Durbin Test

A Durbin Test is a nonparametric statistical test for balanced incomplete designed experiments.

• See: Statistical Test, Friedman Test , Analysis of Variance, One-way Analysis of Variance, Van der Waerden Test, Cochran's Q Test.

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References

2016

• (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/Durbin_test Retrieved 2016-08-21
  • In the analysis of designed experiments, the Friedman test is the most common non-parametric test for complete block designs. The Durbin test is a nonparametric test for balanced incomplete designs that reduces to the Friedman test in the case of a complete block design.

(...) For some experiments, it may not be realistic to run all treatments in all blocks, so one may need to run an incomplete block design. In this case, it is strongly recommended to run a balanced incomplete design. A balanced incomplete block design has the following properties:

1. Every block contains k experimental units.
2. Every treatment appears in r blocks.
3. Every treatment appears with every other treatment an equal number of times.

• Test assumptions: The Durbin test is based on the following assumptions:

1. The b blocks are mutually independent. That means the results within one block do not affect the results within other blocks.
2. The data can be meaningfully ranked (i.e., the data have at least an ordinal scale).

• Test definition: Let R(X_ij) be the rank assigned to X_ij within block i (i.e., ranks within a given row). Average ranks are used in the case of ties. The ranks are summed to obtain

[math]\displaystyle{ R_j = \sum_{i=1}^b R(X_{ij}) }[/math]

The Durbin test is then

1. H₀: The treatment effects have identical effects
2. H_a: At least one treatment is different from at least one other treatment

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