binom.test {ctest} | R Documentation |

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

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

`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. |

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.

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. |

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.

`prop.test`

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

## 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.