On construction of constant block-sum partially balanced incomplete block designs |
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Authors: | Ravindra Khattree |
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Institution: | 1. Department of Mathematics and Statistics, Co-Director, Center for Data Science and Big Data Analytics, and Participating Member, Center for Biomedical Research, Oakland University, Rochester, Michigan, USAkhattree@oakland.edu |
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Abstract: | AbstractConstant block-sum designs are of interest in repeated measures experimentation where the treatments levels are quantitative and it is desired that at the end of the experiments, all units have been exposed to the same constant cumulative dose. It has been earlier shown that the constant block-sum balanced incomplete block designs do not exist. As the next choice, we, in this article, explore and construct several constant block-sum partially balanced incomplete block designs. A natural choice is to first explore these designs via magic squares and Parshvanath yantram is found to be especially useful in generating designs for block size 4. Using other techniques such as pair-sums and, circular and radial arrangements, we generate a large number of constant block-sum partially balanced incomplete block designs. Their relationship with mixture designs is explored. Finally, we explore the optimization issues when constant block-sum may not be possible for the class of designs with a given set of parameters. |
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Keywords: | Circular Designs Constant Block-Sum Designs Group Divisible Designs Magic Circles Magic Squares Mixture Experiments Parshvanath Yantram Partially Balanced Incomplete Block Designs Reuse of Experimental Units or Animals |
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