friedman.test
Friedman Rank Sum Test
Description
Performs a Friedman rank sum test with unreplicated blocked data.
Usage
friedman.test(y, ...) ## Default S3 method: friedman.test(y, groups, blocks, ...) ## S3 method for class 'formula' 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 |
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. |
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 "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 |
data.name | a character string giving the names of the data. |
References
Myles Hollander and Douglas A. Wolfe (1973), Nonparametric Statistical Methods. New York: John Wiley & Sons. Pages 139–146.
See Also
Examples
## 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)
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Licensed under the GNU General Public License.