Friedman Rank Sum Test

Performs a Friedman rank sum test with unreplicated blocked data.

friedman.test(y, ...)

## S3 method for class 'default': friedman.test(y, groups, blocks, \dots)

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

either a numeric vector of data values, or a data matrix.
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.
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.
a formula of the form a ~ b | c, where a, b and c give the data values and corresponding groups and blocks, respectively.
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).
an optional vector specifying a subset of observations to be used.
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.

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.


  • A list with class "htest" containing the following components:
  • statisticthe value of Friedman's chi-squared statistic.
  • parameterthe degrees of freedom of the approximate chi-squared distribution of the test statistic.
  • p.valuethe p-value of the test.
  • methodthe character string "Friedman rank sum test".
  • data.namea character string giving the names of the data.


Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 139--146.

See Also


  • friedman.test
  • friedman.test.default
  • friedman.test.formula
library(stats) ## 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 package stats, version 3.3, License: Part of R 3.3

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