bartlett.test             package:stats             R Documentation

Bartlett Test of Homogeneity of Variances

Description:

     Performs Bartlett's test of the null that the variances in each of
     the groups (samples) are the same.

Usage:

     bartlett.test(x, ...)

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

     ## S3 method for class 'formula':
     bartlett.test(formula, data, subset, na.action, ...)

Arguments:

       x: a numeric vector of data values, or a list of numeric data
          vectors representing the respective samples, or fitted linear
          model objects (inheriting from class '"lm"').

       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 or fitted
     linear models to be compared for homogeneity of variances.  In
     this case, the elements must either all be numeric data vectors or
     fitted linear model objects, 'g' is ignored, and one can simply
     use 'bartlett.test(x)' to perform the test.  If the samples are
     not yet contained in a list, use 'bartlett.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'.

Value:

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

statistic: Bartlett's K-squared 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 '"Bartlett test of homogeneity of
          variances"'.

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

References:

     Bartlett, M. S. (1937). Properties of sufficiency and statistical
     tests. _Proceedings of the Royal Society of London Series A_
     *160*, 268-282.

See Also:

     'var.test' for the special case of comparing variances in two
     samples from normal distributions; 'fligner.test' for a rank-based
     (nonparametric) k-sample test for homogeneity of variances;
     'ansari.test' and 'mood.test' for two rank based two-sample tests
     for difference in scale.

Examples:

     require(graphics)

     plot(count ~ spray, data = InsectSprays)
     bartlett.test(InsectSprays$count, InsectSprays$spray)
     bartlett.test(count ~ spray, data = InsectSprays)

