# binom.test

##### Exact Binomial Test

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

- Keywords
- htest

##### 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.

##### 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.

##### Value

- A list with class
`"htest"`

containing the following components: statistic the number of successes. parameter the number of trials. p.value the p-value of the test. conf.int a confidence interval for the probability of success. estimate the estimated probability of success. null.value the probability of success under the null, `p`

.alternative a character string describing the alternative hypothesis. method the character string `"Exact binomial test"`

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

##### 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

`library(stats)`

```
## 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.
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*