Further Developments

Abstract

In Chapters 5 and 6, two systematic approaches were described for the construction of factorial designs with OFS controlling the interaction efficiences. It is also possible to start with a q₁ × q₂ ×... ×q _n factorial design, d₀, and then to construct an m₁× m₂ ×... × m _n factorial design, d, by deletion or merging of treatment labels in d₀. Even though the resulting design d may not have OFS, it is reasonable to anticipate that the properties of d₀ in terms of the estimation of the interaction contrasts will influence those of d. These aspects will be taken up in the next two sections. In Section 8.4, some efficiency and admissibility results, in the context of factorial designs in general, are considered. Finally, in the concluding section we briefly indicate possible applications of the calculus for factorial arrangements to some other areas.