DunnTest.Rd
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 NA
s. 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
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))
#>
#> Dunn's test of multiple comparisons using rank sums : holm
#>
#> mean.rank.diff pval
#> 2-1 1.8 1.0000
#> 3-1 -0.6 1.0000
#> 3-2 -2.4 1.0000
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
## 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)
#>
#> Kruskal-Wallis rank sum test
#>
#> data: x and g
#> Kruskal-Wallis chi-squared = 0.77143, df = 2, p-value = 0.68
#>
# ...and the pairwise test afterwards
DunnTest(x, g)
#>
#> Dunn's test of multiple comparisons using rank sums : holm
#>
#> mean.rank.diff
#> Subjects with obstructive airway disease-Normal subjects 1.8
#> Subjects with asbestosis-Normal subjects -0.6
#> Subjects with asbestosis-Subjects with obstructive airway disease -2.4
#> pval
#> Subjects with obstructive airway disease-Normal subjects 1.0000
#> Subjects with asbestosis-Normal subjects 1.0000
#> Subjects with asbestosis-Subjects with obstructive airway disease 1.0000
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
## Formula interface.
boxplot(Ozone ~ Month, data = airquality)
DunnTest(Ozone ~ Month, data = airquality)
#>
#> Dunn's test of multiple comparisons using rank sums : holm
#>
#> mean.rank.diff pval
#> 6-5 12.02991453 1.00000
#> 7-5 41.21153846 0.000099 ***
#> 8-5 38.53846154 0.00032 ***
#> 9-5 11.99734748 0.74574
#> 7-6 29.18162393 0.14891
#> 8-6 26.50854701 0.20743
#> 9-6 -0.03256705 1.00000
#> 8-7 -2.67307692 1.00000
#> 9-7 -29.21419098 0.01036 *
#> 9-8 -26.54111406 0.02428 *
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>