Posthoc Durbin test

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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

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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

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## 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")