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A First Course in

Design and Analysis

of Experiments

A First Course in

Design and Analysis

of Experiments

Gary W. Oehlert

University of Minnesota

Cover design by Victoria TomaselliCover illustration by Peter HamlinMinitab is a registered trademark of Minitab, Inc.SAS is a registered trademark of SAS Institute, Inc.S-Plus is a registered trademark of Mathsoft, Inc.Design-Expert is a registered trademark of Stat-Ease, Inc.Library of Congress Cataloging-in-PublicationData.Oehlert, Gary W.

A first course in design and analysis of experiments / Gary W. Oehlert. p. cm.

Includes bibligraphical references and index.

ISBN 0-7167-3510-5

1. Experimental Design I. Title

QA279.O34 2000

519.5-dc2199-059934

Copyright

c?2010 Gary W. Oehlert. All rights reserved. This work is licensed under a "Creative Commons" license. Briefly, you are free to copy, distribute, and transmit this work provided the following conditions are met:

1. You must properly attribute the work.

2. You may not use this work for commercial purposes.

3. You may not alter, transform, or build upon this work.

A complete description of the license may be found at

For Becky

who helped me all the way through and for Christie and Erica who put up with a lot while it was getting done

Contents

Prefacexvii

1 Introduction1

1.1 Why Experiment? . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Components of an Experiment . . . . . . . . . . . . . . . 4

1.3 Terms and Concepts . . . . . . . . . . . . . . . . . . . . . 5

1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.5 More About Experimental Units . . . . . . . . . . . . . . 8

1.6 More About Responses . . . . . . . . . . . . . . . . . . . 10

2 Randomization and Design13

2.1 Randomization Against Confounding . . . . . . . . . . . 14

2.2 Randomizing Other Things . . . . . . . . . . . . . . . . . 16

2.3 Performing a Randomization . . . . . . . . . . . . . . . . 17

2.4 Randomization for Inference . . . . . . . . . . . . . . . . 19

2.4.1 The pairedt-test . . . . . . . . . . . . . . . . . . 20

2.4.2 Two-samplet-test . . . . . . . . . . . . . . . . . 25

2.4.3 Randomization inference and standard inference . 26

2.5 Further Reading and Extensions . . . . . . . . . . . . . . 27

2.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Completely Randomized Designs 31

