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% File src/library/stats/man/chisq.test.Rd
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% File src/library/stats/man/chisq.test.Rd
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% Part of the R package, https://www.R-project.org
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2022 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{chisq.test}
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\name{chisq.test}
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\alias{chisq.test}
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\alias{chisq.test}
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\concept{goodness-of-fit}
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\concept{goodness-of-fit}
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  If \code{simulate.p.value} is \code{FALSE}, the p-value is computed
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  If \code{simulate.p.value} is \code{FALSE}, the p-value is computed
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  from the asymptotic chi-squared distribution of the test statistic;
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  from the asymptotic chi-squared distribution of the test statistic;
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  continuity correction is only used in the 2-by-2 case (if \code{correct}
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  continuity correction is only used in the 2-by-2 case (if \code{correct}
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  is \code{TRUE}, the default).  Otherwise the p-value is computed for a
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  is \code{TRUE}, the default).  Otherwise the p-value is computed for a
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  Monte Carlo test (Hope, 1968) with \code{B} replicates. The default
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  Monte Carlo test \bibcitep{R:Hope:1968} with \code{B} replicates. The default
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  \code{B = 2000} implies a minimum p-value of about 0.0005 (\eqn{1/(B+1)}).
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  \code{B = 2000} implies a minimum p-value of about 0.0005 (\eqn{1/(B+1)}).
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  In the contingency table case, simulation is done by random sampling
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  In the contingency table case, simulation is done by random sampling
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  from the set of all contingency tables with given marginals, and works
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  from the set of all contingency tables with given marginals, and works
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  only if the marginals are strictly positive.  Continuity correction is
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  only if the marginals are strictly positive.  Continuity correction is
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  \item{expected}{the expected counts under the null hypothesis.}
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  \item{expected}{the expected counts under the null hypothesis.}
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  \item{residuals}{the Pearson residuals,
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  \item{residuals}{the Pearson residuals,
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    \code{(observed - expected) / sqrt(expected)}.}
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    \code{(observed - expected) / sqrt(expected)}.}
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  \item{stdres}{standardized residuals,
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  \item{stdres}{standardized residuals,
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    \code{(observed - expected) / sqrt(V)}, where \code{V} is the
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    \code{(observed - expected) / sqrt(V)}, where \code{V} is the
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    residual cell variance (\bibcite{Agresti, 2007, section 2.4.5}
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    residual cell variance \bibcitep{|R:Agresti:2007|section 2.4.5}
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    for the case where \code{x} is a matrix, \code{n * p * (1 - p)} otherwise).}
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    for the case where \code{x} is a matrix, \code{n * p * (1 - p)} otherwise).}
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}
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}
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\seealso{
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\seealso{
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  For goodness-of-fit testing, notably of continuous distributions,
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  For goodness-of-fit testing, notably of continuous distributions,
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  \code{\link{ks.test}}.
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  \code{\link{ks.test}}.
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}
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}
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\source{
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\source{
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  The code for Monte Carlo simulation is a C translation of the Fortran
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  The code for Monte Carlo simulation is a C translation of the Fortran
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  algorithm of Patefield (1981).
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  algorithm of \bibcitet{R:Patefield:1981}.
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}
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}
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\references{
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\references{
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  Hope, A. C. A. (1968).
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  A simplified Monte Carlo significance test procedure.
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  \emph{Journal of the Royal Statistical Society Series B}, \bold{30},
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  582--598.
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  \doi{10.1111/j.2517-6161.1968.tb00759.x}.
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  %% \url{https://www.jstor.org/stable/2984263}.
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  Patefield, W. M. (1981).
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  Algorithm AS 159: An efficient method of generating r x c tables
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  with given row and column totals.
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  \emph{Applied Statistics}, \bold{30}, 91--97.
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  \bibinfo{R:Agresti:2007}{footer}{Page 38.}
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  \doi{10.2307/2346669}.
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  Agresti, A. (2007).
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  \emph{An Introduction to Categorical Data Analysis}, 2nd ed.
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  New York: John Wiley & Sons.
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  Page 38.
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  \bibshow{*}
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}
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}
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\examples{
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\examples{
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## From Agresti(2007) p.39
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## From Agresti(2007) p.39
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M <- as.table(rbind(c(762, 327, 468), c(484, 239, 477)))
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M <- as.table(rbind(c(762, 327, 468), c(484, 239, 477)))