Dunn's Test of Multiple Comparisons
Performs Dunn's test of multiple comparisons using rank sums.
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), ...)
- a numeric vector of data values, or a list of numeric data vectors.
- a vector or factor object giving the group for the
corresponding elements of
x. Ignored if
xis a list.
- the method for adjusting p-values for multiple comparisons. The function is calling
p.adjustand this parameter is directly passed through.
- a character string specifying the alternative hypothesis, must be one of
"less". You can specify just the initial letter.
- logical, indicating if the results should be printed in list mode or as a square matrix. Default is list (TRUE).
- a formula of the form
lhs ~ rhswhere
lhsgives the data values and
rhsthe 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
- 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
- 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.
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
to perform the test. If the samples are not yet contained in a
x must be a numeric data vector, and
be a vector or factor object of the same length as
the group for the corresponding elements of
A list with class
"DunnTest"containing the following components:
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)