DunnTest {DescTools}R Documentation

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), ...)



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 x is a list.


the method for adjusting p-values for multiple comparisons. The function is calling p.adjust and this parameter is directly passed through.


a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "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 ~ rhs where lhs gives the data values and rhs 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").


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:


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.

See Also

kruskal.test, wilcox.test, p.adjust


## 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)

[Package DescTools version 0.99.51 Index]