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El. knyga: Statistical Principles for the Design of Experiments: Applications to Real Experiments

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(University of Reading), (University of Warwick), (University of Southampton)
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This book is about the statistical principles behind the design of effective experiments and focuses on the practical needs of applied statisticians and experimenters engaged in design, implementation and analysis. Emphasising the logical principles of statistical design, rather than mathematical calculation, the authors demonstrate how all available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from real experiments in medicine, industry, agriculture and many experimental disciplines. Numerous exercises are given to help the reader practise techniques and to appreciate the difference that good design can make to an experimental research project. Based on Roger Mead's excellent Design of Experiments, this new edition is thoroughly revised and updated to include modern methods relevant to applications in industry, engineering and modern biology. It also contains seven new chapters on contemporary topics, including restricted randomisation and fractional replication.

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Focuses on the practical needs of applied statisticians and experimenters engaged in design, implementation and analysis in various disciplines.
Preface xi
Part I Overture
1 Introduction
3(6)
1.1 Why a statistical theory of design?
3(1)
1.2 History, computers and mathematics
4(1)
1.3 The influence of analysis on design
5(1)
1.4 Separate consideration of units and treatments
6(1)
1.5 The resource equation
7(2)
2 Elementary ideas of blocking: the randomised complete block design
9(20)
2.1 Controlling variation between experimental units
9(3)
2.2 The analysis of variance identity
12(6)
2.3 Estimation of variance and the comparison of treatment means
18(4)
2.4 Residuals and the meaning of error
22(2)
2.5 The random allocation of treatments to units
24(2)
2.6 Practical choices of blocking patterns
26(3)
3 Elementary ideas of treatment structure
29(13)
3.1 Choice of treatments
29(1)
3.2 Factorial structure
29(1)
3.3 Models for main effects and interactions
30(3)
3.4 The analysis of variance identity
33(3)
3.5 Interpretation of main effects and interactions
36(2)
3.6 Advantages of factorial structure
38(2)
3.7 Treatment effects and treatment models
40(2)
4 General principles of linear models for the analysis of experimental data
42(65)
4.1 Introduction and some examples
42(1)
4.2 The principle of least squares and least squares estimators
43(3)
4.3 Properties of least squares estimators
46(3)
4.4 Overparameterisation, constraints and practical solution of least squares equations
49(6)
4.5 Subdividing the parameters; extra SS
55(5)
4.6 Distributional assumptions and inferences
60(2)
4.7 Contrasts, treatment comparisons and component SS
62(4)
4.8 Covariance -- extension of linear design models
66(13)
4.9 Computers for analysing experimental data
79(28)
Appendix to
Chapter 4
87(1)
4.A2 Least squares estimators for linear models
87(1)
4.A3 Properties of least squares estimators
88(2)
4.A4 Overparameterisation and constraints
90(4)
4.A5 Partitioning the parameter vector and the extra SS principle
94(2)
4.A6 Distributional assumptions and inferences
96(4)
4.A7 Treatment comparisons and component SS
100(2)
4.A8 The general theory of covariance analysis
102(5)
Part II First subject
5 Experimental units
107(17)
5.0 Preliminary examples
107(2)
5.1 Different forms of basic experimental units
109(4)
5.2 Experimental units as collections
113(2)
5.3 A part as the unit and sequences of treatments
115(3)
5.4 Multiple levels of experimental units
118(2)
5.5 Time as a factor and repeated measurements
120(1)
5.6 Protection of units, randomisation restrictions
121(3)
6 Replication
124(18)
6.0 Preliminary example
124(1)
6.1 The need for replication
124(1)
6.2 The completely randomised design
125(3)
6.3 Different levels of variation
128(4)
6.4 Identifying and allowing for different levels of variation
132(4)
6.5 How much replication?
136(6)
7 Blocking and control
142(40)
7.0 Preliminary examples
142(1)
7.1 Design and analysis for very simple blocked experiments
143(3)
7.2 Design principles in blocked experiments
146(7)
7.3 The analysis of block-treatment designs
153(6)
7.4 BIB designs and classes of less balanced designs
159(5)
7.5 Orthogonality, balance and the practical choice of design
164(9)
7.6 Experimental designs for large-scale variety trials
173(9)
8 Multiple blocking systems and cross-over designs
182(36)
8.0 Preliminary examples
182(1)
8.1 Latin square designs and Latin rectangles
182(4)
8.2 Multiple orthogonal classifications and sequences of experiments
186(2)
8.3 Row-and-column designs with more treatments than replicates
188(11)
8.4 Three-dimensional designs
199(2)
8.5 The practical choice of row-and-column design
201(3)
8.6 Cross-over designs -- time as a blocking factor
204(3)
8.7 Cross-over designs for residual or interaction effects
207(11)
9 Multiple levels of information
218(15)
9.0 Preliminary examples
218(1)
9.1 Identifying multiple levels in data
218(2)
9.2 The use of multiple levels of information
220(7)
9.3 Random effects and mixed models
227(2)
9.4 Analysis of multiple level data using REML
229(1)
9.5 Multiple blocking systems
230(3)
10 Randomisation
233(23)
