# 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

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 |

`blocks` |
a vector giving the block for the corresponding elements
of |

`p.adjust.method` |
Method for adjusting p values
(see |

`...` |
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

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")
``` |

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