# friedman.test {stats}

### Description

Performs a Friedman rank sum test with unreplicated blocked data.

### Usage

friedman.test(y, ...) ## S3 method for class 'default': friedman.test((y, groups, blocks, ...)) ## S3 method for class 'formula': friedman.test((formula, data, subset, na.action, ...))

### Arguments

- y
- either a numeric vector of data values, or a data matrix.
- groups
- a vector giving the group for the corresponding elements of
`y`

if this is a vector; ignored if`y`

is a matrix. If not a factor object, it is coerced to one. - blocks
- a vector giving the block for the corresponding elements of
`y`

if this is a vector; ignored if`y`

is a matrix. If not a factor object, it is coerced to one. - formula
- a formula of the form
`a ~ b | c`

, where`a`

,`b`

and`c`

give the data values and corresponding groups and blocks, respectively. - 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

`friedman.test`

can be used for analyzing unreplicated complete block designs (i.e., there is exactly one observation in `y`

for each combination of levels of `groups`

and `blocks`

) where the normality assumption may be violated.

The null hypothesis is that apart from an effect of `blocks`

, the location parameter of `y`

is the same in each of the `groups`

.

If `y`

is a matrix, `groups`

and `blocks`

are obtained from the column and row indices, respectively. `NA`

's are not allowed in `groups`

or `blocks`

; if `y`

contains `NA`

's, corresponding blocks are removed.

### Values

A list with class `"htest"`

containing the following components:

- statistic
- the value of Friedman's chi-squared 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
`"Friedman 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 139--146.

### See Also

### Examples

## Hollander & Wolfe (1973), p. 140ff. ## Comparison of three methods ("round out", "narrow angle", and ## "wide angle") for rounding first base. For each of 18 players ## and the three method, the average time of two runs from a point on ## the first base line 35ft from home plate to a point 15ft short of ## second base is recorded. RoundingTimes <- matrix(c(5.40, 5.50, 5.55, 5.85, 5.70, 5.75, 5.20, 5.60, 5.50, 5.55, 5.50, 5.40, 5.90, 5.85, 5.70, 5.45, 5.55, 5.60, 5.40, 5.40, 5.35, 5.45, 5.50, 5.35, 5.25, 5.15, 5.00, 5.85, 5.80, 5.70, 5.25, 5.20, 5.10, 5.65, 5.55, 5.45, 5.60, 5.35, 5.45, 5.05, 5.00, 4.95, 5.50, 5.50, 5.40, 5.45, 5.55, 5.50, 5.55, 5.55, 5.35, 5.45, 5.50, 5.55, 5.50, 5.45, 5.25, 5.65, 5.60, 5.40, 5.70, 5.65, 5.55, 6.30, 6.30, 6.25), nrow = 22, byrow = TRUE, dimnames = list(1 : 22, c("Round Out", "Narrow Angle", "Wide Angle"))) friedman.test(RoundingTimes) ## => strong evidence against the null that the methods are equivalent ## with respect to speed wb <- aggregate(warpbreaks$breaks, by = list(w = warpbreaks$wool, t = warpbreaks$tension), FUN = mean) wb friedman.test(wb$x, wb$w, wb$t) friedman.test(x ~ w | t, data = wb)

Documentation reproduced from R 3.0.2. License: GPL-2.