25 Nested designs

Abstract

This chapter will explore the practical motivation for, optimality requirements of, and combinatorial assignment properties in, experimental situations with nested blocking factors. Blocking is thus a means of isolating identifiable and unwanted, but unavoidable, variation in experimental material. Nesting of blocks is either because of inherent qualities of the experimental material, or is imposed on the units by the experimental procedure. Resolvability is the most widely studied and employed variation on nesting in block designs. Nested balanced incomplete block designs, in which both the nesting blocks and the sub-blocks form balanced incomplete block design (BIBDs), are the obvious immediate generalizations of resolvable BIBDs to settings in which the nesting blocks cannot accommodate all of the treatments. If the nesting factor is called “blocks,” and the two crossed factors within the nest are called “rows” and “columns,” then each block is recognizable as the setting for a row-column design. The row and column designs with contiguous replicates constitute a class of designs exhibiting crossing and multiple nests in the block structure.