Performs the all-pairs comparison test for different factor levels according to Dwass, Steel, Critchlow and Fligner.
dscfAllPairsTest(x, ...)# S3 method for default
dscfAllPairsTest(x, g, ...)
# S3 method for formula
dscfAllPairsTest(formula, data, subset, na.action, ...)
a numeric vector of data values, or a list of numeric data vectors.
further arguments to be passed to or from methods.
a vector or factor object giving the group for the
corresponding elements of "x".
Ignored with a warning if "x" is a list.
a formula of the form response ~ group where
response gives the data values and group a vector or
factor of the corresponding groups.
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).
an optional vector specifying a subset of observations to be used.
a function which indicates what should happen when
the data contain NAs. Defaults to getOption("na.action").
A list with class "PMCMR" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
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.
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