3.1 Structure of a CRD . . . . . . . . . . . . . . . . . . . . . 31

3.2 Preliminary Exploratory Analysis . . . . . . . . . . . . . 33

3.3 Models and Parameters . . . . . . . . . . . . . . . . . . . 34

viiiCONTENTS

3.4 Estimating Parameters . . . . . . . . . . . . . . . . . . . 39

3.5 Comparing Models: The Analysis of Variance . . . . . . . 44

3.6 Mechanics of ANOVA . . . . . . . . . . . . . . . . . . . 45

3.7 Why ANOVA Works . . . . . . . . . . . . . . . . . . . . 52

3.8 Back to Model Comparison . . . . . . . . . . . . . . . . . 52

3.9 Side-by-Side Plots . . . . . . . . . . . . . . . . . . . . . 54

3.10 Dose-Response Modeling . . . . . . . . . . . . . . . . . . 55

3.11 Further Reading and Extensions . . . . . . . . . . . . . . 58

3.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 60

4 Looking for Specific Differences-Contrasts 65

4.1 Contrast Basics . . . . . . . . . . . . . . . . . . . . . . . 65

4.2 Inference for Contrasts . . . . . . . . . . . . . . . . . . . 68

4.3 Orthogonal Contrasts . . . . . . . . . . . . . . . . . . . . 71

4.4 Polynomial Contrasts . . . . . . . . . . . . . . . . . . . . 73

4.5 Further Reading and Extensions . . . . . . . . . . . . . . 75

4.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5 Multiple Comparisons77

5.1 Error Rates . . . . . . . . . . . . . . . . . . . . . . . . . 78

5.2 Bonferroni-Based Methods . . . . . . . . . . . . . . . . . 81

5.3 The Scheff´e Method forAllContrasts . . . . . . . . . . . 85

5.4 Pairwise Comparisons . . . . . . . . . . . . . . . . . . . . 87

5.4.1 Displaying the results . . . . . . . . . . . . . . . 88

5.4.2 The Studentized range . . . . . . . . . . . . . . . 89

5.4.3 Simultaneous confidence intervals . . . . . . . . . 90

5.4.4 Strong familywise error rate . . . . . . . . . . . . 92

5.4.5 False discovery rate . . . . . . . . . . . . . . . . 96

5.4.6 Experimentwise error rate . . . . . . . . . . . . . 97

5.4.7 Comparisonwise error rate . . . . . . . . . . . . . 98

5.4.8 Pairwise testing reprise . . . . . . . . . . . . . . 98

5.4.9 Pairwise comparisons methods that donotcontrol

combined Type I error rates . . . . . . . . . . . . 98

5.4.10 Confident directions . . . . . . . . . . . . . . . . 100

CONTENTSix

5.5 Comparison with Control or the Best . . . . . . . . . . . . 101

5.5.1 Comparison with a control . . . . . . . . . . . . . 101

5.5.2 Comparison with the best . . . . . . . . . . . . . 104

5.6 Reality Check on Coverage Rates . . . . . . . . . . . . . 105

5.7 A Warning About Conditioning . . . . . . . . . . . . . . . 106

5.8 Some Controversy . . . . . . . . . . . . . . . . . . . . . . 106

5.9 Further Reading and Extensions . . . . . . . . . . . . . . 107

5.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 108

6 Checking Assumptions111

6.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 111

6.2 Transformations . . . . . . . . . . . . . . . . . . . . . . . 113

6.3 Assessing Violations of Assumptions . . . . . . . . . . . . 114

6.3.1 Assessing nonnormality . . . . . . . . . . . . . . 115

6.3.2 Assessing nonconstant variance . . . . . . . . . . 118

6.3.3 Assessing dependence . . . . . . . . . . . . . . . 120

6.4 Fixing Problems . . . . . . . . . . . . . . . . . . . . . . . 124

6.4.1 Accommodating nonnormality . . . . . . . . . . 124

6.4.2 Accommodating nonconstant variance . . . . . . 126

6.4.3 Accommodating dependence . . . . . . . . . . . 133

6.5 Effects of Incorrect Assumptions . . . . . . . . . . . . . . 134

6.5.1 Effects of nonnormality . . . . . . . . . . . . . . 134

6.5.2 Effects of nonconstant variance . . . . . . . . . . 136

6.5.3 Effects of dependence . . . . . . . . . . . . . . . 138

6.6 Implications for Design . . . . . . . . . . . . . . . . . . . 140

6.7 Further Reading and Extensions . . . . . . . . . . . . . . 141

6.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 143

7 Power and Sample Size149

7.1 Approaches to Sample Size Selection . . . . . . . . . . . 149

7.2 Sample Size for Confidence Intervals . . . . . . . . . . . . 151

7.3 Power and Sample Size for ANOVA . . . . . . . . . . . . 153

7.4 Power and Sample Size for a Contrast . . . . . . . . . . . 158

7.5 More about Units and Measurement Units . . . . . . . . . 158

xCONTENTS

7.6 Allocation of Units for Two Special Cases . . . . . . . . . 160

7.7 Further Reading and Extensions . . . . . . . . . . . . . . 161

7.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 162

8 Factorial Treatment Structure 165

8.1 Factorial Structure . . . . . . . . . . . . . . . . . . . . . . 165

8.2 Factorial Analysis: Main Effect and Interaction . . . . . .167

8.3 Advantages of Factorials . . . . . . . . . . . . . . . . . . 170

8.4 Visualizing Interaction . . . . . . . . . . . . . . . . . . . 171

8.5 Models with Parameters . . . . . . . . . . . . . . . . . . . 175

8.6 The Analysis of Variance for Balanced Factorials . . . . . 179

8.7 General Factorial Models . . . . . . . . . . . . . . . . . . 182

8.8 Assumptions and Transformations . . . . . . . . . . . . . 185

8.9 Single Replicates . . . . . . . . . . . . . . . . . . . . . . 186

