Nested balanced incomplete block designs

Abstract

A nested balanced incomplete block design is defined as a design with two systems of blocks, the second nested within the first (each block from the first system containing m blocks from the second), such that ignoring either system leaves a balanced incomplete block design whose blocks are those of the other system. A list is given of such designs having each treatment (or variety) replicated not more than fifteen times. The analysis is given for the general nested balanced incomplete block design; this analysis is an extension of that developed by Yates (1940) for the recovery of inter-block information in balanced incomplete block designs. A design based on a nested balanced incomplete block design was devised by Kleczkowski (1960) for laboratory studies on lesions produced by inoculating bean plants with tobacco necrosis virus.