Performs Ury-Wiggins and Hochberg's all-pairs comparison test for normally distributed data with unequal variances.
uryWigginsHochbergTest(x, ...)# S3 method for default
uryWigginsHochbergTest(x, g,
p.adjust.method = p.adjust.methods, ...)
# S3 method for formula
uryWigginsHochbergTest(formula, data, subset, na.action,
p.adjust.method = 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 normally distributed residuals but unequal groups variances the tests of Ury-Wiggins and Hochberg can be performed. A total of \(m = k(k-1)/2\) hypotheses can be tested. The null hypothesis H\(_{ij}: \mu_i(x) = \mu_j(x)\) is tested in the two-tailed test against the alternative A\(_{ij}: \mu_i(x) \ne \mu_j(x), ~~ i \ne j\).
The p-values are computed from the t-distribution. The type of test depends
on the selected p-value adjustment method (see also p.adjust):
the Ury-Wiggins test is performed
the Hochberg test is performed
Hochberg, Y. (1976) A Modification of the T-Method of Multiple Comparisons for a One-Way Layout With Unequal Variances, Journal of the American Statistical Association 71, 200--203.
Ury, H. and Wiggins, A. D. (1971) Large Sample and Other Multiple Comparisons Among Means, British Journal of Mathematical and Statistical Psychology 24, 174--194.
# NOT RUN {
set.seed(245)
mn <- rep(c(1, 2^(1:4)), each=5)
sd <- rep(1:5, each=5)
x <- mn + rnorm(25, sd = sd)
g <- factor(rep(1:5, each=5))
fit <- aov(x ~ g)
shapiro.test(residuals(fit))
bartlett.test(x ~ g) # var1 != varN
anova(fit)
summary(uryWigginsHochbergTest(x, g))
# }
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