| % File src/library/stats/man/fligner.test.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2018 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{fligner.test} |
| \alias{fligner.test} |
| \alias{fligner.test.default} |
| \alias{fligner.test.formula} |
| \title{Fligner-Killeen Test of Homogeneity of Variances} |
| \description{ |
| Performs a Fligner-Killeen (median) test of the null that the |
| variances in each of the groups (samples) are the same. |
| } |
| \usage{ |
| fligner.test(x, \dots) |
| |
| \method{fligner.test}{default}(x, g, \dots) |
| |
| \method{fligner.test}{formula}(formula, data, subset, na.action, \dots) |
| } |
| \arguments{ |
| \item{x}{a numeric vector of data values, or a list of numeric data |
| vectors.} |
| \item{g}{a vector or factor object giving the group for the |
| corresponding elements of \code{x}. |
| Ignored if \code{x} is a list.} |
| \item{formula}{a formula of the form \code{lhs ~ rhs} where \code{lhs} |
| gives the data values and \code{rhs} the corresponding groups.} |
| \item{data}{an optional matrix or data frame (or similar: see |
| \code{\link{model.frame}}) containing the variables in the |
| formula \code{formula}. By default the variables are taken from |
| \code{environment(formula)}.} |
| \item{subset}{an optional vector specifying a subset of observations |
| to be used.} |
| \item{na.action}{a function which indicates what should happen when |
| the data contain \code{NA}s. Defaults to |
| \code{getOption("na.action")}.} |
| \item{\dots}{further arguments to be passed to or from methods.} |
| } |
| \details{ |
| If \code{x} 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} is ignored, and one can simply |
| use \code{fligner.test(x)} to perform the test. If the samples are |
| not yet contained in a list, use \code{fligner.test(list(x, ...))}. |
| |
| Otherwise, \code{x} must be a numeric data vector, and \code{g} must |
| be a vector or factor object of the same length as \code{x} giving the |
| group for the corresponding elements of \code{x}. |
| |
| 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 \eqn{k}-sample simple linear rank which uses |
| the ranks of the absolute values of the centered samples and weights |
| \eqn{a(i) = \mathrm{qnorm}((1 + i/(n+1))/2)}{a(i) = qnorm((1 + |
| i/(n+1))/2)}. The version implemented here uses median centering in |
| each of the samples (F-K:med \eqn{X^2} in the reference). |
| } |
| \value{ |
| A list of class \code{"htest"} containing the following components: |
| \item{statistic}{the Fligner-Killeen:med \eqn{X^2} test statistic.} |
| \item{parameter}{the degrees of freedom of the approximate chi-squared |
| distribution of the test statistic.} |
| \item{p.value}{the p-value of the test.} |
| \item{method}{the character string |
| \code{"Fligner-Killeen test of homogeneity of variances"}.} |
| \item{data.name}{a character string giving the names of the data.} |
| } |
| \references{ |
| 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. |
| \emph{Technometrics}, \bold{23}, 351--361. |
| \doi{10.2307/1268225}. |
| } |
| \seealso{ |
| \code{\link{ansari.test}} and \code{\link{mood.test}} for rank-based |
| two-sample test for a difference in scale parameters; |
| \code{\link{var.test}} and \code{\link{bartlett.test}} for parametric |
| tests for the homogeneity of variances. |
| } |
| |
| % FIXME: could use something more interesting here |
| \examples{ |
| require(graphics) |
| |
| plot(count ~ spray, data = InsectSprays) |
| fligner.test(InsectSprays$count, InsectSprays$spray) |
| fligner.test(count ~ spray, data = InsectSprays) |
| ## Compare this to bartlett.test() |
| } |
| \keyword{htest} |