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.

fligner.test(x, …)

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

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


a numeric vector of data values, or a list of numeric data vectors.


a vector or factor object giving the group for the corresponding elements of x. Ignored if x is a list.


a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.


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).


an optional vector specifying a subset of observations to be used.


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.


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).


A list of class "htest" containing the following components:


the Fligner-Killeen:med \(X^2\) 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 "Fligner-Killeen test of homogeneity of variances".


a character string giving the names of the data.


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.

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.

  • fligner.test
  • fligner.test.default
  • fligner.test.formula
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 3.6.2, License: Part of R 3.6.2

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