skillingsMackTest() R function from [PMCMRplus]

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 $_0: \theta_i = \theta_j~~(i \ne j)$ is tested against the alternative H $_{\mathrm{A}}: \theta_i \ne \theta_j$ , with at least one inequality beeing strict.


skillingsMackTest(y, ...)

## Default S3 method:
skillingsMackTest(y, groups, blocks, ...)

Arguments

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 "x". Ignored with a warning if "x" is a list.
blocks: a vector or factor object giving the block for the corresponding elements of "x". Ignored with a warning if "x" is a list.
``: further arguments to be passed to or from methods.

Returns

A list with class "htest" containing the following components:

method: a character string indicating what type of test was performed.
data.name: a character string giving the name(s) of the data.
statistic: the estimated quantile of the test statistic.
p.value: the p-value for the test.
parameter: the parameters of the test statistic, if any.
alternative: a character string describing the alternative hypothesis.
estimates: the estimates, if any.
null.value: the estimate under the null hypothesis, if any.

Details

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.

Note

The input vector/matrix 'y' must contain NA.

Examples


## 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)

References

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.

skillingsMackTest function