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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd"><html xmlns="http://www.w3.org/1999/xhtml"><head><title>R: Exact Binomial Test</title> <meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> <link rel="stylesheet" type="text/css" href="R.css" /> </head><body> <table width="100%" summary="page for binom.test {stats}"><tr><td>binom.test {stats}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Exact Binomial Test</h2> <h3>Description</h3> <p>Performs an exact test of a simple null hypothesis about the probability of success in a Bernoulli experiment. </p> <h3>Usage</h3> <pre> binom.test(x, n, p = 0.5, alternative = c("two.sided", "less", "greater"), conf.level = 0.95) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>number of successes, or a vector of length 2 giving the numbers of successes and failures, respectively.</p> </td></tr> <tr valign="top"><td><code>n</code></td> <td> <p>number of trials; ignored if <code>x</code> has length 2.</p> </td></tr> <tr valign="top"><td><code>p</code></td> <td> <p>hypothesized probability of success.</p> </td></tr> <tr valign="top"><td><code>alternative</code></td> <td> <p>indicates the alternative hypothesis and must be one of <code>"two.sided"</code>, <code>"greater"</code> or <code>"less"</code>. You can specify just the initial letter.</p> </td></tr> <tr valign="top"><td><code>conf.level</code></td> <td> <p>confidence level for the returned confidence interval.</p> </td></tr> </table> <h3>Details</h3> <p>Confidence intervals are obtained by a procedure first given in Clopper and Pearson (1934). This guarantees that the confidence level is at least <code>conf.level</code>, but in general does not give the shortest-length confidence intervals. </p> <h3>Value</h3> <p>A list with class <code>"htest"</code> containing the following components: </p> <table summary="R valueblock"> <tr valign="top"><td><code>statistic</code></td> <td> <p>the number of successes.</p> </td></tr> <tr valign="top"><td><code>parameter</code></td> <td> <p>the number of trials.</p> </td></tr> <tr valign="top"><td><code>p.value</code></td> <td> <p>the p-value of the test.</p> </td></tr> <tr valign="top"><td><code>conf.int</code></td> <td> <p>a confidence interval for the probability of success.</p> </td></tr> <tr valign="top"><td><code>estimate</code></td> <td> <p>the estimated probability of success.</p> </td></tr> <tr valign="top"><td><code>null.value</code></td> <td> <p>the probability of success under the null, <code>p</code>.</p> </td></tr> <tr valign="top"><td><code>alternative</code></td> <td> <p>a character string describing the alternative hypothesis.</p> </td></tr> <tr valign="top"><td><code>method</code></td> <td> <p>the character string <code>"Exact binomial test"</code>.</p> </td></tr> <tr valign="top"><td><code>data.name</code></td> <td> <p>a character string giving the names of the data.</p> </td></tr> </table> <h3>References</h3> <p>Clopper, C. J. & Pearson, E. S. (1934). The use of confidence or fiducial limits illustrated in the case of the binomial. <em>Biometrika</em>, <b>26</b>, 404–413. doi: <a href="https://doi.org/10.2307/2331986">10.2307/2331986</a>. </p> <p>William J. Conover (1971), <em>Practical nonparametric statistics</em>. New York: John Wiley & Sons. Pages 97–104. </p> <p>Myles Hollander & Douglas A. Wolfe (1973), <em>Nonparametric Statistical Methods.</em> New York: John Wiley & Sons. Pages 15–22. </p> <h3>See Also</h3> <p><code><a href="prop.test.html">prop.test</a></code> for a general (approximate) test for equal or given proportions. </p> <h3>Examples</h3> <pre> ## 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. </pre> <hr /><div style="text-align: center;">[Package <em>stats</em> version 3.6.0 <a href="00Index.html">Index</a>]</div> </body></html>