Sankhya: The Indian Journal of Statistics

2002, Volume 64, Series B, Pt. 2, 162--178

BLOCK DESIGNS FOR ASYMMETRIC PARALLEL LINE ASSAYS

By

FENG-SHUN CHAI, Academia Sinica, Taipei, Taiwan

SUMMARY. psi$-designs for bioassays are obtained for the general asymmetric cases when the block sizes are possibly different. This is done by establishing a link between trend-free block designs and block designs for bioassays. A $\psi$-design (see Gupta and Mukerjee (1996)) for bioassay is a block design for asymmetric parallel line assays, which estimates $\psi _p,\; \psi _1$ and $\psi ^1_1$ with full information. With the help of the relation, we obtain (i) necessary and sufficient conditions for the existence of a $\psi$-design with unequal block sizes; ~(ii) a complete method of construction of $\psi$-designs.

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

Key words and phrases. Trend-free block designs, parallel line assays, preparation contrast, combined regression contrast, parallelism contrast.

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