durbinAllPairsTest {PMCMRplus}

All-Pairs Comparisons Test for Balanced Incomplete Block Designs

Description

Performs Conover-Iman all-pairs comparison test for a balanced incomplete block design (BIBD).

Usage

durbinAllPairsTest(y, ...)

## Default S3 method:
durbinAllPairsTest(y, groups, blocks, p.adjust.method = p.adjust.methods, ...)

Arguments

y

a numeric vector of data values, or a list of numeric data vectors.

groups

a vector or factor object giving the group for the corresponding elements of "x". Ignored with a warning if "x" is a list.

blocks

a vector or factor object giving the block for the corresponding elements of "x". Ignored with a warning if "x" is a list.

p.adjust.method

method for adjusting p values (see p.adjust)

...

further arguments to be passed to or from methods.

Details

For all-pairs comparisons in a balanced incomplete block design the proposed test of Conover and Imam can be applied. A total of m = k(k-1)/2 hypotheses can be tested. The null hypothesis H_{ij}: \theta_i = \theta_j is tested in the two-tailed test against the alternative A_{ij}: \theta_i \ne \theta_j, ~~ i \ne j.

The p-values are computed from the t distribution. If no p-value adjustment is performed (p.adjust.method = "none"), than a simple protected test is recommended, i.e. the all-pairs comparisons should only be applied after a significant durbinTest. However, any method as implemented in p.adjust.methods can be selected by the user.

Value

A list with class "PMCMR" containing the following components:

method

a character string indicating what type of test was performed.

data.name

a character string giving the name(s) of the data.

statistic

lower-triangle matrix of the estimated quantiles of the pairwise test statistics.

p.value

lower-triangle matrix of the p-values for the pairwise tests.

alternative

a character string describing the alternative hypothesis.

p.adjust.method

a character string describing the method for p-value adjustment.

model

a data frame of the input data.

dist

a string that denotes the test distribution.

References

Conover, W. J., Iman, R. L. (1979) On multiple-comparisons procedures, Tech. Rep. LA-7677-MS, Los Alamos Scientific Laboratory.

Conover, W. J. (1999) Practical nonparametric Statistics, 3rd. Edition, Wiley.

See Also

durbinTest

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]))
durbinAllPairsTest(y)