R: Fligner-Killeen Test of Homogeneity of Variances

fligner.test {stats} | R Documentation

## Fligner-Killeen Test of Homogeneity of Variances

### Description

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

### Usage

    fligner.test(x, ...)

    ## Default S3 method:
    fligner.test(x, g, ...)

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

### 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) = 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. doi: 10.2307/1268225.

### 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

    require(graphics)

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

[Package stats version 4.0.5 Index]