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Design of Experiments : An Introduction Based on Linear Models - Max Morris

Design of Experiments

An Introduction Based on Linear Models

Hardcover Published: 27th July 2010
ISBN: 9781584889236
Number Of Pages: 376

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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.

The core material can be found in the first thirteen chapters. These chapters cover a review of linear statistical models, completely randomized designs, randomized complete blocks designs, Latin squares, analysis of data from orthogonally blocked designs, balanced incomplete block designs, random block effects, split-plot designs, and two-level factorial experiments. The remainder of the text discusses factorial group screening experiments, regression model design, and an introduction to optimal design. To emphasize the practical value of design, most chapters contain a short example of a real-world experiment. Details of the calculations performed using R, along with an overview of the R commands, are provided in an appendix.

This text enables students to fully appreciate the fundamental concepts and techniques of experimental design as well as the real-world value of design. It gives them a profound understanding of how design selection affects the information obtained in an experiment.

It is truly my pleasure to read this book ! after reading this book, I benefitted by gaining insights into the modeling aspect of experimental design, and consequentially it helps me appreciate the idea of statistical efficiency behind each design and understand the tools used in data analysis. ! an excellent reference book that I would recommend to anyone who is serious about learning the nuts and bolts of experimental design and data analysis techniques. --Rong Pan, Journal of Quality Technology, Vol. 43, No. 3, July 2011

