Some useful classes of minimal weakly balanced neighbor designs in circular blocks of two different sizes. Issue 24 (17th December 2022)

• Record Type: Journal Article
• Authors: Rasheed, Muhammad; Noreen, Khadija; Ahmed, Rashid; Tahir, M. H.; Jamal, Farrukh
• Is Part Of: Communications in statistics. Volume 51:Issue 24(2022)
• Page Start: 8822
• Page End: 8839
• Publication Date: 2022-12-17
• Subjects: Direct effects -- neighbor effects -- minimal designs -- minimal neighbor designs; 05B05 -- 62K10 -- 62K05; Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2021.1975135
• Languages: English
• ISSNs: 0361-0926

Abstract

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, 3 v /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.