# bartlett.test

##### Bartlett Test of Homogeneity of Variances

Performs Bartlett's test of the null that the variances in each of the groups (samples) are the same.

- Keywords
- htest

##### Usage

`bartlett.test(x, …)`# S3 method for default
bartlett.test(x, g, …)

# S3 method for formula
bartlett.test(formula, data, subset, na.action, …)

##### Arguments

- x
a numeric vector of data values, or a list of numeric data vectors representing the respective samples, or fitted linear model objects (inheriting from class

`"lm"`

).- g
a vector or factor object giving the group for the corresponding elements of

`x`

. Ignored if`x`

is a list.- formula
a formula of the form

`lhs ~ rhs`

where`lhs`

gives the data values and`rhs`

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

If `x`

is a list, its elements are taken as the samples or fitted
linear models to be compared for homogeneity of variances. In this
case, the elements must either all be numeric data vectors or fitted
linear model objects, `g`

is ignored, and one can simply use
`bartlett.test(x)`

to perform the test. If the samples are not
yet contained in a list, use `bartlett.test(list(x, ...))`

.

Otherwise, `x`

must be a numeric data vector, and `g`

must
be a vector or factor object of the same length as `x`

giving the
group for the corresponding elements of `x`

.

##### Value

A list of class `"htest"`

containing the following components:

Bartlett's K-squared test statistic.

the degrees of freedom of the approximate chi-squared distribution of the test statistic.

the p-value of the test.

the character string
`"Bartlett test of homogeneity of variances"`

.

a character string giving the names of the data.

##### References

Bartlett, M. S. (1937).
Properties of sufficiency and statistical tests.
*Proceedings of the Royal Society of London Series A*
**160**, 268--282.
10.1098/rspa.1937.0109.

##### See Also

`var.test`

for the special case of comparing variances in
two samples from normal distributions;
`fligner.test`

for a rank-based (nonparametric)
\(k\)-sample test for homogeneity of variances;
`ansari.test`

and `mood.test`

for two rank
based two-sample tests for difference in scale.

##### Examples

`library(stats)`

```
# NOT RUN {
require(graphics)
plot(count ~ spray, data = InsectSprays)
bartlett.test(InsectSprays$count, InsectSprays$spray)
bartlett.test(count ~ spray, data = InsectSprays)
# }
```

*Documentation reproduced from package stats, version 3.5.0, License: Part of R 3.5.0*