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, ...)"fligner.test"(x, g, ...)"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
xis a list.
- a formula of the form
lhs ~ rhswhere
lhsgives the data values and
rhsthe 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
- 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
- further arguments to be passed to or from methods.
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
fligner.test(x) to perform the test. If the samples are
not yet contained in a list, use
x must be a numeric data vector, and
be a vector or factor object of the same length as
x giving the
group for the corresponding elements of
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).
A list of class
- 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.
"htest"containing the following components:
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.
require(graphics) plot(count ~ spray, data = InsectSprays) fligner.test(InsectSprays$count, InsectSprays$spray) fligner.test(count ~ spray, data = InsectSprays) ## Compare this to bartlett.test()