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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: Fligner-Killeen Test of Homogeneity of Variances</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 fligner.test {stats}"><tr><td>fligner.test {stats}</td><td style="text-align: right;">R Documentation</td></tr></table> <h2>Fligner-Killeen Test of Homogeneity of Variances</h2> <h3>Description</h3> <p>Performs a Fligner-Killeen (median) test of the null that the variances in each of the groups (samples) are the same. </p> <h3>Usage</h3> <pre> fligner.test(x, ...) ## Default S3 method: fligner.test(x, g, ...) ## S3 method for class 'formula' fligner.test(formula, data, subset, na.action, ...) </pre> <h3>Arguments</h3> <table summary="R argblock"> <tr valign="top"><td><code>x</code></td> <td> <p>a numeric vector of data values, or a list of numeric data vectors.</p> </td></tr> <tr valign="top"><td><code>g</code></td> <td> <p>a vector or factor object giving the group for the corresponding elements of <code>x</code>. Ignored if <code>x</code> is a list.</p> </td></tr> <tr valign="top"><td><code>formula</code></td> <td> <p>a formula of the form <code>lhs ~ rhs</code> where <code>lhs</code> gives the data values and <code>rhs</code> the corresponding groups.</p> </td></tr> <tr valign="top"><td><code>data</code></td> <td> <p>an optional matrix or data frame (or similar: see <code><a href="model.frame.html">model.frame</a></code>) containing the variables in the formula <code>formula</code>. By default the variables are taken from <code>environment(formula)</code>.</p> </td></tr> <tr valign="top"><td><code>subset</code></td> <td> <p>an optional vector specifying a subset of observations to be used.</p> </td></tr> <tr valign="top"><td><code>na.action</code></td> <td> <p>a function which indicates what should happen when the data contain <code>NA</code>s. Defaults to <code>getOption("na.action")</code>.</p> </td></tr> <tr valign="top"><td><code>...</code></td> <td> <p>further arguments to be passed to or from methods.</p> </td></tr> </table> <h3>Details</h3> <p>If <code>x</code> is a list, its elements are taken as the samples to be compared for homogeneity of variances, and hence have to be numeric data vectors. In this case, <code>g</code> is ignored, and one can simply use <code>fligner.test(x)</code> to perform the test. If the samples are not yet contained in a list, use <code>fligner.test(list(x, ...))</code>. </p> <p>Otherwise, <code>x</code> must be a numeric data vector, and <code>g</code> must be a vector or factor object of the same length as <code>x</code> giving the group for the corresponding elements of <code>x</code>. </p> <p>The Fligner-Killeen (median) test has been determined in a simulation study as one of the many tests for homogeneity of variances which is most robust against departures from normality, see Conover, Johnson & Johnson (1981). It is a <i>k</i>-sample simple linear rank which uses the ranks of the absolute values of the centered samples and weights <i>a(i) = qnorm((1 + i/(n+1))/2)</i>. The version implemented here uses median centering in each of the samples (F-K:med <i>X^2</i> in the reference). </p> <h3>Value</h3> <p>A list of class <code>"htest"</code> containing the following components: </p> <table summary="R valueblock"> <tr valign="top"><td><code>statistic</code></td> <td> <p>the Fligner-Killeen:med <i>X^2</i> test statistic.</p> </td></tr> <tr valign="top"><td><code>parameter</code></td> <td> <p>the degrees of freedom of the approximate chi-squared distribution of the test statistic.</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>method</code></td> <td> <p>the character string <code>"Fligner-Killeen test of homogeneity of variances"</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>William J. Conover, Mark E. Johnson and Myrle M. Johnson (1981). A comparative study of tests for homogeneity of variances, with applications to the outer continental shelf bidding data. <em>Technometrics</em>, <b>23</b>, 351–361. doi: <a href="https://doi.org/10.2307/1268225">10.2307/1268225</a>. </p> <h3>See Also</h3> <p><code><a href="ansari.test.html">ansari.test</a></code> and <code><a href="mood.test.html">mood.test</a></code> for rank-based two-sample test for a difference in scale parameters; <code><a href="var.test.html">var.test</a></code> and <code><a href="bartlett.test.html">bartlett.test</a></code> for parametric tests for the homogeneity of variances. </p> <h3>Examples</h3> <pre> require(graphics) plot(count ~ spray, data = InsectSprays) fligner.test(InsectSprays$count, InsectSprays$spray) fligner.test(count ~ spray, data = InsectSprays) ## Compare this to bartlett.test() </pre> <hr /><div style="text-align: center;">[Package <em>stats</em> version 3.6.0 <a href="00Index.html">Index</a>]</div> </body></html>