# kruskal.test

##### Kruskal-Wallis Rank Sum Test

Performs a Kruskal-Wallis rank sum test.

- Keywords
- htest

##### Usage

`kruskal.test(x, …)`# S3 method for default
kruskal.test(x, g, …)

# S3 method for formula
kruskal.test(formula, data, subset, na.action, …)

##### Arguments

- 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.

##### Details

`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`

.

##### Value

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.

##### 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
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.

##### Examples

`library(stats)`

```
# 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)
# }
```

*Documentation reproduced from package stats, version 3.6.0, License: Part of R 3.6.0*