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, …)

x

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.

g

a vector or factor object giving the group for the
corresponding elements of `x`

. Ignored with a warning if
`x`

is a list.

formula

a formula of the form `response ~ group`

where
`response`

gives the data values and `group`

a vector or
factor of the corresponding groups.

data

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)`

.

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 `NA`

s. 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) # }