The treatments used in any experiment will be dictated by the objectives of the study and in some experiments, there may be a large number of treatments of interest.

In multi-factor experiments, it may be impractical to use all combinations of factor levels — if there are many factors or each has several levels, the required number of experimental units may be too great.

More often, there are more experimental units than treatments, but we group them into blocks(in order to minimise unexplained variation. If each block is too small for all treatments, the randomised block designs in the previous chapter cannot be used.

This chapter first explores the consequences of missing treatments in blocks of experimental units (or overall). It then presents some good incomplete designs that can be used with small blocks and/or large numbers of treatments..