durbinTest function

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, ...)

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.
• ``: further arguments to be passed to or from methods.

Returns

A list with class "htest" 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: the estimated quantile of the test statistic.
• p.value: the p-value for the test.
• parameter: the parameters of the test statistic, if any.
• alternative: a character string describing the alternative hypothesis.
• estimates: the estimates, if any.
• null.value: the estimate under the null hypothesis, if any.

Details

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$_0: \theta_i = \theta_j ~ (1 \le i < j \le k)$, is tested against the alternative that at least one $\theta_i \ne \theta_j$.

The p-values are computed from the chi-square distribution.

Note

The function does not test, whether it is a true BIBD. This function does not test for ties.

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]))
durbinTest(y)

References

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.