GSTTest() R function from [PMCMRplus]

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"),
  ...
)

Arguments

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 "x". Ignored with a warning if "x" is a list.
dist: the test distribution. Defaults's to "Chisquare".
formula: a formula of the form response ~ group where response gives the data values and group a vector or factor of the corresponding groups.
data: 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).
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 NAs. Defaults to getOption("na.action").

Returns

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

method: a character string indicating what type of test was performed.
data.name: a character string giving the name(s) of the data.
statistic: the estimated quantile of the test statistic.
p.value: the p-value for the test.
parameter: the parameters of the test statistic, if any.
alternative: a character string describing the alternative hypothesis.
estimates: the estimates, if any.
null.value: the estimate under the null hypothesis, if any.

Details

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 $i$ th group, then for the two-tailed case, the null hypothesis H: c(" $%$ ", " $\n$ ", " $lambda_i / lambda_j = 1 | theta_i = theta_j, i != j$ ") 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.

Note

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).

Examples


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)

References

H.F.L. Meyer-Bahlburg (1970), A nonparametric test for relative spread in k unpaired samples, Metrika 15 , 23--29.

GSTTest function