# posthoc.durbin.test: Posthoc Durbin test In PMCMR: Calculate Pairwise Multiple Comparisons of Mean Rank Sums

## 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

 ```1 2 3 4 5``` ```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.

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.

`durbin.test`, `friedman.test`, `posthoc.friedman.nemenyi.test`, `posthoc.friedman.conover.test`, `TDist` `p.adjust`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31``` ```## 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") ```