R: Exact Binomial Test

binom.test {ctest} | 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.

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

Myles Hollander & Douglas A. Wolfe (1973), Nonparametric statistical inference. New York: John Wiley & Sons. Pages 15–22.

### See Also

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

### 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.

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