R: Posthoc Durbin test

posthoc.durbin.test {PMCMR} | R Documentation

## Posthoc Durbin test

### Description

Pairwise post-hoc test for multiple comparisons of rank sums according to Durbin and Conover for a two-way balanced incomplete block design (BIBD).

### Usage

    posthoc.durbin.test(y, ...)

    ## Default S3 method:
     posthoc.durbin.test(y, groups, blocks,
    p.adjust.method = p.adjust.methods, ...)

### Arguments

`y` | either a numeric vector of data values, or a data matrix.
`groups` | a vector giving the group for the corresponding elements of `y` if this is a vector; ignored if `y` is a matrix. If not a factor object, it is coerced to one.
`blocks` | a vector giving the block for the corresponding elements of `y` if this is a vector; ignored if `y` is a matrix. If not a factor object, it is coerced to one.
`p.adjust.method` | Method for adjusting p values (see `p.adjust`).
`...` | further arguments to be passed to or from methods.

### Details

In the case of an two-way balanced incomplete block design, the Durbin test, `durbin.test` can be employed. The H0 is rejected, if at least one group (treatment) is significantly different. The pairwise multiple comparisons are conducted with this function. The `posthoc.durbin.test` is equivalent to the `posthoc.friedman.conover.test` in the case of a two-way balanced complete block design.

If y is a matrix, than the columns refer to the groups (treatment) and the rows indicate the block.

The statistics refer to the student-t-distribution (`TDist`).

See `vignette("PMCMR")` for details.

### Value

A list with class `"PMCMR"`

`method` | The applied method.
`data.name` | The name of the data.
`p.value` | The two-sided p-value according to the student-t-distribution.
`statistic` | The estimated quantiles of the student-t-distribution.
`p.adjust.method` | The applied method for p-value adjustment.

### Note

The function does not test, whether it is a true BIBD.

This function does not test for ties.

### Author(s)

Thorsten Pohlert

### References

W. J. Conover and R. L. Iman (1979), On multiple-comparisons procedures, Tech. Rep. LA-7677-MS, Los Alamos Scientific Laboratory.

W. J. Conover (1999), Practical nonparametric Statistics, 3rd. Edition, Wiley.

### See Also

`durbin.test`, `friedman.test`, `posthoc.friedman.nemenyi.test`, `posthoc.friedman.conover.test`, `TDist` `p.adjust`

### Examples

    ## Example for an incomplete block design:
    ## Data from Conover (1999, p. 391).
    y <- matrix(c(
    2,NA,NA,NA,3, NA,  3,  3,  3, NA, NA, NA,  3, NA, NA,
      1,  2, NA, NA, NA,  1,  1, NA,  1,  1,
    NA, NA, NA, NA,  2, NA,  2,  1, NA, NA, NA, NA,
      3, NA,  2,  1, NA, NA, NA, NA,  3, NA,  2,  2
    ), ncol=7, nrow=7, byrow=FALSE,
    dimnames=list(1:7, LETTERS[1:7]))
    y
    durbin.test(y)
    posthoc.durbin.test(y, p.adj="none")

    ## Example for a complete block design:
    ## 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)
    friedman.test(y)
    durbin.test(y)
    posthoc.durbin.test(y, p.adj="none")
    posthoc.friedman.conover.test(y, p.adj="none")

[Package PMCMR version 4.2 Index]