The Theory of the Design of Experiments

The Theory of the Design of Experiments
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3 يناير 2022
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The Theory of the Design of Experiments
Honorary Fellow
Nuffield College
Oxford, UK
Professor of Statistics
University of Toronto, Canada
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 simplified 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 variation3.8 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 effects 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 Nonspecific 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 design7.7 Space-filling 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 effort
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 fields
B.4 Finite geometries
B.5 Difference 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 Chapter 3
C.4 Analysis of block designs in Chapter 4C.5 Examples from Chapter 5
C.6 Examples from Chapter 6
C.7 Bibliographic notes
List of tables

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