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AuthorCaliล{132}ski, Tadeusz. author
TitleBlock Designs: A Randomization Approach [electronic resource] : Volume II: Design / by Tadeusz Caliล{132}ski, Sanpei Kageyama
ImprintNew York, NY : Springer New York : Imprint: Springer, 2003
Connect tohttp://dx.doi.org/10.1007/978-1-4419-9246-8
Descript XII, 357 p. online resource

SUMMARY

The book is composed of two volumes, each consisting of five chapters. In Volยญ ume I, following some statistical motivation based on a randomization model, a general theory of the analysis of experiments in block designs has been deยญ veloped. In the present Volume II, the primary aim is to present methods of that satisfy the statistical requirements described in constructing block designs Volume I, particularly those considered in Chapters 3 and 4, and also to give some catalogues of plans of the designs. Thus, the constructional aspects are of predominant interest in Volume II, with a general consideration given in Chapter 6. The main design investigations are systematized by separating the material into two contents, depending on whether the designs provide unit efficiency facยญ tors for some contrasts of treatment parameters (Chapter 7) or not (Chapter 8). This distinction in classifying block designs may be essential from a pracยญ tical point of view. In general, classification of block designs, whether proper or not, is based here on efficiency balance (EB) in the sense of the new termiยญ nology proposed in Section 4. 4 (see, in particular, Definition 4. 4. 2). Most of the attention is given to connected proper designs because of their statistical advantages as described in Volume I, particularly in Chapter 3. When all conยญ trasts are of equal importance, either the class of (v - 1; 0; O)-EB designs, i. e


CONTENT

6 Constructional Approaches and Methods -- 6.0 Basic designs -- 6.1 Dualization -- 6.2 Complementation -- 6.3 Supplementation -- 6.4 Juxtaposition -- 6.5 Merging -- 6.6 Patterned method -- 6.7 Methods of differences -- 6.8 Hadamard matrix -- 6.9 Finite geometry -- 6.10 Orthogonal Latin squares -- 7 Designs with Full Efficiency for Some Contrasts -- 7.1 General consideration -- 7.2 Orthogonal designs -- 7.3 Designs with two efficiency factors -- 7.4 Designs with three efficiency factors -- 7.5 Designs with more efficiency factors -- 8 Designs with No Full Efficiency -- 8.1 General consideration -- 8.2 Designs with one efficiency factor -- 8.3 Designs with two efficiency factors -- 8.4 Designs with three efficiency factors -- 8.5 Designs with more efficiency factors -- 8.6 Tables -- 9 Resolvable Designs -- 9.1 General consideration -- 9.2 Designs with one efficiency factor -- 9.3 Designs with two efficiency factors -- 9.4 Designs with three efficiency factors -- 9.5 Designs with more efficiency factors -- 9.6 Lattice designs -- 9.7 Tables -- 10 Special Designs -- 10.1 Variance-balanced designs -- 10.2 Resistant/Robust designs -- 10.3 Nonbinary designs -- 10.4 Disconnected designs -- Appendix B. Finite Fields -- Appendix C. Finite Geometries -- C.1 Finite projective geometry -- C.2 Finite affine geometry -- C.3 Illustration -- Appendix D. Orthogonal Latin Squares -- References -- Author Index


Statistics Statistics Statistical Theory and Methods



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