Download or read book A Calculus for Factorial Arrangements written by Sudhir Gupta and published by Springer Science & Business Media. This book was released on 2012-09-10 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: Factorial designs were introduced and popularized by Fisher (1935). Among the early authors, Yates (1937) considered both symmetric and asymmetric factorial designs. Bose and Kishen (1940) and Bose (1947) developed a mathematical theory for symmetric priIi't&-powered factorials while Nair and Roo (1941, 1942, 1948) introduced and explored balanced confounded designs for the asymmetric case. Since then, over the last four decades, there has been a rapid growth of research in factorial designs and a considerable interest is still continuing. Kurkjian and Zelen (1962, 1963) introduced a tensor calculus for factorial arrangements which, as pointed out by Federer (1980), represents a powerful statistical analytic tool in the context of factorial designs. Kurkjian and Zelen (1963) gave the analysis of block designs using the calculus and Zelen and Federer (1964) applied it to the analysis of designs with two-way elimination of heterogeneity. Zelen and Federer (1965) used the calculus for the analysis of designs having several classifications with unequal replications, no empty cells and with all the interactions present. Federer and Zelen (1966) considered applications of the calculus for factorial experiments when the treatments are not all equally replicated, and Paik and Federer (1974) provided extensions to when some of the treatment combinations are not included in the experiment. The calculus, which involves the use of Kronecker products of matrices, is extremely helpful in deriving characterizations, in a compact form, for various important features like balance and orthogonality in a general multifactor setting.
Download or read book A Calculus for Factorial Arrangements written by Sudhir Gupta and published by . This book was released on 1989-11-01 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A CALCULUS FOR FACTORIAL ARRANGEMENTS written by B. KURKJIAN and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: A special calculus for the analysis of factorial experiments is introduced. The calculus applies to the general case of asymmetric factorial experiments and is not restricted to symmetric factorials as is the current theory which relies on the theory of finite projective geometry. The concise notation and operations of this calculus point up the relationship of treatment combinations to interactions and the effect of patterns of arrangements on the distribution of relevant quantities. One aim is to carry out complex manipulations and operations with relative ease. The calculus enables many large order arithmetic operations, necessary for analyzing factorial designs, to be partly carried out by logical operations. This should be of importance in programming the analysis of factorial designs on high speed computers. (Author).
Download or read book Contributions to the Calculus for Factorial Arrangements written by James Michael Hardin and published by . This book was released on 1985 with total page 830 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Applications of the Calculus of Factorial Arrangements I Block and Direct Product Designs written by Badrig Kurkjian and published by . This book was released on 1962 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper applies an operational calculus for factorial arrangements to the analysis of randomized block, balanced incomplete block, group divisible and many direct product designs. (The theoretical aspects of the calculus were presented Ann. Math. Stat. June 1962.).
Download or read book Applications of the Calculus for Factorial Arrangements written by W. T. Federer and published by . This book was released on 1964 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book APPLICATIONS OF THE CALCULUS FOR FACTORIAL ARRANGEMENTS 3 TWO WAY ELIMINATION OF HETEROGENEITY written by UNITED STATES. DEPARTMENT OF THE ARMY. MATHEMATICS RESEARCH CENTER. and published by . This book was released on with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book APPLICATIONS OF THE CALCULUS FOR FACTORIAL ARRANGEMENTS 2 UNEQUAL NUMBERS IN THE ANALYSIS OF VARIANCE written by UNITED STATES. DEPARTMENT OF THE ARMY. MATHEMATICS RESEARCH CENTER. and published by . This book was released on with total page 39 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Application of the Calculus for Factorial Arrangements Arbitrary Block Designs written by and published by . This book was released on 1972 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: A unified method of analysis for factorial arrangements in block designs has been developed for arbitrary block designs. The main results shown here an easy way to determine the degrees of freedom for treatments, a systematic approach to find a set of estimable effects, and, in the factorial case, a method to determine which effects are confounded with blocks or aliased with other effects.
Download or read book Applications of the Calculus for Factorial Arrangements Iii Two Way Elimination of Heterogeneity written by M. Zelen and published by . This book was released on 1963 with total page 29 pages. Available in PDF, EPUB and Kindle. Book excerpt: The special notation and operations are presented as developed by Kurkjian and Zelen (1962, Ann. Math. Statist. 33, 600-619) to problems in experimental design. This paper considers general methods for the analysis and construction of designs having two-way elimination of heterogeneity. The general methods of analysis allow for incomplete row balance as well as incomplete blocks (columns) with respect to the treatments. New designs are constructed by taking the direct product of the row and column incidence matrices of two designs. (Author).
