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 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.
"htest"
containing the following components:
References
Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 139--146.
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)