| % File src/library/stats/man/prop.test.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2018 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{prop.test} |
| \title{Test of Equal or Given Proportions} |
| \usage{ |
| prop.test(x, n, p = NULL, |
| alternative = c("two.sided", "less", "greater"), |
| conf.level = 0.95, correct = TRUE) |
| } |
| \alias{prop.test} |
| \arguments{ |
| \item{x}{a vector of counts of successes, a one-dimensional table with |
| two entries, or a two-dimensional table (or 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 or a table.} |
| \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}{a character string specifying the alternative |
| hypothesis, must be one of \code{"two.sided"} (default), |
| \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 where possible.} |
| } |
| \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 is 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. The confidence interval |
| is computed by inverting the score test. |
| |
| 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-squared test statistic.} |
| \item{parameter}{the degrees of freedom of the approximate |
| chi-squared 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.} |
| } |
| \references{ |
| Wilson, E.B. (1927). |
| Probable inference, the law of succession, and statistical inference. |
| \emph{Journal of the American Statistical Association}, \bold{22}, |
| 209--212. |
| \doi{10.2307/2276774}. |
| |
| Newcombe R.G. (1998). |
| Two-Sided Confidence Intervals for the Single Proportion: Comparison |
| of Seven Methods. |
| \emph{Statistics in Medicine}, \bold{17}, 857--872. |
| \doi{10.1002/(SICI)1097-0258(19980430)17:8<857::AID-SIM777>3.0.CO;2-E}. |
| |
| Newcombe R.G. (1998). |
| Interval Estimation for the Difference Between Independent |
| Proportions: Comparison of Eleven Methods. |
| \emph{Statistics in Medicine}, \bold{17}, 873--890. |
| \doi{10.1002/(SICI)1097-0258(19980430)17:8<873::AID-SIM779>3.0.CO;2-I}. |
| } |
| \seealso{\code{\link{binom.test}} for an \emph{exact} test of a binomial |
| hypothesis.} |
| \examples{ |
| heads <- rbinom(1, size = 100, prob = .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} |