On the Yeh-Bradley conjecture on linear trend-free block designs. (English) Zbl 0799.62084

Chai, Feng-Shun; Majumdar, Dibyen

Ann. Stat. 21, No. 4, 2087-2097 (1993).

Summary: C. M. Yeh and R. A. Bradley [Commun. Stat., Theory Methods 12, 1-24 (1983; Zbl 0523.62071)] conjectured that every binary connected block design with blocks of size \(k\) and a constant replication number \(r\) for each treatment can be converted to a linear trend-free design by permuting the positions of treaments within blocks if and only if \(r(k+1) \equiv 0 \pmod 2\). This conjecture is studied. Results include: (i) the conjecture is true whenever the block size is even and (ii) the conjecture is true for BIB designs.

MSC:

62K10	Statistical block designs
05B05	Combinatorial aspects of block designs

Keywords:

elimination of trend effect; system of distinct representatives; universal optimality; BBD; permutations; binary connected block design; linear trend-free design; BIB designs