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Showing 1 to 19 of 19 for “"Incomplete block designs"”.
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Inter-block analysis of incomplete block designs
… large number of balanced and partially balanced incomplete block designs, certain ones have been found which lend themselves nicely to interblock analysis. Besides facilitating this analysis, these designs make possible the use of a new method for studying the relative variability of the inter …
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A characterization of the circularity of certain balanced incomplete block designs.
… We devote a chapter to the use of circular designs in coding theory. It is proven that these structures are not useful in the theory of error-correcting codes, since more efficient codes are known, for example the Reed-Muller codes. However, the theory developed in the earlier chapters does …
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Two-group comparisons in the rank analysis of incomplete block designs
The purpose of this work was to investigate certain two-group comparisons within a paired comparison experimental design.
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Combined intra- and inter-block analysis for factorials in incomplete block designs
… Kramer and Bradley on the use of factorials in incomplete block designs bas been extended to permit both the intra-block and combined intra- and inter-block analyses of factorials in balanced and partially balanced incomplete block designs. In particular, we have obtained a combined intra- and …
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Optimal Row-Column Designs for Correlated Errors and Nested Row-Column Designs for Uncorrelated Errors
… optimality conditions are derived separately for designs in the plane and on the torus using more general linear models than those considered elsewhere in the literature. Examples of universally optimum planar designs are given, and a method is developed for the construction of optimum and near …
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Optimality and Construction of Designs with Generalized Group Divisible Structure
… 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 <em>i</em> in …
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Nearly Balanced and Resolvable Block Designs
… into subsets of more homogeneous units or <em>blocks</em> in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given <em>v</em> treatments to compare, and having available <em>b</em> blocks of <em>k</em> experimental units each, the …
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Delineamento experimental em blocos incompletos : estudo de casos particulares
… dos planos com repetições (BIBDR) - Balanced Incomplete Block Designs with Repeated Blocks (Planos em Blocos Incompletos Equilibrados com Repetições). A construção dos (BIBD) - Balanced Incomplete Block Designs com Repetições (BIBDR) é abordada como um Plano Otimal que proporciona facilidade …
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Cyclic Designs
Cyclic designs are incomplete block designs consisting of sets of blocks where in each set successive blocks are obtained in a cyclic manner from the first block of the set. It is convenient to label the objects (treatments) by the integers 0, 1, …, n-. Then if for a particular set the first block …
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Optimal Blocking for Three Treatments and BIBD Robustness - Two Problems in Design Optimality
… matrix). The other is construction of designs satisfying those conditions. Most papers deal with either optimality conditions, or design construction in accordance with desired combinatorial properties, but not both. This dissertation determines optimal designs for three treatments in …
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Bicircular Matroids with Circuits of at Most Two Sizes
Young in his paper titled, Matroid Designs in 1973, reports that Murty in his paper titled, Equicardinal Matroids and Finite Geometries in 1968, was the first to study matroids with all hyperplanes having the same size. Murty called such a matroid an ``Equicardinal Matroid''. Young renamed such a …
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Structures and properties of repeated measurement designs
… and properties of repeated measurement (RM) designs are investigated from different points of view, such as (i) balancedness or partial balancedness, (ii) construction versus estimation, (iii) underlying linear models, (iv) factorial treatment structure. In studying balanced repeated …
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αₙ-Designs
This thesis defines a broad class of resolvable incomplete block designs for multifactor experiments, called αₙ-designs. A general methodology for their construction is described and is shown to be a natural extension of the method used by Patterson and Williams (1976) in their construction of …
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General Weighted Optimality of Designed Experiments
… weighted information, ultimately targeting those designs that efficiently estimate effects assigned larger weight. This dissertation considers a much broader class of potential weighting systems, and hence weighted criteria, by allowing W to be any symmetric, positive definite matrix. Assuming the …
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Recovery of interblock information
… best linear combination of the intra- and inter-block estimates is Intra-estimatexInter-variance+Inter-estimatexIntra-variance / Intra-variance + Inter-variance ; however, this combined estimate is merely theoretical, since we do not know in practice the exact inter- and intra-variances. A …
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Construction and properties of Box-Behnken designs
Box-Behnken designs are used to estimate parameters in a second-order response surface model (Box and Behnken, 1960). These designs are formed by combining ideas from incomplete block designs (BIBD or PBIBD) and factorial experiments, specifically 2<sup>k</sup> full or 2<sup>k-1</sup> fractional …
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Tópicos de planeamento de experiências : uma abordagem estatística, computacional e matemática
… Randomized Design. Also to consider, are the Block Designs, detailing the Balanced Incomplete Block Designs, and inside, the symmetrical one’s. Finally is described all the Designs based in Squares, such as Latin Squares, Graeco-Latin Squares and Youden Squares, presenting their relations. The …
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Tests of significance for experiments involving paired comparisons
… be extended to ranking experiments in balanced incomplete block designs with more than two treatments per block. To test the null hypothesis of no interaction between preference probabilities and repetitions, against its general alternative, a test method based on the theory of X² homogeneity …