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Optimal blocked main effects plans with nested rows and columns and related designs. (English) Zbl 0862.62065

Summary: Optimal design is studied for factorial experiments in the nested row and column setting. The approach is analogous to that of orthogonal Latin squares: main effects plans are found by the superimposition of one nested row and column design upon another. Conditions are stated for statistical orthogonality of the superimposed components, resulting in orthogonal main effects plans, and a number of constructions are given. Orthogonal collections of sets of Latin squares are introduced. All of the constructed designs are also optimal main effects plans for the row-column and the unstructured block design settings. Further applications are as optimal multidimensional incomplete block designs and as optimal designs for multistage experimentation.

MSC:

62K05 Optimal statistical designs
62K15 Factorial statistical designs
62K10 Statistical block designs
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