# kruskal.test

##### Kruskal-Wallis Rank Sum Test

Performs a Kruskal-Wallis rank sum test.

- Keywords
- htest

##### Usage

`kruskal.test(x, ...)`## S3 method for class 'default':
kruskal.test(x, g, \dots)

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

##### 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: 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"`

.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
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
*conditional* p-values, including in the presence of ties.

##### Examples

`library(stats)`

```
## 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 3.3, License: Part of R 3.3*