DunnTest
Dunn's Test of Multiple Comparisons
Performs Dunn's test of multiple comparisons using rank sums.
 Keywords
 htest
Usage
DunnTest(x, ...)
"DunnTest"(x, g, method = c("holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none"), alternative = c("two.sided", "less", "greater"), out.list = TRUE, ...)
"DunnTest"(formula, data, subset, na.action, ...)
"print"(x, digits = getOption("digits", 3), ...)
Arguments
 x
 a numeric vector of data values, or a list of numeric data vectors.
 g
 a vector or factor object giving the group for the
corresponding elements of
x
. Ignored ifx
is a list.  method
 the method for adjusting pvalues for multiple comparisons. The function is calling
p.adjust
and this parameter is directly passed through.  alternative
 a character string specifying the alternative hypothesis, must be one of
"two.sided"
(default),"greater"
or"less"
. You can specify just the initial letter.  out.list
 logical, indicating if the results should be printed in list mode or as a square matrix. Default is list (TRUE).
 formula
 a formula of the form
lhs ~ rhs
wherelhs
gives the data values andrhs
the corresponding groups.  data
 an optional matrix or data frame (or similar: see
model.frame
) containing the variables in the formulaformula
. By default the variables are taken fromenvironment(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
NA
s. Defaults togetOption("na.action")
.  digits
 controls the number of fixed digits to print.
 ...
 further arguments to be passed to or from methods.
Details
DunnTest
performs the post hoc pairwise multiple comparisons procedure appropriate to follow the rejection of a KruskalWallis test. The KruskalWallis test, being a nonparametric analog of the oneway ANOVA, is an omnibus test of the null hypothesis that none of k groups stochastically dominate one another.
Dunn's test is constructed in part by summing jointly ranked data. The rank sum test, itself a nonparametric analog of the unpaired ttest, is possibly intuitive, but inappropriate as a post hoc pairwise test, because (1) it fails to retain the dependent ranking that produced the KruskalWallis test statistic, and (2) it does not incorporate the pooled variance estimate implied by the null hypothesis of the KruskalWallis test.
If x
is a list, its elements are taken as the samples to be
compared, and hence have to be numeric data vectors. In this case,
g
is ignored, and one can simply use DunnTest(x)
to perform the test. If the samples are not yet contained in a
list, use DunnTest(list(x, ...))
.
Otherwise, x
must be a numeric data vector, and g
must
be a vector or factor object of the same length as x
giving
the group for the corresponding elements of x
.
Value

A list with class
"DunnTest"
containing the following components:References
Dunn, O. J. (1961) Multiple comparisons among means Journal of the American Statistical Association, 56(293):5264.
Dunn, O. J. (1964) Multiple comparisons using rank sums Technometrics, 6(3):241252.
See Also
Examples
## Hollander & Wolfe (1973), 116.
## Mucociliary efficiency from the rate of removal of dust in normal
## subjects, subjects with obstructive airway disease, and subjects
## with asbestosis.
x < c(2.9, 3.0, 2.5, 2.6, 3.2) # normal subjects
y < c(3.8, 2.7, 4.0, 2.4) # with obstructive airway disease
z < c(2.8, 3.4, 3.7, 2.2, 2.0) # with asbestosis
DunnTest(list(x, y, z))
## Equivalently,
x < c(x, y, z)
g < factor(rep(1:3, c(5, 4, 5)),
labels = c("Normal subjects",
"Subjects with obstructive airway disease",
"Subjects with asbestosis"))
# do the kruskal.test first
kruskal.test(x, g)
# ...and the pairwise test afterwards
DunnTest(x, g)
## Formula interface.
boxplot(Ozone ~ Month, data = airquality)
DunnTest(Ozone ~ Month, data = airquality)