kruskal.test {stats}  R Documentation 
KruskalWallis Rank Sum Test
Description
Performs a KruskalWallis rank sum test.
Usage
kruskal.test(x, ...)
## Default S3 method:
kruskal.test(x, g, ...)
## S3 method for class 'formula'
kruskal.test(formula, data, subset, na.action, ...)
Arguments
x 
a numeric vector of data values, or a list of numeric data vectors. Nonnumeric elements of a list will be coerced, with a warning. 
g 
a vector or factor object giving the group for the
corresponding elements of 
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 
... 
further arguments to be passed to or from methods. 
Details
kruskal.test
performs a KruskalWallis 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
.
Value
A list with class "htest"
containing the following components:
statistic 
the KruskalWallis rank sum statistic. 
parameter 
the degrees of freedom of the approximate chisquared distribution of the test statistic. 
p.value 
the pvalue of the test. 
method 
the character string 
data.name 
a character string giving the names of the data. 
References
Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 115–120.
See Also
The Wilcoxon rank sum test (wilcox.test
) as the special
case for two samples;
lm
together with anova
for performing
oneway 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 pvalues, including in the presence of ties.
Examples
## 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)