PMCMRplus (version 1.9.3)

skillingsMackTest: Skillings-Mack Test

Description

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.

Usage

skillingsMackTest(y, ...)
# S3 method for default
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.

Value

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.

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.

See Also

friedmanTest, durbinTest

Examples

# NOT RUN {
## 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)
# }