ABSTRACT
To this point, we have discussed experiments that are executed to understand differences among a finite set of treatments. In some cases, all treatments in this set are included in the experiment; this is true of all experiments for “unstructured” treatments (Chapters 3-8), and for full factorial experiments, either blocked or unblocked (Chapters 9-12). In contrast, fractional factorial designs (Chapter 13) do not include all treatments from the set. The consequence of incomplete experimentation is that treatment effects cannot be uniquely estimated unless additional assumptions can be made that effectively eliminate some model parameters. For example, regular fractional factorial experiments support estimation of effect strings – linear combinations of aliased effects – under the complete factorial model; they allow estimation of individual effects only under the assumption of a reduced model including no more than one effect in each aliased group. For treatment sets of finite size, the choice between an experiment that includes all treatments and an experiment that does not requires balancing of experimental costs and prior knowledge about the system under study. Experiments that include all treatments generally cost more than those that do not, but may be unnecessary if higher-order factorial effects are reasonably assumed to be negligible.