10.1 What is the population?
233(1)
10.2 Random treatment allocation
234(2)
10.3 Randomisation tests
236(5)
10.4 Randomisation theory of the analysis of experimental data
241(5)
10.5 Practical implications of the two theories of analysis of experimental data
246(2)
10.6 Practical randomisation
248(8)
11 Restricted randomisation
256(19)
11.0 Preliminary example
256(1)
11.1 Time-trend resistant run orders and designs
256(1)
11.2 Modelling spatial variation
257(3)
11.3 Neighbour balance
260(1)
11.4 Advantages and disadvantages of restricting randomisation
261(2)
11.5 Ignoring blocking in the data analysis
263(1)
11.6 Covariance or blocking
264(2)
11.7 Sequential allocation of treatments in clinical trials
266(9)
Part III Second subject
12 Experimental objectives, treatments and treatment structures
275(30)
12.0 Preliminary examples
275(1)
12.1 Different questions and forms of treatments
275(2)
12.2 Comparisons between treatments
277(5)
12.3 Presentation of results
282(1)
12.4 Qualitative or quantitative factors
283(6)
12.5 Treatment structures
289(5)
12.6 Incomplete structures and varying replication
294(4)
12.7 Treatments as a sample
298(1)
12.8 Screening and selection experiments
299(6)
13 Factorial structure and particular forms of effects
305(29)
13.0 Preliminary example
305(1)
13.1 Factors with two levels only
305(5)
13.2 Improved yield comparisons in terms of effects
310(5)
13.3 Analysis by considering sums and differences
315(4)
13.4 Factors with three or more levels
319(5)
13.5 The use of only a single replicate
324(3)
13.6 Analysis of unreplicated factorials
327(7)
14 Fractional replication
334(29)
14.0 Preliminary examples
334(1)
14.1 The use of a fraction of a complete factorial experiment
335(1)
14.2 Half-replicates of 2n factorials
336(4)
14.3 Simple fractions for factors with more than two levels
340(5)
14.4 Smaller fractions for 2n structures
345(4)
14.5 Irregular fractions for 2n structures
349(4)
14.6 Other fractions for three-level factors and for mixed levels
353(6)
14.7 Very small fractions for main effect estimation
359(4)
15 Incomplete block size for factorial experiments
363(62)
15.0 Preliminary examples
363(1)
15.1 Small blocks and many factorial combinations
363(7)
15.2 Factors with a common number of levels
370(5)
15.3 Incompletely confounded effects
375(3)
15.4 Partial confounding
378(11)
15.5 Confounding for general block size and factor levels
389(7)
15.6 The negative approach to confounding for two-level factors
396(6)
15.7 Confounding theory for other factorial structures
402(10)
15.8 Confounding in fractional replicates
412(5)
15.9 Confounding in row-and-column designs
417(8)
16 Quantitative factors and response functions
425(23)
16.0 Preliminary examples
425(1)
16.1 The use of response functions in the analysis of data
425(4)
16.2 Design objectives
429(1)
16.3 Specific parameter estimation
430(7)
16.4 Optimal design theory
437(2)
16.5 Discrimination
439(1)
16.6 Designs for competing criteria
440(3)
16.7 Systematic designs
443(5)
17 Multifactorial designs for quantitative factors
448(27)
17.0 Preliminary examples
448(1)
17.1 Experimental objectives
448(3)
17.2 Response surface designs based on factorial treatment structures
451(5)
17.3 Prediction properties of response surface designs
456(4)
17.4 Lack of fit and confirmatory runs
460(1)
17.5 Blocking response surface designs
461(3)
17.6 Experiments with mixtures
464(4)
17.7 Non-linear response surfaces
468(7)
18 Split-unit designs
475(38)
18.0 Preliminary examples
475(1)
18.1 The practical need for split units
475(7)
18.2 Advantages and disadvantages of split-unit designs
482(2)
18.3 Extensions of the split-unit idea
484(9)
18.4 Identification of multiple strata designs
493(3)
18.5 Systematic treatment variation within main units
496(2)
18.6 The split-unit design as an example of confounding
498(4)
18.7 Non-orthogonal split-unit designs
502(4)
18.8 Linked experiments
506(7)
Part IV Coda
19 Multiple experiments and new variation
513(15)
19.1 The need for additional variation
513(1)
19.2 Planned replication of experiments
514(7)
19.3 Introducing additional factors in experiments
521(2)
19.4 Practical context experiments
523(2)
19.5 Combined experimental analysis
525(3)
20 Sequential aspects of experiments and experimental programmes
528(10)
20.1 Experimentation is sequential
528(1)
20.2 Using prior information in designing experiments
529(1)
20.3 Sequences of experiments in selection programmes
530(2)
20.4 Sequences of experiments in screening programmes
532(1)
20.5 Sequences of experiments in pharmaceutical trials
532(2)
20.6 Sequential nature within clinical trials
534(1)
20.7 Sequences of experiments in response optimisation
535(2)
20.8 Continuous on-line experimentation
537(1)
0 Designing useful experiments
538(27)
0.0 Some more real problems
538(1)
0.1 Design principles or practical design
539(1)
0.2 Resources and experimental units
540(2)
0.3 Treatments and detailed objectives
542(3)
0.4 The resource equation and the estimation of the error variance
545(1)
0.5 The marriage of resources and treatments
546(5)
0.6 Three particular problems
551(7)
0.7 Computer design packages and catalogues of designs
558(7)
References 565(3)
Index 568
R. Mead is Emeritus Professor of Applied Statistics at the University of Reading. S. G. Gilmour is Professor of Statistics in the Southampton Statistical Sciences Research Institute at the University of Southampton. A. Mead is Senior Teaching Fellow in the School of Life Sciences at the University of Warwick.
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