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Construction of Congruent Classes of Pairwise Balanced Design Using Lotto Design

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  • Popoola, Osuolale Peter

Abstract

Balanced Incomplete Block Designs (BIBDs) are commonly used when the number of experimental treatments is less than the block size. However, there are cases when the block sizes available for an experiment are not the same. Hence the use of a Pairwise Balanced Design (PBD). A PBD (n, K, λ) is a block design where n is the number of treatments, K= {k1, k2…, kb} is the set of sizes of a block, and λ is the number of times a pair of treatments appears together within blocks. Also, little is known about the construction of PBDs using Lotto Designs (LDs). Methods of constructing PBDs in literature are complex. The aim of this study, therefore, was to provide a simple method for constructing PBDs when K= {3, 4} and {3, 4, 5}. The specific objectives were to: (i) investigate various methods of constructing PBDs (ii) establish conditions for the identification of LDs that qualify as PBDs, and (iii) provide a simple method for constructing two classes of PBDs from LDs; The study utilized Li’s inequality ⌊pr/(t-1)⌋((t-1)¦2)+((pr-⌊pr/(t-1)⌋)¦( 2) (t-1))

Suggested Citation

  • Popoola, Osuolale Peter, 2019. "Construction of Congruent Classes of Pairwise Balanced Design Using Lotto Design," EconStor Theses, ZBW - Leibniz Information Centre for Economics, number 268718, September.
    • Handle: RePEc:zbw:esthes:268718
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    References listed on IDEAS

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    1. Kageyama, Sanpei, 1988. "Existence of variance-balanced binary designs with fewer experimental units," Statistics & Probability Letters, Elsevier, vol. 7(1), pages 27-28, July.
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