Generalized Siegel-Tukey Test of Homogeneity of Scales
Performs a Siegel-Tukey k-sample rank dispersion test.
GSTTest(x, ...)
## Default S3 method:
GSTTest(x, g, dist = c("Chisquare", "KruskalWallis"), ...)
## S3 method for class 'formula'
GSTTest(
formula,
data,
subset,
na.action,
dist = c("Chisquare", "KruskalWallis"),
...
)x |
a numeric vector of data values, or a list of numeric data vectors. |
... |
further arguments to be passed to or from methods. |
g |
a vector or factor object giving the group for the
corresponding elements of |
dist |
the test distribution. Defaults's to |
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 |
Meyer-Bahlburg (1970) has proposed a generalized Siegel-Tukey
rank dispersion test for the k-sample case.
Likewise to the fligner.test, this test
is a nonparametric test for testing the homogegeneity of
scales in several groups.
Let theta_i, and lambda_i denote
location and scale parameter of the ith group,
then for the two-tailed case, the null hypothesis
H:
lambda_i / lambda_j = 1 | theta_i = theta_j, i != j is
tested against the alternative,
A: lambda_i / lambda_j != 1
with at least one inequality beeing strict.
The data are combinedly ranked according to Siegel-Tukey. The ranking is done by alternate extremes (rank 1 is lowest, 2 and 3 are the two highest, 4 and 5 are the two next lowest, etc.).
Meyer-Bahlburg (1970) showed, that the Kruskal-Wallis H-test
can be employed on the Siegel-Tukey ranks.
The H-statistic is assymptotically
chi-squared distributed with v = k - 1 degree
of freedom, the default test distribution is consequently
dist = "Chisquare". If dist = "KruskalWallis" is selected,
an incomplete beta approximation is used for the calculation
of p-values as implemented in the function
pKruskalWallis of the package
SuppDists.
A list with class "htest" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
If ties are present, a tie correction is performed and a warning message is given. The GSTTest is sensitive to median differences, likewise to the Siegel-Tukey test. It is thus appropriate to apply this test on the residuals of a one-way ANOVA, rather than on the original data (see example).
H.F.L. Meyer-Bahlburg (1970), A nonparametric test for relative spread in k unpaired samples, Metrika 15, 23–29.
GSTTest(count ~ spray, data = InsectSprays) ## as means/medians differ, apply the test to residuals ## of one-way ANOVA ans <- aov(count ~ spray, data = InsectSprays) GSTTest( residuals( ans) ~ spray, data =InsectSprays)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.