Block Designs: A Randomization Approach

Volume II: Design

Tadeusz Calinski, Sanpei Kageyama (Autoren)

Buch | Softcover

357 Seiten

2002 | 2003 ed.
Springer-Verlag New York Inc.
978-0-387-95470-7 (ISBN)

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The book is composed of two volumes, each consisting of five chapters. In Vol ume I, following some statistical motivation based on a randomization model, a general theory of the analysis of experiments in block designs has been de 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 fac tors for some contrasts of treatment parameters (Chapter 7) or not (Chapter 8). This distinction in classifying block designs may be essential from a prac 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 termi 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 con trasts are of equal importance, either the class of (v - 1; 0; O)-EB designs, i. e.

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.

Erscheint lt. Verlag	31.10.2002
Reihe/Serie	Lecture Notes in Statistics ; 170
Zusatzinfo	XII, 357 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-95470-8 / 0387954708
ISBN-13	978-0-387-95470-7 / 9780387954707
Zustand	Neuware