Some sufficient conditions for the E- and MV-optimality of block designs having blocks of unequal size

Abstract

SummaryIn this paper we consider experimental situations in which v treatments are to be tested in b blocks where b~ blocks contain k, experimental units, i=1,..., p, kl<k2<... <kp. The idea of a group divisible (GD) design is extended to that of a group divisible design with unequal block sizes (GDUB design) and then a number of results concerning the E-and NIV-optimality of GD designs are generalized to the case of GDUB designs.

A Link Between theE-Value and the Robustness of Block Designs

“…The class of group divisible designs with unequal block sizes (GDUBs) is introduced by Lee and Jacroux (1987) to provide a source of designs with good optimality…”

E-optimality of some row and column designs

“…Let us consider the block design described by Lee and Jacroux (1987). This design is E-optimal in the class ~(10, [2 * 1~o, 4 * 1~5]').…”

C365. Some newE- andMV-optimal group divisible designs with unequal block sizes

“…Note that Algorithm B improves (barely) the observed local nonrandomness owing to the slight reordering of the output ri. Lee and Jacroux (1985) found the conditions for a group divisible design with unequal block sizes to be E-and MV-optimal. Lee and Jacroux (1987) constructed such designs in the range r 4 2 5 , using the table of Clatworthy (1973) for group divisible designs.…”