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 data frame containing the variables in the model 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 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)