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Home  >  volume 36 (no1)

Study for Discriminating Non-Trojan Semi-Latin Square Designs Having Twenty Five Treatments in Blocks of Size Five by Ibrahim Yusuf Ibrahim, Abubakar Yahaya and Shehu Bala (Pages 397-400)
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Semi-Latin Square Design (SLSD) is an approach in Statistical Experimental Design under Incomplete Block Design (IBD) aimed at reducing the size of a Complete Block Design (CBD) without necessarily compromising efficiency and better results. In this article, we present two non-Trojan SLSDseach having twenty five treatments in block sizes of five purposely to discriminate between them. These designs were found to have different parameter concurrences, hence the need to distinguish between them and determine which among them should be preferred over the other. This study investigated the contrasts properties and ascertained the “best” design by finding and comparing the variances of elementary contrasts of treatments for the two designs. It was found that, the design newly constructed by this study and denoted asГ_1possesses minimal value of the average variance of elementary treatment contrasts, minimal number of distinct pairwise treatments’ variances as well as minimal values of the minimum and maximum variances when compared with another similar design reported in earlier studiesdenoted asГ_2. Hence, for the purpose of experimentation, Г_1 should be preferred over Г_2.

    Keywords: Elementary Contrasts, Optimal Design, Trojan Designs, Connected Design, Information Matrix, Incomplete-Block Design