R: Skillings-Mack Test

skillingsMackTest {PMCMRplus} | R Documentation

## 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: 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.

### Usage

    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.

### 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.

### 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.

### Note

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

### 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

    ## 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)

[Package PMCMRplus version 1.6.1 Index]