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PMCMRplus (version 1.9.3)

dscfAllPairsTest: Multiple Comparisons of Mean Rank Sums

Description

Performs the all-pairs comparison test for different factor levels according to Dwass, Steel, Critchlow and Fligner.

Usage

dscfAllPairsTest(x, ...)

# S3 method for default dscfAllPairsTest(x, g, ...)

# S3 method for formula dscfAllPairsTest(formula, data, subset, na.action, ...)

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.

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").

Value

A list with class "PMCMR" 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

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

p.adjust.method

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

Details

For all-pairs comparisons in an one-factorial layout with non-normally distributed residuals the DSCF all-pairs comparison test can be used. A total of \(m = k(k-1)/2\) hypotheses can be tested. The null hypothesis H\(_{ij}: F_i(x) = F_j(x)\) is tested in the two-tailed test against the alternative A\(_{ij}: F_i(x) \ne F_j(x), ~~ i \ne j\). As opposed to the all-pairs comparison procedures that depend on Kruskal ranks, the DSCF test is basically an extension of the U-test as re-ranking is conducted for each pairwise test.

The p-values are estimated from the studentized range distriburtion.

References

Douglas, C. E., Fligner, A. M. (1991) On distribution-free multiple comparisons in the one-way analysis of variance, Communications in Statistics - Theory and Methods 20, 127--139.

Dwass, M. (1960) Some k-sample rank-order tests. In Contributions to Probability and Statistics, Edited by: I. Olkin, Stanford: Stanford University Press.

Steel, R. G. D. (1960) A rank sum test for comparing all pairs of treatments, Technometrics 2, 197--207

See Also

Tukey, pairwise.wilcox.test