R: F Test to Compare Two Variances

var.test {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.

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.

[Package stats version 2.9.0 ]