Durbin test is a non-parametric statistical test for balanced incomplete designs that reduces to the Friedman test in the case of a complete block design. In the analysis of designed experiments, the Friedman test is the most common non-parametric test for complete block designs.

In a randomized block design, k treatments are applied to b blocks. In a complete block design, every treatment is run for every block and the data are arranged as follows:

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:

The Durbin test is based on the following assumptions:

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

The Durbin test is then

The test statistic is

where