GSTTest: Generalized Siegel-Tukey Test of Homogeneity of Scales
In PMCMRplus: Calculate Pairwise Multiple Comparisons of Mean Rank Sums Extended

GSTTest

R Documentation

Generalized Siegel-Tukey Test of Homogeneity of Scales

Description

Performs a Siegel-Tukey k-sample rank dispersion test.

Usage

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 `NA`s. Defaults to `getOption("na.action")`.

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 ith group, then for the two-tailed case, the null hypothesis H: \lambda_i / \lambda_j = 1 | \theta_i = \theta_j, ~ i \ne j is tested against the alternative, A: \lambda_i / \lambda_j \ne 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.

Value

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.

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).

References

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

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)

PMCMRplus documentation built on May 29, 2024, 8:34 a.m.