ABSTRACT
Blocking is one of the most important principles in experimental design. In this chapter we address the issue of designing complete factorial experiments with incomplete blocks. As the number of factors increases, the total number of treatment combinations soon becomes very large. Two challenges to the experimenter arise. There may not be enough resources or time to run a complete factorial experiment. Second, even if a complete factorial experiment is feasible, incomplete blocks may have to be used since a block accommodating all the treatment combinations may be too large to have acceptable within-block variability, or not all the treatment combinations can be run in the same setting. We focus on the latter issue here and address the former in later chapters. If some factorial effects (for example, the higher-order effects) are deemed less important or are negligible, then one can design an experiment so that these effects are estimated by less precise interblock contrasts. They are said to be confounded with blocks and are sacrificed to achieve better precision for the other more important effects. We also discuss similar issues for row-column designs where some factorial effects are confounded with rows or columns. In split-plot and strip-plot experiments, due to practical considerations, certain main effects must be confounded with blocks, rows, or columns.
