Design of Experiments: An Introduction Based on Linear Models

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ISBN: 9781584889236 | 1584889233
Cover: Hardcover
Copyright: 7/27/2010

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Offering deep insight into the connections between design choice and the resulting statistical analysis, Design of Experiments: An Introduction Based on Linear Models explores how experiments are designed using the language of linear statistical models. The book presents an organized framework for understanding the statistical aspects of experimental design as a whole within the structure provided by general linear models, rather than as a collection of seemingly unrelated solutions to unique problems.

Preface	p. xvii
Introduction	p. 1
Example: rainfall and grassland	p. 1
Basic elements of an experiment	p. 2
Treatments and material	p. 3
Control and comparison	p. 4
Responses and measurement processes	p. 5
Replication, blocking, and randomization	p. 6
Validity and optimality	p. 7
Experiments and experiment-like studies	p. 8
4 Models and data analyst	p. 9
Conclusion	p. 9
Exercises	p. 10
Linear statistical models	p. 13
Linear vector spaces	p. 13
Basic linear model	p. 14
The hat matrix, least-squares estimates, and design information matrix	p. 14
Example	p. 16
The partitioned linear model	p. 18
The reduced normal equations	p. 19
Example	p. 21
Linear and quadratic forms	p. 23
Estimation and information	p. 24
Pure error and lack of fit	p. 26
Hypothesis testing and information	p. 28
8.1 Example	p. 29
Blocking and information	p. 30
Conclusion	p. 31
Exercises	p. 31
Completely randomized designs	p. 37
Introduction	p. 37
Example: radiation and rats	p. 37
Models	p. 38
Graphical logic	p. 40
Matrix formulation	p. 41
Influence of the design on estimation	p. 44
Allocation	p. 45
Overall experiment size	p. 48
Influence of design on hypothesis testing	p. 49
Conclusion	p. 50
Exercises	p. 50
Randomized complete blocks and related designs	p. 55
Introduction	p. 55
Example: structural reinforcement bars	p. 56
A model	p. 57
Graphical logic	p. 58
Matrix formulation	p. 59
Influence of design on estimation	p. 61
Experiment size	p. 63
Influence of design on hypothesis testing	p. 63
Orthogonality and ôCondition Eö	p. 64
Conclusion	p. 67
Exercises	p. 67
Latin squares and related designs	p. 73
Introduction	p. 73
Example: web page links	p. 75
Replicated Latin squares	p. 76
A model	p. 77
Graphical logic	p. 79
Matrix formulation	p. 80
Influence of design on quality of inference	p. 83
More general constructions: Graeco-Latin squares	p. 84
Conclusion	p. 87
Exorcises	p. 87
Some data analysis for CRDs and orthogonally blocked designs	p. 93
Introduction	p. 93
Diagnostics	p. 93
Residuals	p. 93
Modified Levene test	p. 95
General test for lack of fit	p. 96
Tukey one-degree-of-freedom test	p. 97
Power transformations	p. 97
Basic inference	p. 100
Multiple comparisons	p. 100
Tukey intervals	p. 101
Dunnett intervals	p. 102
Simulation based intervals for specific problems	p. 102
Scheffé intervals	p. 103
Numerical example	p. 104
Conclusion	p. 105
Exercises	p. 106
Balanced incomplete block designs	p. 109
Introduction	p. 109
Example: drugs and blood pressure	p. 110
Existence and construction of BIBDS	p. 111
A model	p. 112
Graphical logic	p. 112
Example: dishwashing detergents	p. 113
Matrix formulation	p. 114
Basic analysis: an example	p. 118
Influence of design on quality of inference	p. 119
More general constructions	p. 121
Extended complete block designs	p. 121
Partially balanced incomplete block designs	p. 122
Conclusion	p. 124
Exercises	p. 124
Random block effects	p. 129
Introduction	p. 129
Inter- and intra-block analysis	p. 129
Complete block designs (CBDs) and augmented CBDs	p. 132
Balanced incomplete block designs (BIBDs)	p. 134
Combined estimator	p. 135
Example: dishwashing detergents reprise	p. 136
Why can information be ôrecoveredö?	p. 137
CBD reprise	p. 138
Conclusion	p. 139
Exercises	p. 139
Factorial treatment structure	p. 143
Introduction	p. 143
Example: strength of concrete	p. 144
