fligner.test Fligner-Killeen Test of Homogeneity of Variances
Description
Performs a Fligner-Killeen (median) test of the null that the variances in each of the groups (samples) are the same.
Usage
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 |
formula |
a formula of the form |
data |
an optional matrix or data frame (or similar: see |
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 |
... |
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 |
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. doi: 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.
Examples
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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Licensed under the GNU General Public License.