Durbin test
Description
The omnibus test according to Durbin tests whether k groups (or treatments) in a twoway balanced incomplete block design (BIBD) have identical effects.
Usage
1 2 3 4 5 6 7 8 9  durbin.test(y, ...)
## Default S3 method:
durbin.test(y, groups, blocks,
...)
## S3 method for class 'formula'
durbin.test(formula, data, subset,
na.action, ...)

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 
formula 
a formula of the form 
data 
an optional matrix or data frame (or similar: see

subset 
an optional vector specifying a subset of observations to be used. 
na.action 
a function which indicates what should happen when
the data contain 
... 
further arguments to be passed to or from methods. 
Details
The friedman.test
can be used to test k groups (treatments) for
identical effects in a twoway balanced complete
block design. In the case of an twoway balanced incomplete block
design, the Durbin test
can be employed. The H0 is rejected, if at least one group (treatment) is
significantly different. The Durbin test is equivalent to the Friedman test in
the case of a twoway balanced complete block design.
If y is a matrix, than the columns refer to the groups (treatment) and the rows indicate the block.
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 pvalue according to the studentized range distribution. 
statistic 
The estimated upper quantile of the studentized range distribution. 
p.adjust.method 
Defaults to "none" 
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 (1999), Practical nonparametric Statistics, 3rd. Edition, Wiley.
N. A. Heckert and J. J. Filliben (2003). NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions. National Institute of Standards and Technology Handbook Series, June 2003.
See Also
friedman.test
,
posthoc.durbin.test
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  ## 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)
## 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 Naconcentration (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)

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