

   TTeesstt ffoorr EEqquuaall oorr GGiivveenn PPrrooppoorrttiioonnss

        prop.test(x, n = NULL, p = NULL, alternative = "two.sided",
                  conf.level = 0.95, correct = TRUE)

   AArrgguummeennttss::

          x: a vector of counts of successes or a matrix with 2
             columns giving the counts of successes and fail-
             ures, respectively.

          n: a vector of counts of trials; ignored if `x' is a
             matrix.

          p: a vector of probabilities of success.  The length
             of `p' must be the same as the number of groups
             specified by `x', and its elements must be greater
             than 0 and less than 1.

   alternative: indicates the alternative hypothesis and must
             be one of `"two.sided"', `"greater"' or `"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.

   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 pro-
             portions are equal; ignored otherwise.

    correct: a logical indicating whether Yates' continuity
             correction should be applied.

   DDeessccrriippttiioonn::

        `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.

   DDeettaaiillss::

        Only groups with finite numbers of successes and fail-
        ures are used.  Counts of successes and failures must
        be nonnegative and hence not greater than the corre-
        sponding numbers of trials which must be positive.  All
        finite counts should be integers.

        If `p' is `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 proba-
        bility of success in the second group, as specified by
        `alternative'.  A confidence interval for the differ-
        ence of proportions with confidence level as specified
        by `conf.level' and clipped to [-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 `"two.sided"', the
        returned confidence interval is `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 `p', or
        .5 if `p' is not given.  The alternative is that the
        probability of success if less than, not equal to, or
        greater than `p' or 0.5, respectively, as specified by
        `alternative'.  A confidence interval for the underly-
        ing proportion with confidence level as specified by
        `conf.level' and clipped to [0,1] is returned.  Conti-
        nuity correction is used only if it does not exceed the
        difference between sample and null proportions in abso-
        lute value.

        Finally, if `p' is given and there are more than 2
        groups, the null tested is that the underlying proba-
        bilities of success are those given by `p'.  The alter-
        native is always `"two.sided"', the returned confidence
        interval is `NULL', and continuity correction is never
        used.

   VVaalluuee::

        A list with class `"htest"' containing the following
        components:

   statistic: the value of Pearson's chi-square test statistic.

   parameter: the degrees of freedom of the approximate chi-
             square distribution of the test statistic.

    p.value: the p-value of the test.

   estimate: a vector with the sample proportions `x/n'.

   conf.int: a confidence interval for the true proportion if
             there is one group, or for the difference in pro-
             portions if there are 2 groups and `p' is not
             given, or `NULL' otherwise.  In the cases where it
             is not `NULL', the returned confidence interval
             has an asymptotic confidence level as specified by
             `conf.level', and is appropriate to the specified
             alternative hypothesis.

   null.value: the value of `p' if specified by the null, or
             `NULL' otherwise.

   alternative: a character string describing the alternative.

     method: a character string indicating the method used, and
             whether Yates' continuity correction was applied.

   data.name: a character string giving the names of the data.

   EExxaammpplleess::

        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)

