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.
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.
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).
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.
# 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()
# }
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