PMCMR (version 4.0)

posthoc.durbin.test: 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, ...)
## S3 method for class 'default':
posthoc.durbin.test(y, groups, blocks,
p.adjust.method = p.adjust.methods, \dots)

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.

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.

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.

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")