friedman.test
Friedman Rank Sum Test
Performs a Friedman rank sum test with unreplicated blocked data.
 Keywords
 htest
Usage
friedman.test(y, ...)
"friedman.test"(y, groups, blocks, ...)
"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 ify
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 ify
is a matrix. If not a factor object, it is coerced to one.  formula
 a formula of the form
a ~ b  c
, wherea
,b
andc
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 formulaformula
. By default the variables are taken fromenvironment(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 togetOption("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.
Value

A list with class
 statistic
 the value of Friedman's chisquared statistic.
 parameter
 the degrees of freedom of the approximate chisquared distribution of the test statistic.
 p.value
 the pvalue of the test.
 method
 the character string
"Friedman rank sum test"
.  data.name
 a character string giving the names of the data.
"htest"
containing the following components:
References
Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 139146.
See Also
Examples
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)