8.10 Pooling Terms into Error . . . . . . . . . . . . . . . . . . 191

8.11 Hierarchy . . . . . . . . . . . . . . . . . . . . . . . . . . 192

8.12 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 197

9 A Closer Look at Factorial Data 203

9.1 Contrasts for Factorial Data . . . . . . . . . . . . . . . . . 203

9.2 Modeling Interaction . . . . . . . . . . . . . . . . . . . . 209

9.2.1 Interaction plots . . . . . . . . . . . . . . . . . . 209

9.2.2 One-cell interaction . . . . . . . . . . . . . . . . 210

9.2.3 Quantitative factors . . . . . . . . . . . . . . . . 212

9.2.4 Tukey one-degree-of-freedom for nonadditivity . . 217

9.3 Further Reading and Extensions . . . . . . . . . . . . . . 220

9.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 222

10 Further Topics in Factorials 225

10.1 Unbalanced Data . . . . . . . . . . . . . . . . . . . . . . 225

10.1.1 Sums of squares in unbalanced data . . . . . . . . 226

10.1.2 Building models . . . . . . . . . . . . . . . . . . 227

10.1.3 Testing hypotheses . . . . . . . . . . . . . . . . . 230

10.1.4 Empty cells . . . . . . . . . . . . . . . . . . . . . 233

10.2 Multiple Comparisons . . . . . . . . . . . . . . . . . . . 234

CONTENTSxi

10.3 Power and Sample Size . . . . . . . . . . . . . . . . . . . 235

10.4 Two-Series Factorials . . . . . . . . . . . . . . . . . . . . 236

10.4.1 Contrasts . . . . . . . . . . . . . . . . . . . . . . 237

10.4.2 Single replicates . . . . . . . . . . . . . . . . . . 240

10.5 Further Reading and Extensions . . . . . . . . . . . . . . 244

10.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 245

11 Random Effects253

11.1 Models for Random Effects . . . . . . . . . . . . . . . . . 253

11.2 Why Use Random Effects? . . . . . . . . . . . . . . . . . 256

11.3 ANOVA for Random Effects . . . . . . . . . . . . . . . . 257

11.4 Approximate Tests . . . . . . . . . . . . . . . . . . . . . 260

11.5 Point Estimates of Variance Components . . . . . . . . . . 264

11.6 Confidence Intervals for Variance Components . . . . . . 267

11.7 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 271

11.8 Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

11.9 Further Reading and Extensions . . . . . . . . . . . . . . 274

11.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 275

12 Nesting, Mixed Effects, and Expected Mean Squares 279

12.1 Nesting Versus Crossing . . . . . . . . . . . . . . . . . . 279

12.2 Why Nesting? . . . . . . . . . . . . . . . . . . . . . . . . 283

12.3 Crossed and Nested Factors . . . . . . . . . . . . . . . . . 283

12.4 Mixed Effects . . . . . . . . . . . . . . . . . . . . . . . . 285

12.5 Choosing a Model . . . . . . . . . . . . . . . . . . . . . . 288

12.6 Hasse Diagrams and Expected Mean Squares . . . . . . . 289

12.6.1 Test denominators . . . . . . . . . . . . . . . . . 290

12.6.2 Expected mean squares . . . . . . . . . . . . . . 293

12.6.3 Constructing a Hasse diagram . . . . . . . . . . . 296

12.7 Variances of Means and Contrasts . . . . . . . . . . . . . 298

12.8 Unbalanced Data and Random Effects . . . . . . . . . . . 304

12.9 Staggered Nested Designs . . . . . . . . . . . . . . . . . 306

12.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 307

xiiCONTENTS

13 Complete Block Designs315

13.1 Blocking . . . . . . . . . . . . . . . . . . . . . . . . . . . 315

13.2 The Randomized Complete Block Design . . . . . . . . . 316

13.2.1 Why and when to use the RCB . . . . . . . . . . 318

13.2.2 Analysis for the RCB . . . . . . . . . . . . . . . 319

13.2.3 How well did the blocking work? . . . . . . . . . 322

13.2.4 Balance and missing data . . . . . . . . . . . . . 324

13.3 Latin Squares and Related Row/Column Designs . . . . . 324

13.3.1 The crossover design . . . . . . . . . . . . . . . . 326

13.3.2 Randomizing the LS design . . . . . . . . . . . . 327

13.3.3 Analysis for the LS design . . . . . . . . . . . . . 327

13.3.4 Replicating Latin Squares . . . . . . . . . . . . . 330

13.3.5 Efficiency of Latin Squares . . . . . . . . . . . . 335

13.3.6 Designs balanced for residual effects . . . . . . . 338

13.4 Graeco-Latin Squares . . . . . . . . . . . . . . . . . . . . 343

13.5 Further Reading and Extensions . . . . . . . . . . . . . . 344

13.6 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 345

14 Incomplete Block Designs357

14.1 Balanced Incomplete Block Designs . . . . . . . . . . . . 358

14.1.1 Intrablock analysis of the BIBD . . . . . . . . . . 360

14.1.2 Interblock information . . . . . . . . . . . . . . . 364

14.2 Row and Column Incomplete Blocks . . . . . . . . . . . . 368

14.3 Partially Balanced Incomplete Blocks . . . . . . . . . . . 370

14.4 Cyclic Designs . . . . . . . . . . . . . . . . . . . . . . . 372

14.5 Square, Cubic, and Rectangular Lattices . . . . . . . . . . 374

14.6 Alpha Designs . . . . . . . . . . . . . . . . . . . . . . . . 376

14.7 Further Reading and Extensions . . . . . . . . . . . . . . 378

14.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 379

CONTENTSxiii

15 Factorials in Incomplete Blocks-Confounding 387

