Physical Sciences and Mathematics Commons^™

Nested Balanced Incomplete Block Designs, J. P. Morgan, D. A. Preece, D. H. Rees

Mathematics & Statistics Faculty Publications

If the blocks of a balanced incomplete block design (BIBD) with v treatments and with parameters (v; b₁;r;k₁) are each partitioned into sub-blocks of size k₂, and the b₂ =b₁k₁=k2 sub-blocks themselves constitute a BIBD with parameters (v; b₂;r;k₂), then the system of blocks, sub-blocks and treatments is, by de4nition, a nested BIBD (NBIBD). Whist tournaments are special types of NBIBD with k₁ =2k₂= 4. Although NBIBDs were introduced in the statistical literature in 1967 and have subsequently received occasional attention there, …