dscfAllPairsTest function

Multiple Comparisons of Mean Rank Sums

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

dscfAllPairsTest(x, ...)

## Default S3 method:
dscfAllPairsTest(x, g, ...)

## S3 method for class '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").

Returns

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