| 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 y if this is a vector; ignored if y
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 if y
is a matrix. If not a factor object, it is coerced to one. |
formula |
a formula of the form a ~ b | c, where a,
b and c 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
formula formula. By default the variables are taken from
environment(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 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:
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. |
Myles Hollander & Douglas A. Wolfe (1973), Nonparametric statistical inference. 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),
nr = 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)