# fligner.test

##### Fligner-Killeen Test of Homogeneity of Variances

Performs a Fligner-Killeen (median) test of the null that the variances in each of the groups (samples) are the same.

- Keywords
- htest

##### Usage

`fligner.test(x, ...)`## S3 method for class 'default':
fligner.test(x, g, \dots)

## S3 method for class 'formula':
fligner.test(formula, data, subset, na.action, \dots)

##### Arguments

- x
- a numeric vector of data values, or a list of numeric data vectors.
- 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 to be
compared for homogeneity of variances, and hence have to be numeric
data vectors. In this case, `g`

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

to perform the test. If the samples are
not yet contained in a list, use `fligner.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`

.

The Fligner-Killeen (median) test has been determined in a simulation study as one of the many tests for homogeneity of variances which is most robust against departures from normality, see Conover, Johnson & Johnson (1981). It is a $k$-sample simple linear rank which uses the ranks of the absolute values of the centered samples and weights $a(i) = \mathrm{qnorm}((1 + i/(n+1))/2)$. The version implemented here uses median centering in each of the samples (F-K:med $X^2$ in the reference).

##### Value

- A list of class
`"htest"`

containing the following components: statistic the Fligner-Killeen:med $X^2$ test statistic. parameter the degrees of freedom of the approximate chi-squared distribution of the test statistic. p.value the p-value of the test. method the character string `"Fligner-Killeen test of homogeneity of variances"`

.data.name a character string giving the names of the data.

##### References

William J. Conover, Mark E. Johnson and Myrle M. Johnson (1981).
A comparative study of tests for homogeneity of variances, with
applications to the outer continental shelf bidding data.
*Technometrics* **23**, 351--361.

##### See Also

`ansari.test`

and `mood.test`

for rank-based
two-sample test for a difference in scale parameters;
`var.test`

and `bartlett.test`

for parametric
tests for the homogeneity of variances.

##### Examples

`library(stats)`

```
require(graphics)
plot(count ~ spray, data = InsectSprays)
fligner.test(InsectSprays$count, InsectSprays$spray)
fligner.test(count ~ spray, data = InsectSprays)
## Compare this to bartlett.test()
```

*Documentation reproduced from package stats, version 3.3, License: Part of R 3.3*