Durbin Test
Performs Durbin's tests whether k groups (or treatments) in a two-way balanced incomplete block design (BIBD) have identical effects.
durbinTest(y, ...) ## Default S3 method: durbinTest(y, groups, blocks, ...)
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 |
... |
further arguments to be passed to or from methods. |
For testing a two factorial layout of a balanced incomplete block design whether the k groups have identical effects, the Durbin test can be performed. The null hypothesis, H_0: θ_i = θ_j ~ (1 ≤ i < j ≤ k), is tested against the alternative that at least one θ_i \ne θ_j.
The p-values are computed from the chi-square distribution.
A list with class "htest" containing the following components:
a character string indicating what type of test was performed.
a character string giving the name(s) of the data.
the estimated quantile of the test statistic.
the p-value for the test.
the parameters of the test statistic, if any.
a character string describing the alternative hypothesis.
the estimates, if any.
the estimate under the null hypothesis, if any.
The function does not test, whether it is a true BIBD. This function does not test for ties.
Conover,W. J. (1999) Practical nonparametric Statistics, 3rd. Edition, Wiley.
Heckert, N. A., Filliben, J. J. (2003) NIST Handbook 148: Dataplot Reference Manual, Volume 2: Let Subcommands and Library Functions. National Institute of Standards and Technology Handbook Series, June 2003.
## 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])) durbinTest(y)
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