Performs van-der-Waerden all-pairs comparison normal scores test.
vanWaerdenAllPairsTest(x, ...)# S3 method for default
vanWaerdenAllPairsTest(
x,
g,
p.adjust.method = c("single-step", p.adjust.methods),
...
)
# S3 method for formula
vanWaerdenAllPairsTest(
formula,
data,
subset,
na.action,
p.adjust.method = c("single-step", p.adjust.methods),
...
)
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.
method for adjusting p values (see p.adjust).
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 van-der-Waerden's
normal scores transformation can be used prior to
an all-pairs comparison test. 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\(_{ij}: F_i(x) \ne F_j(x), ~~ i \ne j\).
For p.adjust.method = "single-step" the
Tukey's studentized range distribution is used to calculate
p-values (see Tukey). Otherwise, the
t-distribution is used for the calculation of p-values
with a latter p-value adjustment as
performed by p.adjust.
Conover, W. J., Iman, R. L. (1979) On multiple-comparisons procedures, Tech. Rep. LA-7677-MS, Los Alamos Scientific Laboratory.
van der Waerden, B. L. (1952) Order tests for the two-sample problem and their power, Indagationes Mathematicae 14, 453--458.