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 NAs. 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.