prop.test               package:stats               R Documentation

Test of Equal or Given Proportions

Description:

     '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.

Usage:

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

Arguments:

       x: a vector of counts of successes or a matrix with 2 columns
          giving the counts of successes and failures, 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: a character string specifying the alternative hypothesis,
          must be one of '"two.sided"' (default), '"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 proportions are equal; ignored otherwise.

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

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 '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
     probability of success in the second group, as specified by
     'alternative'.  A confidence interval for the difference 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
     underlying proportion with confidence level as specified by
     'conf.level' and clipped to [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 'p' is given and there are more than 2 groups, the
     null tested is that the underlying probabilities of success are
     those given by 'p'.  The alternative is always '"two.sided"', the
     returned confidence interval is 'NULL', and continuity correction
     is never used.

Value:

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

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

parameter: the degrees of freedom of the approximate chi-squared
          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 proportions 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.

References:

     Wilson, E.B. (1927) Probable inference, the law of succession, and
     statistical inference. _J. Am. Stat. Assoc._, *22*, 209-212.

     Newcombe R.G. (1998) Two-Sided Confidence Intervals for the Single
     Proportion: Comparison of Seven Methods. _Statistics in Medicine_
     *17*, 857-872.

     Newcombe R.G. (1998) Interval Estimation for the Difference
     Between Independent Proportions: Comparison of Eleven Methods.
     _Statistics in Medicine_ *17*, 873-890.

See Also:

     'binom.test' for an _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)