15.1 Confounding the Two-Series Factorial . . . . . . . . . . . 388

15.1.1 Two blocks . . . . . . . . . . . . . . . . . . . . . 389

15.1.2 Four or more blocks . . . . . . . . . . . . . . . . 392

15.1.3 Analysis of an unreplicated confounded two-series 397

15.1.4 Replicating a confounded two-series . . . . . . . 399

15.1.5 Double confounding . . . . . . . . . . . . . . . . 402

15.2 Confounding the Three-Series Factorial . . . . . . . . . . 403

15.2.1 Building the design . . . . . . . . . . . . . . . . 404

15.2.2 Confounded effects . . . . . . . . . . . . . . . . 407

15.2.3 Analysis of confounded three-series . . . . . . . . 408

15.3 Further Reading and Extensions . . . . . . . . . . . . . . 409

15.4 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 410

16 Split-Plot Designs417

16.1 What Is a Split Plot? . . . . . . . . . . . . . . . . . . . . 417

16.2 Fancier Split Plots . . . . . . . . . . . . . . . . . . . . . . 419

16.3 Analysis of a Split Plot . . . . . . . . . . . . . . . . . . . 420

16.4 Split-Split Plots . . . . . . . . . . . . . . . . . . . . . . . 428

16.5 Other Generalizations of Split Plots . . . . . . . . . . . . 434

16.6 Repeated Measures . . . . . . . . . . . . . . . . . . . . . 438

16.7 Crossover Designs . . . . . . . . . . . . . . . . . . . . . 441

16.8 Further Reading and Extensions . . . . . . . . . . . . . . 441

16.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 442

17 Designs with Covariates453

17.1 The Basic Covariate Model . . . . . . . . . . . . . . . . . 454

17.2 When Treatments Change Covariates . . . . . . . . . . . . 460

17.3 Other Covariate Models . . . . . . . . . . . . . . . . . . . 462

17.4 Further Reading and Extensions . . . . . . . . . . . . . . 466

17.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 466

xivCONTENTS

18 Fractional Factorials471

18.1 Why Fraction? . . . . . . . . . . . . . . . . . . . . . . . . 471

18.2 Fractioning the Two-Series . . . . . . . . . . . . . . . . . 472

18.3 Analyzing a2k-q. . . . . . . . . . . . . . . . . . . . . . 479

18.4 Resolution and Projection . . . . . . . . . . . . . . . . . . 482

18.5 Confounding a Fractional Factorial . . . . . . . . . . . . . 485

18.6 De-aliasing . . . . . . . . . . . . . . . . . . . . . . . . . 485

18.7 Fold-Over . . . . . . . . . . . . . . . . . . . . . . . . . . 487

18.8 Sequences of Fractions . . . . . . . . . . . . . . . . . . . 489

18.9 Fractioning the Three-Series . . . . . . . . . . . . . . . . 489

18.10 Problems with Fractional Factorials . . . . . . . . . . . . 492

18.11 Using Fractional Factorials in Off-Line Quality Control . . 493

18.11.1 Designing an off-line quality experiment . . . . . 494

18.11.2 Analysis of off-line quality experiments . . . . . . 495

18.12 Further Reading and Extensions . . . . . . . . . . . . . . 498

18.13 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 499

19 Response Surface Designs509

19.1 Visualizing the Response . . . . . . . . . . . . . . . . . . 509

19.2 First-Order Models . . . . . . . . . . . . . . . . . . . . . 511

19.3 First-Order Designs . . . . . . . . . . . . . . . . . . . . . 512

19.4 Analyzing First-Order Data . . . . . . . . . . . . . . . . . 514

19.5 Second-Order Models . . . . . . . . . . . . . . . . . . . . 517

19.6 Second-Order Designs . . . . . . . . . . . . . . . . . . . 522

19.7 Second-Order Analysis . . . . . . . . . . . . . . . . . . . 526

19.8 Mixture Experiments . . . . . . . . . . . . . . . . . . . . 529

19.8.1 Designs for mixtures . . . . . . . . . . . . . . . . 530

19.8.2 Models for mixture designs . . . . . . . . . . . . 533

19.9 Further Reading and Extensions . . . . . . . . . . . . . . 535

19.10 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 536

CONTENTSxv

20 On Your Own543

20.1 Experimental Context . . . . . . . . . . . . . . . . . . . . 543

20.2 Experiments by the Numbers . . . . . . . . . . . . . . . . 544

20.3 Final Project . . . . . . . . . . . . . . . . . . . . . . . . . 548

Bibliography549

A Linear Models for Fixed Effects 563

A.1 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 A.2 Least Squares . . . . . . . . . . . . . . . . . . . . . . . . 566 A.3 Comparison of Models . . . . . . . . . . . . . . . . . . . 568 A.4 Projections . . . . . . . . . . . . . . . . . . . . . . . . . 570 A.5 Random Variation . . . . . . . . . . . . . . . . . . . . . . 572 A.6 Estimable Functions . . . . . . . . . . . . . . . . . . . . . 576 A.7 Contrasts . . . . . . . . . . . . . . . . . . . . . . . . . . 578 A.8 The Scheff´e Method . . . . . . . . . . . . . . . . . . . . . 579 A.9 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 580

B Notation583

C Experimental Design Plans 607

C.1 Latin Squares . . . . . . . . . . . . . . . . . . . . . . . . 607 C.1.1 Standard Latin Squares . . . . . . . . . . . . . . 607 C.1.2 Orthogonal Latin Squares . . . . . . . . . . . . . 608 C.2 Balanced Incomplete Block Designs . . . . . . . . . . . . 609 C.3 Efficient Cyclic Designs . . . . . . . . . . . . . . . . . . 615 C.4 Alpha Designs . . . . . . . . . . . . . . . . . . . . . . . . 616 C.5 Two-Series Confounding and Fractioning Plans . . . . . . 617

