Sankhya: The Indian Journal of Statistics

1997, Volume 59, Series B, Pt. 2, 164-180

A-OPTIMAL BLOCK DESIGNS WITH UNEQUAL BLOCK SIZES FOR COMPARING TWO DISJOINT SETS OF TREATMENTS

By

SEEMA JAGGI,

And

V. K. GUPTA, *Indian Agricultural Statistics Research Institute, New Delhi*

SUMMARY. This article studies an experimental setting in which it is desired to compare v1 test treatments with v2 control treatments and the experimental units are arranged in b blocks, where each of the bh blocks contains kh experimental units, h = 1,….., p.Under this setting a general algorithm has been developed to generate A-optimal block designs for making such comparisons , when the block sizes are small and also the sizes do not vary widely. As a particular case the algorithm has been obtained when there are two types of block sizes i.e. k1 = 2 and k2 = 3. Further a sufficient condition is obtained to established the A-optimality of designs when there is no restriction on the block sizes. A method of construction of variance balanced designs with unequal block sizes for comparing treatments belonging to two disjoint sets are given. The A-efficiency of the designs constructed is investigated. A catalogue of such designs for two control treatments alongwith their A-efficiencies is prepared.

*AMS (1991) subject classification.* 62K05, 62K10

*Key words and phrases*. BTDTUB designs, PBIB designs, A-efficiency