Some useful classes of minimal weakly balanced neighbor designs in circular blocks of two different sizes

Muhammad Rasheed, Khadija Noreen, Rashid Ahmed, M. H. Tahir and Farrukh Jamal

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 24, 8822-8839

Abstract: Neighbor designs (NDs) are used to balance out the neighbor effects. Among these designs, minimal NDs are economical, therefore, these are preferred by experimenters. Unfortunately, minimal NDs cannot be constructed for all combinations of v (number of treatments) and k (block sizes). Minimal weakly balanced NDs (WBNDs) are recommended in the situations where minimal NDs could not be constructed. In this article, some generators are developed to obtain minimal circular WBNDs (MCWBNDs) in blocks of two different sizes. In our proposed designs, 3v/2 unordered pairs of distinct treatments appear twice as neighbors while all other pairs appear once. In these designs, we lose [300/(v−1)]% neighbor balance while saving at least [50(v−4)/(v−1)]% experimental material.

Date: 2022
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DOI: 10.1080/03610926.2021.1975135

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