Introduction
Blocking is the division of experimental material into blocks or sets of homogeneous experimental units. Proper blocking can control the source of variability which is not of primary interest and thus can reduce the experimental error. If the number of treatments is the same as the block size, a randomized block design can be used. However, if the number of treatments exceeds the block size, an incomplete block design (IBD) should be considered.
An IBD of size (v, k, r) is an arrangement of v treatments set out in b blocks, each of size k( < v) such that each treatment occurs in r blocks where vr = bk and no treatment occurs more than once in any block. The following is an IBD of size (v, k, r) = (4, 2, 3) (Note that all IBDs in this article are displayed with blocks as columns.):
An IBD is said to be r ∕ s-resolvable if the blocks can be divided into sreplicate sets (of blocks) and each set is an IBD of size (v, k, r ∕ s). A 1-resolvable IBD is a resolvable IBD (see the...
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References and Further Reading
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Nguyen, NK., Blagoeva, K.T. (2011). Incomplete Block Designs. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_299
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