The Theory of the Design of Experiments
D.R. COXHonorary Fellow
Nuffield College
Oxford, UK AND N. REID Professor of Statistics University of Toronto, Canada
Preface
1 Some general concepts
1.1 Types of investigation
1.2 Observational studies
1.3 Some key terms
1.4 Requirements in design
1.5 Interplay between design and analysis
1.6 Key steps in design
1.7 A simpli ed model
1.8 A broader view
1.9 Bibliographic notes
1.10 Further results and exercises
2 Avoidance of bias
2.1 General remarks
2.2 Randomization
2.3 Retrospective adjustment for bias
2.4 Some more on randomization
2.5 More on causality
2.6 Bibliographic notes
2.7 Further results and exercises
3 Control of haphazard variation
3.1 General remarks
3.2 Precision improvement by blocking
3.3 Matched pairs
3.4 Randomized block design
3.5 Partitioning sums of squares
3.6 Retrospective adjustment for improving precision
3.7 Special models of error variation
3.8 Bibliographic notes
3.9 Further results and exercises
4 Specialized blocking techniques
4.1 Latin squares
4.2 Incomplete block designs
4.3 Cross-over designs
4.4 Bibliographic notes
4.5 Further results and exercises
5 Factorial designs: basic ideas
5.1 General remarks
5.2 Example
5.3 Main e ects and interactions
5.4 Example: continued
5.5 Two level factorial systems
5.6 Fractional factorials
5.7 Example
5.8 Bibliographic notes
5.9 Further results and exercises
6 Factorial designs: further topics
6.1 General remarks
6.2 Confounding in 2k designs
6.3 Other factorial systems
6.4 Split plot designs
6.5 Nonspeci c factors
6.6 Designs for quantitative factors
6.7 Taguchi methods
6.8 Conclusion
6.9 Bibliographic notes
6.10 Further results and exercises
7 Optimal design
7.1 General remarks
7.2 Some simple examples
7.3 Some general theory
7.4 Other optimality criteria
7.5 Algorithms for design construction
7.6 Nonlinear design
7.7 Space- lling designs
7.8 Bayesian design
7.9 Optimality of traditional designs
7.10 Bibliographic notes
7.11 Further results and exercises
8 Some additional topics
8.1 Scale of e ort
8.2 Adaptive designs
8.3 Sequential regression design
8.4 Designs for one-dimensional error structure
8.5 Spatial designs
8.6 Bibliographic notes
8.7 Further results and exercises
A Statistical analysis
A.1 Introduction
A.2 Linear model
A.3 Analysis of variance
A.4 More general models; maximum likelihood
A.5 Bibliographic notes
A.6 Further results and exercises
B Some algebra
B.1 Introduction
B.2 Group theory
B.3 Galois elds
B.4 Finite geometries
B.5 Di erence sets
B.6 Hadamard matrices
B.7 Orthogonal arrays
B.8 Coding theory
B.9 Bibliographic notes
B.10 Further results and exercises
C Computational issues
C.1 Introduction
C.2 Overview
C.3 Randomized block experiment from Chapter3
C.4 Analysis of block designs in Chapter 4
C.5 Examples from Chapter 5
C.6 Examples from Chapter 6
C.7 Bibliographic notes
References
List of tables
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