Design and Analysis of Experiments with R

618 Pages·2014·6.04 MB·English

by  Lawson

Design and Analysis
of Experiments
with R
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Texts in Statistical Science
Design and Analysis
of Experiments
with R
John Lawson
Brigham Young University
Provo, Utah, USA
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Contents
Preface xi
List of Examples xv
1 Introduction 1
1.1 Statistics and Data Collection 1
1.2 Beginnings of Statistically Planned Experiments 2
1.3 Definitions and Preliminaries 2
1.4 Purposes of Experimental Design 5
1.5 Types of Experimental Designs 6
1.6 Planning Experiments 7
1.7 Performing the Experiments 9
1.8 Use of R Software 12
1.9 Review of Important Concepts 12
1.10 Exercises 15
2 Completely Randomized Designs with One Factor 17
2.1 Introduction 17
2.2 Replication and Randomization 17
2.3 A Historical Example 19
2.4 Linear Model for CRD 20
2.5 Verifying Assumptions of the Linear Model 29
2.6 Analysis Strategies When Assumptions Are Violated 31
2.7 Determining the Number of Replicates 38
2.8 Comparison of Treatments after the F-test 41
2.9 Review of Important Concepts 49
2.10 Exercises 51
3 Factorial Designs 55
3.1 Introduction 55
3.2 Classical One at a Time versus Factorial Plans 55
3.3 Interpreting Interactions 57
3.4 Creating a Two-Factor Factorial Plan in R 60
3.5 Analysis of a Two-Factor Factorial in R 61
3.6 Factorial Designs with Multiple Factors—CRFD 80
3.7 Two-Level Factorials 85
vii
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viii CONTENTS
3.8 Verifying Assumptions of the Model 102
3.9 Review of Important Concepts 106
3.10 Exercises 108
4 Randomized Block Designs 113
4.1 Introduction 113
4.2 Creating an RCB in R 114
4.3 Model for RCB 116
4.4 An Example of an RCB 117
4.5 Determining the Number of Blocks 121
4.6 Factorial Designs in Blocks 122
4.7 Generalized Complete Block Design 124
4.8 Two Block Factors LSD 128
4.9 Review of Important Concepts 133
4.10 Exercises 135
4.11 Appendix—Data from the Golf Experiment 140
5 Designs to Study Variances 141
5.1 Introduction 141
5.2 Random Factors and Random Sampling Experiments 142
5.3 One-Factor Sampling Designs 144
5.4 Estimating Variance Components 145
5.5 Two-Factor Sampling Designs 155
5.6 Nested Sampling Experiments (NSE) 164
5.7 Staggered Nested Designs 167
5.8 Designs with Fixed and Random Factors 173
5.9 Graphical Methods to Check Model Assumptions 180
5.10 Review of Important Concepts 188
5.11 Exercises 190
6 Fractional Factorial Designs 193
6.1 Introduction 193
6.2 Half-Fractions of 2k Designs 194
6.3 Quarter and Higher Fractions of 2k Designs 204
6.4 Criteria for Choosing Generators for 2k−p Designs 206
6.5 Augmenting Fractional Factorials 218
6.6 Plackett-Burman (PB) and Model Robust Screening Designs 229
6.7 Mixed Level Factorials and Orthogonal Arrays (OAs) 242
6.8 Definitive Screening Designs 248
6.9 Review of Important Concepts 250
6.10 Exercises 252
7 Incomplete and Confounded Block Designs 261
7.1 Introduction 261
7.2 Balanced Incomplete Block (BIB) Designs 262
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CONTENTS ix
7.3 Analysis of Incomplete Block Designs 264
7.4 BTIB and PBIB Designs 267
7.5 Row Column Designs 271
7.6 Confounded 2k and 2k−p Designs 272
7.7 Confounding 3-Level and p-Level Factorial Designs 285
7.8 Blocking Mixed Level Factorials and OAs 287
7.9 Partially Confounded Blocked Factorial (PCBF) 295
7.10 Review of Important Concepts 300
7.11 Exercises 303
8 Split-Plot Designs 307
8.1 Introduction 307
8.2 Split-Plot Experiments with CRD in Whole Plots CRSP 308
8.3 RCB in Whole Plots RBSP 315
8.4 Analysis Unreplicated 2k Split-Plot Designs 323
8.5 2k−p Fractional Factorials in Split Plots (SPFFs) 328
8.6 Sample Size and Power Issues for Split-Plot Designs 341
8.7 Review of Important Concepts 343
8.8 Exercises 345
9 Crossover and Repeated Measures Designs 351
9.1 Introduction 351
9.2 Crossover Designs (CODs) 351
9.3 Simple AB, BA Crossover Designs for Two Treatments 352
9.4 Crossover Designs for Multiple Treatments 361
9.5 Repeated Measures Designs 366
9.6 Univariate Analysis of Repeated Measures Designs 368
9.7 Review of Important Concepts 377
9.8 Exercises 379
10 Response Surface Designs 383
10.1 Introduction 383
10.2 Fundamentals of Response Surface Methodology 383
10.3 Standard Designs for Second Order Models 387
10.4 Creating Standard Response Surface Designs in R 396
10.5 Non-Standard Response Surface Designs 400
10.6 Fitting the Response Surface Model with R 407
10.7 Determining Optimum Operating Conditions 413
10.8 Blocked Response Surface (BRS) Designs 426
10.9 Response Surface Split-Plot (RSSP) Designs 430
10.10 Review of Important Concepts 439
10.11 Exercises 441
11 Mixture Experiments 447
11.1 Introduction 447
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