# var.test

##### F Test to Compare Two Variances

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

- Keywords
- htest

##### 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

`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:

the value of the F test statistic.

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

the p-value of the test.

a confidence interval for the ratio of the population variances.

the ratio of the sample variances of `x`

and
`y`

.

the ratio of population variances under the null.

a character string describing the alternative hypothesis.

the character string
`"F test to compare two variances"`

.

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

`library(stats)`

```
# NOT RUN {
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.
# }
```

*Documentation reproduced from package stats, version 3.6.0, License: Part of R 3.6.0*