# binom.test: Exact Binomial Test

## Description

Performs an exact test of a simple null hypothesis about the
probability of success in a Bernoulli experiment.

## Usage

binom.test(x, n, p = 0.5,
alternative = c("two.sided", "less", "greater"),
conf.level = 0.95)

## Arguments

x

number of successes, or a vector of length 2 giving the
numbers of successes and failures, respectively.

n

number of trials; ignored if `x`

has length 2.

p

hypothesized probability of success.

alternative

indicates the alternative hypothesis and must be
one of `"two.sided"`

, `"greater"`

or `"less"`

.
You can specify just the initial letter.

conf.level

confidence level for the returned confidence
interval.

## Value

A list with class `"htest"`

containing the following components:

statisticthe number of successes.

parameterthe number of trials.

p.valuethe p-value of the test.

conf.inta confidence interval for the probability of success.

estimatethe estimated probability of success.

null.valuethe probability of success under the null,
`p`

.

alternativea character string describing the alternative
hypothesis.

methodthe character string `"Exact binomial test"`

.

data.namea character string giving the names of the data.

## Details

Confidence intervals are obtained by a procedure first given in
Clopper and Pearson (1934). This guarantees that the confidence level
is at least `conf.level`

, but in general does not give the
shortest-length confidence intervals.

## References

Clopper, C. J. & Pearson, E. S. (1934).
The use of confidence or fiducial limits illustrated in the case of
the binomial.
*Biometrika*, **26**, 404--413.

William J. Conover (1971),
*Practical nonparametric statistics*.
New York: John Wiley & Sons.
Pages 97--104.

Myles Hollander & Douglas A. Wolfe (1973),
*Nonparametric Statistical Methods.*
New York: John Wiley & Sons.
Pages 15--22.

## See Also

`prop.test`

for a general (approximate) test for equal or
given proportions.

## Examples

# NOT RUN {
## Conover (1971), p. 97f.
## Under (the assumption of) simple Mendelian inheritance, a cross
## between plants of two particular genotypes produces progeny 1/4 of
## which are "dwarf" and 3/4 of which are "giant", respectively.
## In an experiment to determine if this assumption is reasonable, a
## cross results in progeny having 243 dwarf and 682 giant plants.
## If "giant" is taken as success, the null hypothesis is that p =
## 3/4 and the alternative that p != 3/4.
binom.test(c(682, 243), p = 3/4)
binom.test(682, 682 + 243, p = 3/4) # The same.
## => Data are in agreement with the null hypothesis.
# }