Download or read book Applications of the Calculus for Factorial Arrangements Ii Unequal Numbers in the Analysis of Variance written by W. T. Federer and published by . This book was released on 1964 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper develops a new theory for the analysis of disproportionate numbers of observations in multi-factor classifications. The principal theoretical result enables a generalized sum of squares in the analysis of variance to be written explicitly. Use of this result leads to minimum calculations compared to other methods now in general use. A numerical example is presented illustrating the calculations. (Author).
Download or read book Factorial Designs written by B. L. Raktoe and published by John Wiley & Sons. This book was released on 1981 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Preliminaries and notation. Some facets of fatorial design. Orthogonal polynomial model and estimation of its parameters. Constraints and criteria in Characterization of unbiased designs. Resolution and confounding in factorial designs. On orthogonality and balancedness of factorial designs. Resolution and confounding in factorial designs. On orthogonality and balancedness of factorial designs. Randomized factorial designs and regular factorial designs. Factorial designs of resolution III. Factorial designs of resolutions IV and V. Search factorial designs. Some know methods for constructing factorial designs.
Download or read book Fractional Factorial Plans written by Aloke Dey and published by John Wiley & Sons. This book was released on 2009-09-25 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: A one-stop reference to fractional factorials and relatedorthogonal arrays. Presenting one of the most dynamic areas of statistical research,this book offers a systematic, rigorous, and up-to-date treatmentof fractional factorial designs and related combinatorialmathematics. Leading statisticians Aloke Dey and Rahul Mukerjeeconsolidate vast amounts of material from the professionalliterature--expertly weaving fractional replication, orthogonalarrays, and optimality aspects. They develop the basic theory offractional factorials using the calculus of factorial arrangements,thereby providing a unified approach to the study of fractionalfactorial plans. An indispensable guide for statisticians inresearch and industry as well as for graduate students, FractionalFactorial Plans features: * Construction procedures of symmetric and asymmetric orthogonalarrays. * Many up-to-date research results on nonexistence. * A chapter on optimal fractional factorials not based onorthogonal arrays. * Trend-free plans, minimum aberration plans, and search andsupersaturated designs. * Numerous examples and extensive references.
Download or read book Journal of Research of the National Bureau of Standards written by United States. National Bureau of Standards and published by . This book was released on 1963 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Modern Theory of Factorial Design written by Rahul Mukerjee and published by Springer Science & Business Media. This book was released on 2007-01-15 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last twenty years have witnessed a significant growth of interest in optimal factorial designs, under possible model uncertainty, via the minimum aberration and related criteria. This book gives, for the first time in book form, a comprehensive and up-to-date account of this modern theory. Many major classes of designs are covered in the book. While maintaining a high level of mathematical rigor, it also provides extensive design tables for research and practical purposes. Apart from being useful to researchers and practitioners, the book can form the core of a graduate level course in experimental design.
Download or read book Cyclic Designs written by J. A. John and published by Springer. This book was released on 2013-11-11 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biggest single influence on the development of the subject of design of experiments over the past quarter-century has been the availability of computers. Prior to the computer it was essential that any design had a straightforward method of analysis, which meant that the mathematical and combinatorial properties of the designs were of primary importance. Many of the designs proposed and studied also possessed important statistical properties and thus continue to be practically useful but, now that ease of analysis is less important, a very large number of these designs no longer have any real value. With the advent ofthe computer it has become possible to study families of designs which have relatively simple methods of construction and which provide large numbers of designs. Within a family, the designs which satisfy certain desirable statistical, rather than mathematical, properties can then be identified using a combin ation of theory and computing. One of the primary aims of this monograph is to study families of block and row-column designs, both unifactor and multifactor, whose methods of construction are cyclical in nature; hence the title Cyclic Designs. The usual practice adopted in books on the design of experiments is to follow the description of a particular design by its method of analysis and, possibly, a numerical example.
Download or read book Design and Analysis of Experiments Volume 2 written by Klaus Hinkelmann and published by John Wiley & Sons. This book was released on 2005-05-13 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development and introduction of new experimental designs in the last fifty years has been quite staggering, brought about largely by an ever-widening field of applications. Design and Analysis of Experiments, Volume 2: Advanced Experimental Design is the second of a two-volume body of work that builds upon the philosophical foundations of experimental design set forth by Oscar Kempthorne half a century ago and updates it with the latest developments in the field. Designed for advanced-level graduate students and industry professionals, this text includes coverage of incomplete block and row-column designs; symmetrical, asymmetrical, and fractional factorial designs; main effect plans and their construction; supersaturated designs; robust design, or Taguchi experiments; lattice designs; and cross-over designs.