D Tables621

Index647

Prefacexvii

Preface

This text covers the basic topics in experimental design andanalysis and is intended for graduate students and advanced undergraduates. Students should have had an introductory statistical methods courseat about the level of Moore and McCabe'sIntroduction to the Practiceof Statistics(Moore and McCabe 1999) and be familiar witht-tests,p-values, confidence intervals, and the basics of regression and ANOVA. Most of the text soft-pedals theory and mathematics, but Chapter 19 on response surfaces is a little tougher sled- ding (eigenvectors and eigenvalues creep in through canonical analysis), and Appendix A is an introduction to the theory of linear models.I use the text in a service course for non-statisticians and in a course forfirst-year Masters students in statistics. The non-statisticians come from departments scattered all around the university including agronomy, ecology, educational psychol- ogy, engineering, food science, pharmacy, sociology, and wildlife. I wrote this book for the same reason that many textbooks get written: there was no existing book that did things the way I thought was best. I start with single-factor, fixed-effects, completely randomizeddesigns and cover them thoroughly, including analysis, checking assumptions, and power. I then add factorial treatment structure and random effects to the mix. At this stage, we have a single randomization scheme, a lot of different models for data, and essentially all the analysis techniques we need. Inext add block- ing designs for reducing variability, covering complete blocks, incomplete blocks,and confoundingin factorials. After this I introduce split plots, which can be considered incomplete block designs but really introduce the broader subject of unit structures. Covariate models round out the discussion of vari- ance reduction. I finish with specialtreatment structures,including fractional factorials and response surface/mixture designs. This outline is similar in contentto a dozen other design texts; how is this book different? •I include many exercises where the student is required tochoosean appropriate experimental design for a given situation, orrecognizethe design that was used. Many of the designs in question are fromearlier chapters, not the chapter where the question is given. Theseare impor- tant skills that often receive short shrift. See examples onpages 500 and 502. xviiiPreface •I use Hasse diagrams to illustrate models, find test denominators, and compute expected mean squares. I feel that the diagrams provide a much easier and more understandable approach to these problems than the classicapproachwith tables ofsubscriptsand live anddeadindices. I believe that Hasse diagrams should see wider application. •I spend time trying to sort out the issues with multiple comparisons procedures. These confuse many students, and most texts seem to just present a laundry list of methods and no guidance. •I try to get students to look beyond saying main effects and/or interac- tions are significant and to understand the relationships inthe data. I want them to learn that understanding what the data have to say is the goal. ANOVA is a tool we use at the beginning of an analysis; itis not the end. •I describe the difference in philosophy between hierarchical model building and parameter testing in factorials, and discuss how this be- comes crucial for unbalanced data. This is important because the dif- ferent philosophies can lead to different conclusions, andmany texts avoid the issue entirely. •There are three kinds of "problems" in this text, which I havedenoted exercises, problems, and questions. Exercises are intended to be sim- pler than problems, with exercises being more drill on mechanics and problems being more integrative. Not everyone will agree with my classification. Questions are not necessarily more difficult than prob- lems, but they cover more theoretical or mathematical material. Data files for the examples and problems can be downloaded from the Freeman web site athttp://www.whfreeman.com/. A second re- source is Appendix B, which documents the notation used in the text. This text contains many formulae, but I try to use formulae only when I think that they will increase a reader's understanding of the ideas. In several settings where closed-form expressions for sums of squaresor estimates ex- ist, I do not presentthem becauseI do not believe that they help (for example, the Analysis of Covariance). Similarly, presentations of normal equations do not appear. Instead, I approach ANOVA as a comparison of models fit by least squares, and let the computing software take care of the details of fit- ting. Future statisticians will need to learn the process inmore detail, and Appendix A gets them started with the theory behind fixed effects. Speaking of computing, examples in this text use one of four packages: MacAnova, Minitab, SAS, and S-Plus. MacAnova is a homegrownpackage that we use here at Minnesota because we can distribute it freely; it runs

