friedman.test(y, groups, blocks)
NAs are allowed, but all data
for each block in which at least one element of
y is
NA
will be removed.
Infs are allowed, and are not removed as they are
rankable.
y, giving the group (treatment) for
each corresponding element of
y.
NAs or
Infs are not allowed.
If
groups is not a factor or category object, it will be coerced to one.
y, giving the block membership for
each corresponding element of
y.
NAs and
Infs are not allowed.
If
blocks is not a factor or category object, it will be coerced to one.
y corresponding to each combination of the
levels of
groups and
blocks.
"htest", containing the following components:
names
attribute
"Friedman chi-square". See section DETAILS for a definition.
statistic. Component
parameters has
names attribute
"df".
"two.sided", to reflect that the implicit alternative hypothesis is
two-sided.
y,
groups and
blocks.
In the context of a two-way layout with factors
groups and
blocks, a
typical null hypothesis is that the true location parameter for
y, net of
the
blocks effect, is the
same in each of the
groups. The alternative hypothesis is that it is
different in at least one of the
groups. See Hollander and Wolfe (1973)
for alternate models.
The Friedman test is appropriate for data arising from an unreplicated
complete block design: one in which exactly one observation was collected
from each experimental unit, or block, under each treatment. The elements
of
y are assumed to consist of a
groups effect, plus a
blocks effect,
plus independent and identically distributed residual errors. The interaction
between
groups and
blocks is assumed to be zero.
The returned
p.value should be interpreted carefully. It is only a
large-sample approximation whose validity increases with the number of blocks.
Hollander, M. and Wolfe, D. A. (1973).
Nonparametric Statistical Methods.
New York: John Wiley.
Lehmann, E. L. (1975).
Nonparametrics: Statistical Methods Based on Ranks.
Oakland, Calif.: Holden-Day.
treatments <- factor(rep(c("Trt1", "Trt2", "Trt3"), each=4))
people <- factor(rep(c("Subject1", "Subject2", "Subject3", "Subject4"), 3))
y <- c(0.73,0.76,0.46,0.85,0.48,0.78,0.87,0.22,0.51,0.03,0.39,0.44)
friedman.test(y, treatments, people)
# Now suppose the data is in the form of a matrix, rows are people and
# columns are treatments.
# Generate 'ymat' and the factor objects:
ymat <- matrix(c(0.73,0.76,0.46,0.85,0.48,0.78,0.87,0.22,0.51,
0.03,0.39,0.44), ncol=3)
bl <- factor(as.vector(row(ymat)))
gr <- factor(as.vector(col(ymat)))
friedman.test(ymat, gr, bl) # same answer as above