The Application of Algebraic Methods in Balanced Incomplete Block ...

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The Application of Algebraic Methods in Balanced Incomplete Block ...

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Jun 14, 2018 - A balanced incomplete block design contains finite set P with v ... In certain experiments using randomized block design (RBD), we may not be ...

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The Application of Algebraic Methods in Balanced Incomplete Block Design To cite this article: Muhammad Abdy and Wahida Sanusi 2018 J. Phys.: Conf. Ser. 1028 012123

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2nd International Conference on Statistics, Mathematics, Teaching, and Research IOP Publishing IOP Conf. Series: Journal of Physics: Conf. Series 1028 (2018) 1234567890 ‘’“” 012123 doi:10.1088/1742-6596/1028/1/012123

The Application of Algebraic Incomplete Block Design

Methods

in

Balanced

Muhammad Abdy* and Wahida Sanusi Department of Mathematics, FMIPA Universitas Negeri Makassar, Indonesia [email protected] Abstract. A balanced incomplete block design contains finite set P with v elements called varieties and a collection of set B consisting of b sets called blocks to qualify: (i). each block contains k varieties, (ii). Each variety occurs in every r blocks, (iii). Each pair of varieties occurs in exactly  block. In this paper we discuss the use of algebraic method to construct such designs. Keywords— Algebraic, BIBD

1. Introduction In certain experiments using randomized block design (RBD), we may not be able to run all treatment combinations in each block. Situations like this usually occur because of shortages experimental equipment or facilities or the physical size of the block. To solve this problem, we can use a randomized block design where each treatment does not need to exist in every block. The design is known as balanced incomplete block design (BIBD). If all treatment comparisons are equally important, the treatment combinations used in each block should be selected in a balanced manner, so that any pair of treatments occur together the same number of times as any other pair. Thus, a BIBD is an incomplete block design in which any two treatments appear together an equal number of times. Suppose that there are a treatments and each block can hold exactly k (k