Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 351--361

DETERMINATION AND CONSTRUCTION OF A-OPTIONAL DESIGNS FOR COMPARING TWO SETS OF TREATMENTS

By

MIKE JACROUX, *Washington State University*

SUMMARY. In this paper we consider experimental situations in which *t* test treatments are to be compared to *s* controls in *b* blocks of size *k*. A design is said to be A-optimal in such situations if it minimizes the sum of the variances of the least squares estimates for treatment differences between the test treatments and the controls. The conditions given for A-optimality in Majumdar (1986) are extended and somewhat simplified. Examples are also given to demonstrate how the results given here can be applied as well as compared with some corresponding results given in Jacroux (1998).

*AMS (1991) subject classification.* Primary 62K05; secondary 62K10.

*Key words and phrases. *Incidence matrix, two-way additive model,
extended balanced treatment incomplete block design.