Multiphase experiments with at least one later laboratory phase. II. Nonorthogonal designs

Principles and laws that apply to nonorthogonal multiphase experiments are developed and illustrated using examples that are nonorthogonal but structure-balanced, not structure, but first-order, balanced or unbalanced, thus exposing the differences between the different design types. The design of such experiments using standard designs, a catalogue of designs and computer searches is exemplified. Factor–allocation diagrams are employed to depict the allocations in the examples, and used in producing the anatomies of designs or, when possible, the related skeleton-analysis-of-variance tables, to assess the properties of designs. The formulation of mixed models based on them is also described. Tools used for structure-balanced experiments are also shown to be applicable to those experiments that are not.