Abstract
There exists a set of designs which form a subclass of semi-Latin rectangles. These designs, besides being semi-Latin rectangles, exhibit an additional property of balance; where no two distinct pairs of symbols (treatments) differ in their concurrences, that is, each pair of distinct treatments concur a constant number of times in the design. Such a design exists for a limited set of parameter combinations. We designate it a balanced semi-Latin rectangle (BSLR) and give some properties, and necessary conditions for its existence. Furthermore, algorithms for constructing the design for experimental situations where there are two treatments in each row-column intersection (block) are also given.
Original language | English |
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Article number | 51 |
Number of pages | 11 |
Journal | Journal of Statistical Theory and Practice |
Volume | 14 |
Issue number | 3 |
Early online date | 8 Jul 2020 |
DOIs | |
Publication status | Published - Sept 2020 |
Keywords
- Balanced incomplete block design (BIBD)
- Balanced semi-Latin rectangle (BSLR)
- Optimal design
- Quotient block design (QBD)
- Regular-graph design (RGD)