fligner.test              package:ctest              R Documentation

Fligner-Killeen Test for 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, g, ...)
     fligner.test(formula, data, subset, na.action, ...)

Arguments:

       x: a numeric vector of data values, or a list of numeric data
          vectors.

       g: a vector or factor object giving the group for the
          corresponding elements of `x'. Ignored if `x' is a list.

 formula: a formula of the form `lhs ~ rhs' where `lhs' gives the data
          values and `rhs' the corresponding groups.

    data: an optional data frame containing the variables in the model
          formula.

  subset: an optional vector specifying a subset of observations to be
          used.

na.action: a function which indicates what should happen when the data
          contain `NA's.  Defaults to `getOption("na.action")'.

     ...: further arguments to be passed to or from methods.

Details:

     If `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, `g' is ignored, and one can
     simply use `fligner.test(x)' to perform the test.  If the samples
     are not yet contained in a list, use `fligner.test(list(x, ...))'.

     Otherwise, `x' must be a numeric data vector, and `g' must be a
     vector or factor object of the same length as `x' giving the group
     for the corresponding elements of `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 k-sample simple
     linear rank which uses the ranks of the absolute values of the
     centered samples and weights a(i) = qnorm((1 + i/(n+1))/2).  The
     version implemented here uses median centering in each of the
     samples (F-K:med X^2 in the reference).

Value:

     A list of class `"htest"' containing the following components: 

statistic: the Fligner-Killeen:med X^2 test statistic.

parameter: the degrees of freedom of the approximate chi-squared
          distribution of the test statistic.

 p.value: the p-value of the test.

  method: the character string `"Fligner-Killeen test for homogeneity
          of variances"'.

data.name: a character string giving the names of the data.

References:

     W. J. Conover & Mark E. Johnson & Myrie M. Johnson (1981). A
     comparative study of tests for homogeneity of variances, with
     applications to the outer continental shelf bidding data.
     Technometrics 23, 351-361.

See Also:

     `ansari.test' and `mood.test' for rank-based two-sample test for a
     difference in scale parameters; `var.test' and `bartlett.test' for
     parametric tests for the homogeneity of variances.

Examples:

     data(InsectSprays)
     plot(count ~ spray, data = InsectSprays)
     fligner.test(InsectSprays$count, InsectSprays$spray)
     fligner.test(count ~ spray, data = InsectSprays)
     ## Compare this to bartlett.test()

