R: Exact Binomial Test

binom.test {stats}

R Documentation

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.

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. doi:10.2307/2331986.

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.

Examples

## 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.

[Package stats version 4.4.1 Index]