friedman.test {stats}  R Documentation 
Performs a Friedman rank sum test with unreplicated blocked data.
friedman.test(y, ...)
## Default S3 method:
friedman.test(y, groups, blocks, ...)
## S3 method for class 'formula'
friedman.test(formula, data, subset, na.action, ...)
y 
either a numeric vector of data values, or a data matrix. 
groups 
a vector giving the group for the corresponding
elements of 
blocks 
a vector giving the block for the corresponding
elements of 
formula 
a formula of the form 
data 
an optional matrix or data frame (or similar: see

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 
... 
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:
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 
data.name 
a 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.
## 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)