The R Project SVN R

\name{prop.test}
\title{Test for Equal or Given Proportions}
\usage{
prop.test(x, n = NULL, p = NULL, alternative = "two.sided",
          conf.level = 0.95, correct = TRUE)
}
\alias{prop.test}
\arguments{
    \item{x}{a vector of counts of successes or a matrix with 2 columns
    giving the counts of successes and failures, respectively.}
    \item{n}{a vector of counts of trials; ignored if \code{x} is a
    matrix.}
    \item{p}{a vector of probabilities of success.  The length of
    \code{p} must be the same as the number of groups specified by
    \code{x}, and its elements must be greater than 0 and less than
    1.}
    \item{alternative}{indicates the alternative hypothesis and must be
    one of \code{"two.sided"}, \code{"greater"} or \code{"less"}.
    You can specify just the initial letter.  Only used for testing
    the null that a single proportion equals a given value, or that
    two proportions are equal; ignored otherwise.}
    \item{conf.level}{confidence level of the returned confidence
    interval.  Must be a single number between 0 and 1.  Only used
    when testing the null that a single proportion equals a given
    value, or that two proportions are equal; ignored otherwise.}
    \item{correct}{a logical indicating whether Yates' continuity
        correction should be applied.}
}
\description{
    \code{prop.test} can be used for testing the null that the
    proportions (probabilities of success) in several groups are the
    same, or that they equal certain given values.
}
\details{
    Only groups with finite numbers of successes and failures are used.
    Counts of successes and failures must be nonnegative and hence not
    greater than the corresponding numbers of trials which must be
    positive.  All finite counts should be integers.

    If \code{p} is \code{NULL} and there is more than one group, the
    null tested is that the proportions in each group are the same.  If
    there are two groups, the alternatives are that the probability of
    success in the first group is less than, not equal to, or greater
    than the probability of success in the second group, as specified by
    \code{alternative}.  A confidence interval for the difference of
    proportions with confidence level as specified by \code{conf.level}
    and clipped to \eqn{[-1,1]} is returned.  Continuity correction is 
    used only if it does not exceed the difference of the sample 
    proportions in absolute value.  Otherwise, if there are more than 2
    groups, the alternative is always \code{"two.sided"}, the returned
    confidence interval is \code{NULL}, and continuity correction is
    never used.

    If there is only one group, then the null tested is that the
    underlying probability of success is \code{p}, or .5 if \code{p} is
    not given.  The alternative is that the probability of success if
    less than, not equal to, or greater than \code{p} or 0.5,
    respectively, as specified by \code{alternative}.  A confidence
    interval for the underlying proportion with confidence level as
    specified by \code{conf.level} and clipped to \eqn{[0,1]} is
    returned.  Continuity correction is used only if it does not exceed
    the difference between sample and null proportions in absolute
    value.

    Finally, if \code{p} is given and there are more than 2 groups, the
    null tested is that the underlying probabilities of success are
    those given by \code{p}.  The alternative is always
    \code{"two.sided"}, the returned confidence interval is \code{NULL},
    and continuity correction is never used.
}
\value{
    A list with class \code{"htest"} containing the following
    components:
    \item{statistic}{the value of Pearson's chi-square test statistic.}
    \item{parameter}{the degrees of freedom of the approximate
    chi-square distribution of the test statistic.}
    \item{p.value}{the p-value of the test.}
    \item{estimate}{a vector with the sample proportions \code{x/n}.}
    \item{conf.int}{a confidence interval for the true proportion if
    there is one group, or for the difference in proportions if
    there are 2 groups and \code{p} is not given, or \code{NULL}
    otherwise.  In the cases where it is not \code{NULL}, the
    returned confidence interval has an asymptotic confidence level
    as specified by \code{conf.level}, and is appropriate to the
    specified alternative hypothesis.}
    \item{null.value}{the value of \code{p} if specified by the null, or
    \code{NULL} otherwise.}
    \item{alternative}{a character string describing the alternative.}
    \item{method}{a character string indicating the method used, and
        whether Yates' continuity correction was applied.}
    \item{data.name}{a character string giving the names of the data.}
}
\examples{
heads <- rbinom(1, size=100, pr = .5)
prop.test(heads, 100)          # continuity correction TRUE by default
prop.test(heads, 100, correct = FALSE)

## Data from Fleiss (1981), p. 139.
## H0: The null hypothesis is that the four populations from which
##     the patients were drawn have the same true proportion of smokers.
## A:  The alternative is that this proportion is different in at
##     least one of the populations.

smokers  <- c( 83, 90, 129, 70 )
patients <- c( 86, 93, 136, 82 )
prop.test(smokers, patients)
}
\keyword{htest}