# 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 one-dimensional table with two entries, or a two-dimensional 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 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 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 `"htest"`

containing the following
components:

`x/n`

.`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.`p`

if specified by the null, or
`NULL`

otherwise.##### 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

`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)
```

*Documentation reproduced from package stats, version 3.3.3, License: Part of R 3.3.3*