All-Pairs Comparisons Test for Balanced Incomplete Block Designs
Performs Conover-Iman all-pairs comparison test for a balanced incomplete block design (BIBD).
durbinAllPairsTest(y, ...) ## Default S3 method: durbinAllPairsTest(y, groups, blocks, p.adjust.method = p.adjust.methods, ...)
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 |
blocks |
a vector or factor object 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. |
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}: θ_i = θ_j is tested in the two-tailed test against the alternative A_{ij}: θ_i \ne θ_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.
A list with class "PMCMR" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
lower-triangle matrix of the estimated quantiles of the pairwise test statistics.
lower-triangle matrix of the p-values for the pairwise tests.
a character string describing the alternative hypothesis.
a character string describing the method for p-value adjustment.
a data frame of the input data.
a string that denotes the test distribution.
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.
## 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)
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