Dunn's Test of Multiple Comparisons
Performs Dunn's test of multiple comparisons using rank sums.
DunnTest(x, ...)
## Default S3 method:
DunnTest(x, g,
method = c("holm", "hochberg", "hommel", "bonferroni", "BH",
"BY", "fdr", "none"),
alternative = c("two.sided", "less", "greater"),
out.list = TRUE, ...)
## S3 method for class 'formula'
DunnTest(formula, data, subset, na.action, ...)
## S3 method for class 'DunnTest'
print(x, digits = getOption("digits", 3), ...)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 |
method |
the method for adjusting p-values for multiple comparisons. The function is calling |
alternative |
a character string specifying the alternative hypothesis, must be one of |
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 |
data |
an optional matrix or data frame (or similar: see
|
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 |
digits |
controls the number of fixed digits to print. |
... |
further arguments to be passed to or from methods. |
DunnTest performs the post hoc pairwise multiple comparisons procedure appropriate to follow the rejection of a Kruskal-Wallis test. The Kruskal-Wallis test, being a non-parametric analog of the one-way 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 non-parametric analog of the unpaired t-test, is possibly intuitive, but inappropriate as a post hoc pairwise test, because (1) it fails to retain the dependent ranking that produced the Kruskal-Wallis test statistic, and (2) it does not incorporate the pooled variance estimate implied by the null hypothesis of the Kruskal-Wallis 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.
A list with class "DunnTest" containing the following components:
res |
an array containing the mean rank differencens and the according p-values |
Andri Signorell <andri@signorell.net>, the interface is based on R-Core code
Dunn, O. J. (1961) Multiple comparisons among means Journal of the American Statistical Association, 56(293):52-64.
Dunn, O. J. (1964) Multiple comparisons using rank sums Technometrics, 6(3):241-252.
## 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.