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.

William J. Conover (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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