Experimentation order in factorial designs with 8 or 16 runs

Abstract

Randomizing the order of experimentation in a factorial design does not always achieve the desired effect of neutralizing the influence of unknown factors. In fact, with some very reasonable assumptions, an important proportion of random orders afford the same degree of protection as that obtained by experimenting in the design matrix standard order. In addition, randomization can induce a big number of changes in factor levels and thus make experimentation expensive and difficult. This paper discusses this subject and suggests experimentation orders for designs with 8 or 16 runs that combine an excellent level of protection against the influence of unknown factors, with the minimum number of changes in factor levels.

Keywords:

• Randomization
• experimentation order
• factorial design
• bias protection
• minimum number of level changes

Acknowledgements

The authors would like to thank Alberto Luceño (Universidad de Cantabria), Tony Greenfield (Greenfield Research) and Frøydis Bjerke (Matforsk) for their helpful comments on an earlier draft of this paper, and also the referee for catching our mistakes and making useful comments.