Nonparametric Statistical Methods, 3rd Edition

7.8 A Distribution-Free Test for General Alternatives for Data From an Arbitrary Incomplete Block Design (Skillings–Mack)

Not every set of data resulting from less than a randomized complete block design satisfies the necessary constraints (see Section 7.6) to be analyzed by the Durbin–Skillings–Mack procedure for balanced incomplete block designs. In this section we present a general procedure for analyzing data from a two-way layout where there are either zero or one observation for each treatment–block combination but where there is not necessarily any nice pattern to the particular combinations for which we do not have observations. Such an incomplete data configuration could, of course, be intentionally designed this way, but it could also be the consequence of missing observations from an experiment that was intended to yield data for a randomized complete block design.

For this general two-way layout setting, let denote the number of treatments for which an observation is present in block , for . (If for block , we remove that block from the analysis. Therefore, throughout ...