var.test                package:stats                R Documentation

F Test to Compare Two Variances

Description:

     Performs an F test to compare the variances of two samples from
     normal populations.

Usage:

     var.test(x, ...)

     ## Default S3 method:
     var.test(x, y, ratio = 1,
              alternative = c("two.sided", "less", "greater"),
              conf.level = 0.95, ...)

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

Arguments:

    x, y: numeric vectors of data values, or fitted linear model
          objects (inheriting from class '"lm"').

   ratio: the hypothesized ratio of the population variances of 'x' and
          'y'.

alternative: a character string specifying the alternative hypothesis,
          must be one of '"two.sided"' (default), '"greater"' or
          '"less"'.  You can specify just the initial letter.

conf.level: confidence level for the returned confidence interval.

 formula: a formula of the form 'lhs ~ rhs' where 'lhs' is a numeric
          variable giving the data values and 'rhs' a factor with two
          levels giving 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:

     The null hypothesis is that the ratio of the variances of the
     populations from which 'x' and 'y' were drawn, or in the data to
     which the linear models 'x' and 'y' were fitted, is equal to
     'ratio'.

Value:

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

statistic: the value of the F test statistic.

parameter: the degrees of the freedom of the F distribution of the test
          statistic.

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

conf.int: a confidence interval for the ratio of the population
          variances.

estimate: the ratio of the sample variances of 'x' and 'y'.

null.value: the ratio of population variances under the null.

alternative: a character string describing the alternative hypothesis.

  method: the character string '"F test to compare two variances"'.

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

See Also:

     'bartlett.test' for testing homogeneity of variances in more than
     two samples from normal distributions; 'ansari.test' and
     'mood.test' for two rank based (nonparametric) two-sample tests
     for difference in scale.

Examples:

     x <- rnorm(50, mean = 0, sd = 2)
     y <- rnorm(30, mean = 1, sd = 1)
     var.test(x, y)                  # Do x and y have the same variance?
     var.test(lm(x ~ 1), lm(y ~ 1))  # The same.