Prefacexix

on Macintosh, Windows, and Unix; and it does everything we need. You can downloadMacAnova(any version and documentation,eventhesource)from http://www.stat.umn.edu/˜gary/macanova. Minitab and SAS are widely used commercial packages. I hadn't used Minitab in twelve years when I started using it for examples; I found it incredibly easy to use. The menu/dialog/spreadsheet interface was very intuitive. Infact, I only opened the manual once, and that was when I was trying to figure out howto do general contrasts (which I was never able to figure out). SAS is far and away the market leader in statistical software. You can do practically every kind of analysis in SAS, but as a novice I spent many hours with the manuals trying to get SAS to do any kind of analysis. In summary, many people swear by SAS, but I found I mostly swore at SAS. I use S-Plus extensivelyin research; here I've just used it for a couple of graphics. I need to acknowledge many people who helped me get this job done. First are the students and TA's in the courses where I used preliminary ver- sions. Many of you made suggestions and pointed out mistakes; in particular I thank John Corbett, Alexandre Varbanov, and Jorge de la Vega Gongora. Many others of you contributed data; your footprints are scattered throughout the examples and exercises. Next I have benefited from helpful discussions with my colleagues here in Minnesota, particularly Kit Bingham, Kathryn Chaloner, Sandy Weisberg, and Frank Martin. I thank Sharon Lohr for in- troducing me to Hasse diagrams, and I received much helpful criticism from reviewers, including Larry Ringer (Texas A&M), Morris Southward (New Mexico State), Robert Price (East Tennessee State), AndrewSchaffner (Cal Poly-San Luis Obispo), Hiroshi Yamauchi (Hawaii-Manoa), and William Notz (Ohio State). My editor Patrick Farace and others at Freeman were a great help. Finally, I thank my family and parents, who supported me in this for years (even if my father did say it looked like a foreign language!). They say you should never let the camel's nose into the tent, because once the nose is in, there's no stopping the rest of the camel.In a similar vein, student requests for copies of lecture notes lead to student requests for typed lecture notes, which lead to student requests for morecomplete typed lecture notes, which lead...well, in my case it leads to a textbook on de- sign and analysis of experiments, which you are reading now.Over the years my students have preferred various more primitive incarnations of this text to other texts; I hope you find this text worthwhile too.

Gary W. Oehlert

Chapter 1IntroductionResearchers use experiments to answer questions. Typical questions mightExperiments

answer questionsbe: •Is a drug a safe, effective cure for a disease? This could be a test of how AZT affects the progress of AIDS. •Which combination of protein and carbohydrate sources provides the best nutrition for growing lambs? •How will long-distance telephone usage change if our company offers a different rate structure to our customers? •Will an ice cream manufactured with a new kind of stabilizer be as palatable as our current ice cream? •Does short-term incarceration of spouse abusers deter future assaults? •Under what conditions should I operate my chemical refinery,given this month's grade of raw material? This book is meant to help decision makers and researchers design good experiments, analyze them properly, and answer their questions.

1.1 Why Experiment?

Considerthe spousalassaultexamplementioned above. Justice officials needquotesdbs_dbs26.pdfusesText_32

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