Performs a Kruskal-Wallis rank sum test.
kruskal.test(x, …)# S3 method for default
kruskal.test(x, g, …)
# S3 method for formula
kruskal.test(formula, data, subset, na.action, …)
a numeric vector of data values, or a list of numeric data vectors. Non-numeric elements of a list will be coerced, with a warning.
a vector or factor object giving the group for the
corresponding elements of x. Ignored with a warning if
x is a list.
a formula of the form response ~ group where
response gives the data values and group a vector or
factor of 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").
further arguments to be passed to or from methods.
A list with class "htest" containing the following components:
the Kruskal-Wallis rank sum statistic.
the degrees of freedom of the approximate chi-squared distribution of the test statistic.
the p-value of the test.
the character string "Kruskal-Wallis rank sum test".
a character string giving the names of the data.
kruskal.test performs a Kruskal-Wallis rank sum test of the
null that the location parameters of the distribution of x
are the same in each group (sample). The alternative is that they
differ in at least one.
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 kruskal.test(x)
to perform the test. If the samples are not yet contained in a
list, use kruskal.test(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.
Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 115--120.
The Wilcoxon rank sum test (wilcox.test) as the special
case for two samples;
lm together with anova for performing
one-way location analysis under normality assumptions; with Student's
t test (t.test) as the special case for two samples.
wilcox_test in package
coin for exact, asymptotic and Monte Carlo
conditional p-values, including in the presence of ties.
# NOT RUN {
## 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
kruskal.test(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"))
kruskal.test(x, g)
## Formula interface.
require(graphics)
boxplot(Ozone ~ Month, data = airquality)
kruskal.test(Ozone ~ Month, data = airquality)
# }
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