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Full-Text Articles in Physical Sciences and Mathematics
Nearly Balanced And Resolvable Block Designs, Brian Henry Reck
Nearly Balanced And Resolvable Block Designs, Brian Henry Reck
Mathematics & Statistics Theses & Dissertations
One of the fundamental principles of experimental design is the separation of heterogeneous experimental units into subsets of more homogeneous units or blocks in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given v treatments to compare, and having available b blocks of k experimental units each, the thoughtful statistician asks, “What is the optimal allocation of the treatments to the units?” This is the basic block design problem. Let nij be the number of times treatment i is used in block j and let N be the v x b matrix N …
Optimality And Construction Of Designs With Generalized Group Divisible Structure, Sudesh K. Srivastav
Optimality And Construction Of Designs With Generalized Group Divisible Structure, Sudesh K. Srivastav
Mathematics & Statistics Theses & Dissertations
This thesis is an investigation of the optimality and construction problems attendant to the assignment of v treatments to experimental units in b blocks of size k, paying special attention to settings for which equal replication of the treatments is not possible. The model is that of one way elimination of heterogeneity, in which the expectation of an observation on treatment i in block j is Ti + βj (treatment effect + block effect), where Ti and βj are unknown constants, 1 ≤ i ≤ v and 1 ≤ j ≤ b. All observations are assumed to …