# fligner.test

0th

Percentile

##### 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 default
fligner.test(x, g, …)# S3 method for 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 $a(i) = \mathrm{qnorm}((1 + i/(n+1))/2)$. 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. 10.2307/1268225.

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.

##### Aliases
• fligner.test
• fligner.test.default
• fligner.test.formula
##### Examples
library(stats) # NOT RUN { 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 3.5.0, License: Part of R 3.5.0

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