prop.test
Test of Equal or Given Proportions
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.
 Keywords
 htest
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, a onedimensional table with two entries, or a twodimensional table (or 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 or a table.  p
 a vector of probabilities of success. The length of
p
must be the same as the number of groups specified byx
, 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 where possible.
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 is 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
 statistic
 the value of Pearson's chisquared test statistic.
 parameter
 the degrees of freedom of the approximate chisquared distribution of the test statistic.
 p.value
 the pvalue 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, orNULL
otherwise. In the cases where it is notNULL
, the returned confidence interval has an asymptotic confidence level as specified byconf.level
, and is appropriate to the specified alternative hypothesis.  null.value
 the value of
p
if specified by the null, orNULL
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.
"htest"
containing the following
components:
References
Wilson, E.B. (1927) Probable inference, the law of succession, and statistical inference. J. Am. Stat. Assoc., 22, 209212.
Newcombe R.G. (1998) TwoSided Confidence Intervals for the Single Proportion: Comparison of Seven Methods. Statistics in Medicine 17, 857872.
Newcombe R.G. (1998) Interval Estimation for the Difference Between Independent Proportions: Comparison of Eleven Methods. Statistics in Medicine 17, 873890.
See Also
binom.test
for an exact test of a binomial
hypothesis.
Examples
library(stats)
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)
Community examples
There seems to be a bug in this example > during both runs the test output(in the right window) specifies 'without continuity correction', even though the author comments state otherwise. On another note, the bottom bar seems to be covering the 'Post comment' button(firefox) prop.test()