Prefacep. xvii
Introductionp. 1
Example: rainfall and grasslandp. 1
Basic elements of an experimentp. 2
Treatments and materialp. 3
Control and comparisonp. 4
Responses and measurement processesp. 5
Replication, blocking, and randomizationp. 6
Validity and optimalityp. 7
Experiments and experiment-like studiesp. 8
4 Models and data analystp. 9
Conclusionp. 9
Exercisesp. 10
Linear statistical modelsp. 13
Linear vector spacesp. 13
Basic linear modelp. 14
The hat matrix, least-squares estimates, and design information matrixp. 14
Examplep. 16
The partitioned linear modelp. 18
The reduced normal equationsp. 19
Examplep. 21
Linear and quadratic formsp. 23
Estimation and informationp. 24
Pure error and lack of fitp. 26
Hypothesis testing and informationp. 28
8.1 Examplep. 29
Blocking and informationp. 30
Conclusionp. 31
Exercisesp. 31
Completely randomized designsp. 37
Introductionp. 37
Example: radiation and ratsp. 37
Modelsp. 38
Graphical logicp. 40
Matrix formulationp. 41
Influence of the design on estimationp. 44
Allocationp. 45
Overall experiment sizep. 48
Influence of design on hypothesis testingp. 49
Conclusionp. 50
Exercisesp. 50
Randomized complete blocks and related designsp. 55
Introductionp. 55
Example: structural reinforcement barsp. 56
A modelp. 57
Graphical logicp. 58
Matrix formulationp. 59
Influence of design on estimationp. 61
Experiment sizep. 63
Influence of design on hypothesis testingp. 63
Orthogonality and ôCondition Eöp. 64
Conclusionp. 67
Exercisesp. 67
Latin squares and related designsp. 73
Introductionp. 73
Example: web page linksp. 75
Replicated Latin squaresp. 76
A modelp. 77
Graphical logicp. 79
Matrix formulationp. 80
Influence of design on quality of inferencep. 83
More general constructions: Graeco-Latin squaresp. 84
Conclusionp. 87
Exorcisesp. 87
Some data analysis for CRDs and orthogonally blocked designsp. 93
Introductionp. 93
Diagnosticsp. 93
Residualsp. 93
Modified Levene testp. 95
General test for lack of fitp. 96
Tukey one-degree-of-freedom testp. 97
Power transformationsp. 97
Basic inferencep. 100
Multiple comparisonsp. 100
Tukey intervalsp. 101
Dunnett intervalsp. 102
Simulation based intervals for specific problemsp. 102
Scheffé intervalsp. 103
Numerical examplep. 104
Conclusionp. 105
Exercisesp. 106
Balanced incomplete block designsp. 109
Introductionp. 109
Example: drugs and blood pressurep. 110
Existence and construction of BIBDSp. 111
A modelp. 112
Graphical logicp. 112
Example: dishwashing detergentsp. 113
Matrix formulationp. 114
Basic analysis: an examplep. 118
Influence of design on quality of inferencep. 119
More general constructionsp. 121
Extended complete block designsp. 121
Partially balanced incomplete block designsp. 122
Conclusionp. 124
Exercisesp. 124
Random block effectsp. 129
Introductionp. 129
Inter- and intra-block analysisp. 129
Complete block designs (CBDs) and augmented CBDsp. 132
Balanced incomplete block designs (BIBDs)p. 134
Combined estimatorp. 135
Example: dishwashing detergents reprisep. 136
Why can information be ôrecoveredö?p. 137
CBD reprisep. 138
Conclusionp. 139
Exercisesp. 139
Factorial treatment structurep. 143
Introductionp. 143
Example: strength of concretep. 144
An overparameterized modelp. 144
Graphical logicp. 147
Matrix development for the overparameterized modelp. 148
An equivalent, full-rank modelp. 152
Matrix development, for the full-rank modelp. 154
Estimationp. 155
Partitioning of variability and hypothesis testingp. 157
Factorial experiments as CRDs, CBDs, LSDs, and BIBDsp. 159
Model reductionp. 160
Conclusionp. 162
Exercisesp. 163
Split-plot designsp. 167
Introductionp. 167
Example: strength of fabricsp. 168
Example: english tutoringp. 169
SPD(R, B)p. 169
A modelp. 170
Analysisp. 171
SPD(B, B)p. 175
A modelp. 176
Analysisp. 177
More than two experimental factorsp. 178
More than two strata of experimental unitsp. 178
Conclusionp. 180
Exercisesp. 182
Two-level factorial experiments: basicsp. 187
Introductionp. 187
Example: bacteria and nucleasep. 187
Two-level factorial structurep. 188
Estimation of treatment contrastsp. 193
Full modelp. 193
Reduced modelp. 193
Examplesp. 195
Testing factorial effectsp. 196
Individual model terms, experiment with replicationp. 196
Multiple model terms, experiments with replicationp. 197
Experiments without replicationp. 197
Additional guidelines for model editingp. 200
Conclusionp. 201
Exercisesp. 201
Two-level factorial experiments: blockingp. 207
Introductionp. 207
Modelsp. 207
Notationp. 208
Complete blocksp. 208
Example: gophers and burrow plugsp. 210
Balanced incomplete block designs (BIBDs)p. 210
Regular blocks of size 2f-1p. 211
Random blocksp. 214
Partial confoundingp. 215
Regular blocks of size 22f-2p. 216
Regular blocks: general casep. 219
Conclusionp. 222
Exercisesp. 223
Two-level factorial experiments: fractional factorialsp. 227
Introductionp. 227
Regular fractional factorial designsp. 227
Analysisp. 230
Example: bacteria and bacteriocinp. 231
Comparison of fractionsp. 231
Resolutionp. 231
Comparing fractions of equal resolution: aberrationp. 233
Blocking regular fractional factorial designsp. 234
Augmenting regular fractional factorial designsp. 235
Combining fractionsp. 235
Fold-over designsp. 237
Blocking combined fractionsp. 239
Irregular fractional factorial designsp. 240
Conclusionp. 242
Exercisesp. 243
Factorial group screening experimentsp. 247
Introductionp. 247
Example: semiconductors and simulationp. 248
Factorial structure of group screening designsp. 250
Group screening design considerationsp. 253
Effect cancellingp. 253
Screening failurep. 253
Aliasingp. 254
Screening efficiencyp. 255
Case studyp. 256
Conclusionp. 257
Exercisesp. 258
Regression experiments: first-order polynomial modelsp. 261
Introductionp. 261
Example: bacteria and elastasep. 262
Polynomial modelsp. 263
Designs for first-order modelsp. 264
Two-level designsp. 264
Simplex designsp. 265
Blocking experiments for first-order modelsp. 266
Split-plot regression experimentsp. 269
Example: bacteria and elastase reprisep. 269
Diagnosticsp. 271
Use of a center pointp. 271
General test for lack-of-fitp. 272
Conclusionp. 276
Exercisesp. 276
Regression experiments: second-order polynomial modelsp. 281
Introductionp. 281
Example: nasal spraysp. 281
Quadratic polynomial modelsp. 282
Designs for second-order modelsp. 284
Complete three-level factorial designsp. 284
Central composite designsp. 286
Box-Behnken designsp. 287
Augmented pairs designsp. 288
Design scaling and informationp. 289
Orthogonal blockingp. 291
Split-plot designsp. 292
Examplep. 292
Bias due to omitted model termsp. 293
Conclusionp. 296
Exercisesp. 296
Introduction to optimal designp. 299
Introductionp. 299
Optimal design fundamentalsp. 299
Optimality criteriap. 301
A-optimalityp. 301
D-optimalityp. 303
Other criteriap. 304
Examplesp. 304
Algorithmsp. 309
Conclusionp. 310
Exercisesp. 311
Calculations using Rp. 313
Solution notes for selected exercisesp. 321
Referencesp. 341
Indexp. 347
Table of Contents provided by Ingram. All Rights Reserved.

ISBN: 9781584889236
ISBN-10: 1584889233
Series: Chapman & Hall/CRC Texts in Statistical Science
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 376
Published: 27th July 2010
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.5 x 15.9  x 2.41
Weight (kg): 0.68
Edition Number: 1

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