An overparameterized model	p. 144
Graphical logic	p. 147
Matrix development for the overparameterized model	p. 148
An equivalent, full-rank model	p. 152
Matrix development, for the full-rank model	p. 154
Estimation	p. 155
Partitioning of variability and hypothesis testing	p. 157
Factorial experiments as CRDs, CBDs, LSDs, and BIBDs	p. 159
Model reduction	p. 160
Conclusion	p. 162
Exercises	p. 163
Split-plot designs	p. 167
Introduction	p. 167
Example: strength of fabrics	p. 168
Example: english tutoring	p. 169
SPD(R, B)	p. 169
A model	p. 170
Analysis	p. 171
SPD(B, B)	p. 175
A model	p. 176
Analysis	p. 177
More than two experimental factors	p. 178
More than two strata of experimental units	p. 178
Conclusion	p. 180
Exercises	p. 182
Two-level factorial experiments: basics	p. 187
Introduction	p. 187
Example: bacteria and nuclease	p. 187
Two-level factorial structure	p. 188
Estimation of treatment contrasts	p. 193
Full model	p. 193
Reduced model	p. 193
Examples	p. 195
Testing factorial effects	p. 196
Individual model terms, experiment with replication	p. 196
Multiple model terms, experiments with replication	p. 197
Experiments without replication	p. 197
Additional guidelines for model editing	p. 200
Conclusion	p. 201
Exercises	p. 201
Two-level factorial experiments: blocking	p. 207
Introduction	p. 207
Models	p. 207
Notation	p. 208
Complete blocks	p. 208
Example: gophers and burrow plugs	p. 210
Balanced incomplete block designs (BIBDs)	p. 210
Regular blocks of size 2^f-1	p. 211
Random blocks	p. 214
Partial confounding	p. 215
Regular blocks of size 22^f-2	p. 216
Regular blocks: general case	p. 219
Conclusion	p. 222
Exercises	p. 223
Two-level factorial experiments: fractional factorials	p. 227
Introduction	p. 227
Regular fractional factorial designs	p. 227
Analysis	p. 230
Example: bacteria and bacteriocin	p. 231
Comparison of fractions	p. 231
Resolution	p. 231
Comparing fractions of equal resolution: aberration	p. 233
Blocking regular fractional factorial designs	p. 234
Augmenting regular fractional factorial designs	p. 235
Combining fractions	p. 235
Fold-over designs	p. 237
Blocking combined fractions	p. 239
Irregular fractional factorial designs	p. 240
Conclusion	p. 242
Exercises	p. 243
Factorial group screening experiments	p. 247
Introduction	p. 247
Example: semiconductors and simulation	p. 248
Factorial structure of group screening designs	p. 250
Group screening design considerations	p. 253
Effect cancelling	p. 253
Screening failure	p. 253
Aliasing	p. 254
Screening efficiency	p. 255
Case study	p. 256
Conclusion	p. 257
Exercises	p. 258
Regression experiments: first-order polynomial models	p. 261
Introduction	p. 261
Example: bacteria and elastase	p. 262
Polynomial models	p. 263
Designs for first-order models	p. 264
Two-level designs	p. 264
Simplex designs	p. 265
Blocking experiments for first-order models	p. 266
Split-plot regression experiments	p. 269
Example: bacteria and elastase reprise	p. 269
Diagnostics	p. 271
Use of a center point	p. 271
General test for lack-of-fit	p. 272
Conclusion	p. 276
Exercises	p. 276
Regression experiments: second-order polynomial models	p. 281
Introduction	p. 281
Example: nasal sprays	p. 281
Quadratic polynomial models	p. 282
Designs for second-order models	p. 284
Complete three-level factorial designs	p. 284
Central composite designs	p. 286
Box-Behnken designs	p. 287
Augmented pairs designs	p. 288
Design scaling and information	p. 289
Orthogonal blocking	p. 291
Split-plot designs	p. 292
Example	p. 292
Bias due to omitted model terms	p. 293
Conclusion	p. 296
Exercises	p. 296
Introduction to optimal design	p. 299
Introduction	p. 299
Optimal design fundamentals	p. 299
Optimality criteria	p. 301
A-optimality	p. 301
D-optimality	p. 303
Other criteria	p. 304
Examples	p. 304
Algorithms	p. 309
Conclusion	p. 310
Exercises	p. 311
Calculations using R	p. 313
Solution notes for selected exercises	p. 321
References	p. 341
Index	p. 347
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Design of Experiments: An Introduction Based on Linear Models

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