Skillings-Mack Test
Performs Skillings-Mack rank sum test for partially balanced incomplete block designs or partially balanced random block designs. The null hypothesis H_0: θ_i = θ_j~~(i \ne j) is tested against the alternative H_{\mathrm{A}}: θ_i \ne θ_j, with at least one inequality beeing strict.
skillingsMackTest(y, ...) ## Default S3 method: skillingsMackTest(y, groups, blocks, ...)
y |
a numeric vector of data values, or a list of numeric data vectors. |
groups |
a vector or factor object giving the group for the
corresponding elements of |
blocks |
a vector or factor object giving the block for the
corresponding elements of |
... |
further arguments to be passed to or from methods. |
The function has implemented the test of Skillings and Mack (1981). The test statistic is assymptotically chi-squared distributed with df = k - 1 degrees of freedom.
A list with class "htest"
containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
The input vector/matrix 'y'
must contain NA
.
Skillings, J. H., Mack, G.A. (1981) On the use of a Friedman-type statistic in balanced and unbalanced block designs, Technometrics 23, 171–177.
## Example from Hollander and Wolfe 1999, ## originally appeared in Brady 1969. x <- cbind(c(3,1,5,2,0,0,0,0), c(5,3,4,NA,2,2,3,2), c(15,18,21,6,17,10,8,13)) colnames(x) <- c("R", "A", "B") rownames(x) <- 1:8 skillingsMackTest(x) ## Compare with Friedman Test for CRB ## Sachs, 1997, p. 675 ## Six persons (block) received six different diuretics ## (A to F, treatment). ## The responses are the Na-concentration (mval) ## in the urine measured 2 hours after each treatment. y <- matrix(c( 3.88, 5.64, 5.76, 4.25, 5.91, 4.33, 30.58, 30.14, 16.92, 23.19, 26.74, 10.91, 25.24, 33.52, 25.45, 18.85, 20.45, 26.67, 4.44, 7.94, 4.04, 4.4, 4.23, 4.36, 29.41, 30.72, 32.92, 28.23, 23.35, 12, 38.87, 33.12, 39.15, 28.06, 38.23, 26.65),nrow=6, ncol=6, dimnames=list(1:6, LETTERS[1:6])) print(y) friedmanTest(y) skillingsMackTest(y)
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