the name(s) of the data.
\item[\code{observed}] the observed counts.
\item[\code{expected}] the expected counts under the null hypothesis.
\item[\code{residuals}] the Pearson residuals, \code{(observed - expected)
      / sqrt(expected)}.
\end{ldescription}
\end{Value}
\begin{References}\relax
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.
\end{References}
\begin{Examples}
\begin{ExampleCode}
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)'!
\end{ExampleCode}
\end{Examples}

