Fligner-Killeen Test of Homogeneity of Variances

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Description

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

Usage

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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 NAs. 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.

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

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require(graphics)

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

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