kruskal.test {stats}R Documentation

Kruskal-Wallis Rank Sum Test


Performs a Kruskal-Wallis rank sum test.


kruskal.test(x, ...)

## Default S3 method:
kruskal.test(x, g, ...)

## S3 method for class 'formula':
kruskal.test(formula, data, subset, na.action, ...)


x a numeric vector of data values, or a list of numeric data vectors.
g a vector or factor object giving the group for the corresponding elements of x. Ignored if x is a list.
formula a formula of the form lhs ~ rhs where lhs gives the data values and rhs the corresponding groups.
data an optional data frame containing the variables in the model formula.
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 NAs. Defaults to getOption("na.action").
... further arguments to be passed to or from methods.


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.


A list with class "htest" containing the following components:

statistic the Kruskal-Wallis rank sum statistic.
parameter the degrees of freedom of the approximate chi-squared distribution of the test statistic.
p.value the p-value of the test.
method the character string "Kruskal-Wallis rank sum test". a character string giving the names of the data.


Myles Hollander & Douglas A. Wolfe (1973), Nonparametric statistical inference. 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 one-way location analysis under normality assumptions; with Student's t test (t.test) as the special case for two samples.


## 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.
boxplot(Ozone ~ Month, data = airquality)
kruskal.test(Ozone ~ Month, data = airquality)

[Package stats version 2.2.1 Index]