Fractional Replications of [Spu(2)] Factorial Treatment Structures

I n Chapter 8 it was noted that high-order interaction effects are rarelysignificant. Because of this it was shown that one is able to conduct experiments more efficiently by confounding some of the high-order interaction effects with blocking effects. As another consequence of this observation, it is often possible to obtain information about all main effects and low-order interaction effects without even completing a full replication of the factorial experiment, a tremendous advantage for experiments involving large numbers of factors. The only disadvantage in conducting less than a full replicate of a factorial experiment is that many of the main effects and low-order interaction effects will be confounded with high-order interaction effects. But if the higher-order interaction effects rarely exist, then no loss of information about the low-order effects occurs. The design and analysis of these kinds of experiments is the subject of this chapter.