# 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 class 'default':
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, \dots)

##### 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.

##### 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)`

```
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 3.3, License: Part of R 3.3*

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