fligner.test              package:stats              R Documentation

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, ...)

     ## Default S3 method:
     fligner.test(x, g, ...)

     ## S3 method for class 'formula':
     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 matrix or data frame (or similar: see
          'model.frame') containing the variables in the formula
          'formula'.  By default the variables are taken from
          'environment(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 of homogeneity of
          variances"'.

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

References:

     William J. Conover & Mark E. Johnson & Myrle 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:

     require(graphics)

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

