var.test                package:ctest                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, y, ratio = 1, alternative = c("two.sided", "less", "greater"),
              conf.level = 0.95, ...)
     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 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:

     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 distribtion 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.

