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A Simple Construction Procedure for Eesolvable Incomplete Block Designs for any Number of Treatments
Author(s) -
Khare Meena,
Federer W. T.
Publication year - 1981
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710230203
Subject(s) - block (permutation group theory) , mathematics , combinatorics , simple (philosophy) , prime (order theory) , zero (linguistics) , discrete mathematics , philosophy , linguistics , epistemology
A simple, straightforward procedure, which requires no special tables or generators, is presented for constructing resolvable incomplete block designs for v=pk , v=p 2 k, …, treatments, for k ≥ p , in incomplete blocks of size k. Also, it is shown, how to obtain incomplete block designs for any v in blocks of size k and k +1. The procedure allows construction of balanced incomplete block designs for p = k a prime number. For p = n not a prime number, incomplete block designs can be obtained by the procedure, but are not balanced. However, for p s being the smallest prime factor of n, p s + 1 for v = n 2 , p s 2 + p s + 1 for v = n 3 , …, arrangements can be obtained for which the occurrence of any treatment pair in the blocks is either zero or one. This is called a zero‐one concurrence design. Procedures are described for obtaining additional zero‐one concurrence arrangements. It is shown that the efficiency of these designs is maximum. Both intra‐block and inter‐block analyses are described.