stats (version 3.4.0)

var.test: 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, …)
# S3 method for default
var.test(x, y, ratio = 1,
         alternative = c("two.sided", "less", "greater"),
         conf.level = 0.95, …)
# S3 method for 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 NAs. Defaults to getOption("na.action").

…

further arguments to be passed to or from methods.

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.

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.

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.