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Design of experiments : an introduction based on linear models / Max Morris. — London : Chapman & Hall, 2011. – (51.727/M877) |
Contents
Contents
Preface
1 Introduction
1.1 Example: rainfall and grassland
1.2 Basic elements of an experiment
1.3 Experiments and experiment-like studies
1.4 Models and data analysis
1.5 Conclusion
1.6 Exercises
2 Linear statistical models
2.1 Linear vector spaces
2.2 Basic linear model
2.3 The hat matrix， least-squares estimates， and design information matrix
2.4 The partitioned linear model
2.5 The reduced normal equations
2.6 Linear and quadratic forms
2.7 Estimation and information
2.8 Hypothesis testing and information
2.9 Blocking and information
2.10 Conclusion
2.11 Exercises
3 Completely randomized designs
3.1 Introduction
3.2 Models
3.3 Matrix formulation
3.4 Influence of the design on estimation
3.5 Influence of design on hypothesis testing
3.6 Conclusion
3.7 Exercises
4 Randomized complete blocks and related designs
4.1 Introduction
4.2 A model
4.3 Matrix formulation
4.4 Influence of design on estimation
4.5 Influence of design on hypothesis testing
4.6 Orthogonality and "Condition E"
4.7 Conclusion
4.8 Exercises
5 Latin squares and related designs
5.1 Introduction
5.2 Replicated Latin squares
5.3 A model
5.4 Matrix formulation
5.5 Influence of design on quality of inference
5.6 More general constructions: Graeco-Latin squares
5.7 Conclusion
5.8 Exercises
6 Some data analysis for CRDs and orthogonally blocked designs
6.1 Introduction
6.2 Diagnostics
6.3 Power transformations
6.4 Basic inference
6.5 Multiple comparisons
6.6 Conclusion
6.7 Exercises
7 Balanced incomplete block designs
7.1 Introduction
7.2 A model
7.3 Matrix formulation
7.4 Influence of design on quality of inference
7.5 More general constructions
7.6 Conclusion
7.7 Exercises
8 Random block effects
8.1 Introduction
8.2 Inter- and intra-block analysis
8.3 Complete block designs (CBDs) and augmented CBDs
8.4 Balanced incomplete block designs (BIBDs)
8.5 Combined estimator
8.6 Why can information be "recovered"?
8.7 CBD reprise
8.8 Conclusion
8.9 Exercises
9 Factorial treatment structure
9.1 Introduction
9.2 An overparameterized model
9.3 An equivalent full-rank model
9.4 Estimation
9.5 Partitioning of variability and hypothesis testing
9.6 Factorial experiments as CRDs， CBDs， LSDs， and BIBDs
9.7 Model reduction
9.8 Conclusion
9.9 Exercises
10 Split-plot designs
10.1 Introduction
10.2 SPD(R，B)
10.3 SPD(B，B)
10.4 More than two experimental factors
10.5 More than two strata of experimental units
10.6 Conclusion
10.7 Exercises
11 Two-level factorial experiments: basics
11.1 Introduction
11.2 Example: bacteria and nuclease
11.3 Two-level factorial structure
11.4 Estimation of treatment contrasts
11.5 Testing factorial effects
11.6 Additional guidelines for model editing
11.7 Conclusion
11.8 Exercises
12 Two-level factorial experiments: blocking
12.1 Introduction
12.2 Complete blocks
12.3 Balanced incomplete block designs (BIBDs)
12.4 Regular blocks of size 2f 1
12.5 Regular blocks of size 2f-2
12.6 Regular blocks: general case
12.7 Conclusion
12.8 Exercises
13 Two-level factorial experiments: fractional factorials
13.1 Introduction
13.2 Regular fractional factorial designs
13.3 Analysis
13.4 Example: bacteria and bacteriocin
13.5 Comparison of fractions
13.6 Blocking regular fractional factorial designs
13.7 Augmenting regular fractional factorial designs
13.8 Irregular fractional factorial designs
13.9 Conclusion
13.10 Exercises
14 Factorial group screening experiments
14.1 Introduction
14.2 Example: semiconductors and simulation
14.3 Factorial structure of group screening designs
14.4 Group screening design considerations
14.5 Case study
14.6 Conclusion
14.7 Exercises
15 Regression experiments: first-order polynomial models
15.1 Introduction
15.2 Polynomial models
15.3 Designs for first-order models
15.4 Blocking experiments for first-order models
15.5 Split-plot regression experiments
15.6 Diagnostics
15.7 Conclusion
15.8 Exercises
16 Regression experiments: second-order polynomial models
16.1 Introduction
16.2 Quadratic polynomial models
16.3 Designs for second-order models
16.4 Design scaling and information
16.5 Orthogonal blocking
16.6 Split-plot designs
16.7 Bias due to omitted model terms
16.8 Conclusion
16.9 Exercises
17 Introduction to optimal design
17.1 Introduction
17.2 Optimal design fundamentals
17.3 Optimality criteria
17.4 Algorithms
17.5 Conclusion
17.6 Exercises
Appendix A: Calculations using R
Appendix B: Solution notes for selected exercises
References
Index
