A Complete Class of Type 1 Optimal Block Designs with Unequal Replications

Article Type

Research Article

Publication Title

Journal of Statistical Theory and Practice


For block designs comparing v treatments in b incomplete blocks of size k, consider settings where bk = vr + 1 and r(k- 1 ) = λ(v- 1) for integers r and λ. These settings admit designs that possess the symmetry of balanced incomplete block designs and which, though nonbinary, are candidates for optimality in some standard senses. For k = 3, earlier authors have established a class of one binary and one nonbinary design that is complete with respect to all type 1 optimality criteria. Here a solution for the complete class problem for type 1 optimality is obtained for k = 5. The complete class includes two binary and two nonbinary designs.



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