R: Generalized Siegel-Tukey Test of Homogeneity of Scales

GSTTest {PMCMRplus} | 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 != 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.

### 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.

### See Also

`fligner.test`, `pKruskalWallis`, `Chisquare`, `fligner.test`

### 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)

[Package PMCMRplus version 1.7.0 Index]