desctable/man/chisq.test.Rd

% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/convenience_functions.R
\name{chisq.test}
\alias{chisq.test}
\alias{chisq.test.default}
\alias{chisq.test.formula}
\title{Pearson's Chi-squared Test for Count Data}
\source{
The code for Monte Carlo simulation is a C translation of the Fortran algorithm of Patefield (1981).
}
\usage{
chisq.test(x, y, correct, p, rescale.p, simulate.p.value, B)

\method{chisq.test}{default}(x, y = NULL, correct = TRUE,
  p = rep(1/length(x), length(x)), rescale.p = FALSE,
  simulate.p.value = FALSE, B = 2000)

\method{chisq.test}{formula}(x, y = NULL, correct = T,
  p = rep(1/length(x), length(x)), rescale.p = F,
  simulate.p.value = F, B = 2000)
}
\arguments{
\item{x}{a numeric vector, or matrix, or formula of the form \code{lhs ~ rhs} where \code{lhs} and \code{rhs} are factors. \code{x} and \code{y} can also both be factors.}

\item{y}{a numeric vector; ignored if \code{x} is a matrix or a formula. If \code{x} is a factor, \code{y} should be a factor of the same length.}

\item{correct}{a logical indicating whether to apply continuity
    correction when computing the test statistic for 2 by 2 tables: one
    half is subtracted from all \eqn{|O - E|} differences; however, the
    correction will not be bigger than the differences themselves.  No correction
    is done if \code{simulate.p.value = TRUE}.}

\item{p}{a vector of probabilities of the same length of \code{x}.
    An error is given if any entry of \code{p} is negative.}

\item{rescale.p}{a logical scalar; if TRUE then \code{p} is rescaled
    (if necessary) to sum to 1.  If \code{rescale.p} is FALSE, and
    \code{p} does not sum to 1, an error is given.}

\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 test.}
}
\value{
A list with class \code{"htest"} containing the following components:
statistic: the value the chi-squared test statistic.

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.

 p.value: the p-value for the test.

  method: a character string indicating the type of test performed, and
          whether Monte Carlo simulation or continuity correction was
          used.

data.name: a character string giving the name(s) of the data.

observed: the observed counts.

expected: the expected counts under the null hypothesis.

residuals: the Pearson residuals, ‘(observed - expected) /
          sqrt(expected)’.

  stdres: standardized residuals, \code{(observed - expected) / sqrt(V)},
          where \code{V} is the residual cell variance (Agresti, 2007,
          section 2.4.5 for the case where \code{x} is a matrix, ‘n * p * (1
          - p)’ otherwise).
}
\description{
\code{chisq.test} performs chi-squared contingency table tests and goodness-of-fit tests, with an added method for formulas.
}
\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, then a _goodness-of-fit test_ is performed
(\code{x} is treated as a one-dimensional contingency table).  The
entries of \code{x} must be non-negative integers.  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: the entries of \code{x} must be
non-negative integers.  Otherwise, \code{x} and \code{y} must be vectors or
factors of the same length; cases with missing values are removed,
the objects are coerced to factors, and the contingency table is
computed from these.  Then Pearson's chi-squared test is performed
of the null hypothesis that the joint distribution of the cell
counts in a 2-dimensional contingency table is the product of the
row and column marginals.

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}, the default).  Otherwise the p-value is
computed for a Monte Carlo test (Hope, 1968) with \code{B} replicates.

In the contingency table case simulation is done by random
sampling from the set of all contingency tables with given
marginals, and works only if the marginals are strictly positive.
Continuity correction is never used, and the statistic is quoted
without it.  Note that this is not the usual sampling situation
assumed for the chi-squared test but rather that for Fisher's
exact test.

In the goodness-of-fit case simulation is done by random sampling
from the discrete distribution specified by \code{p}, each sample being
of size \code{n = sum(x)}.  This simulation is done in R and may be
slow.
}
\examples{
\dontrun{
## From Agresti(2007) p.39
M <- as.table(rbind(c(762, 327, 468), c(484, 239, 477)))
dimnames(M) <- list(gender = c("F", "M"),
                    party = c("Democrat","Independent", "Republican"))
(Xsq <- chisq.test(M))  # Prints test summary
Xsq$observed   # observed counts (same as M)
Xsq$expected   # expected counts under the null
Xsq$residuals  # Pearson residuals
Xsq$stdres     # standardized residuals


## Effect of simulating p-values
x <- matrix(c(12, 5, 7, 7), ncol = 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
x <- c(89,37,30,28,2)
p <- c(40,20,20,15,5)
try(
chisq.test(x, p = p)                # gives an error
)
chisq.test(x, p = p, rescale.p = TRUE)
                                # works
p <- c(0.40,0.20,0.20,0.19,0.01)
                                # Expected count in category 5
                                # is 1.86 < 5 ==> chi square approx.
chisq.test(x, p = p)            #               maybe doubtful, but is ok!
chisq.test(x, p = p, simulate.p.value = TRUE)

## Case B. Raw data
x <- trunc(5 * runif(100))
chisq.test(table(x))            # NOT 'chisq.test(x)'!

###
}
}
\references{
Hope, A. C. A. (1968) A simplified Monte Carlo significance test
procedure.  _J. Roy, Statist. Soc. B_ *30*, 582-598.

Patefield, W. M. (1981) Algorithm AS159.  An efficient method of
generating r x c tables with given row and column totals.
_Applied Statistics_ *30*, 91-97.

Agresti, A. (2007) _An Introduction to Categorical Data Analysis,
2nd ed._, New York: John Wiley & Sons.  Page 38.
}
\seealso{
For goodness-of-fit testing, notably of continuous distributions, \code{\link{ks.test}}.
}