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Full-Text Articles in Physical Sciences and Mathematics
Nested Balanced Incomplete Block Designs, J. P. Morgan, D. A. Preece, D. H. Rees
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, …