دانلود کتاب A first course in design and analysis of experiments

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Preface......Page 18
1.1 Why Experiment?......Page 22
1.2 Components of an Experiment......Page 25
1.3 Terms and Concepts......Page 26
1.4 Outline......Page 28
1.5 More About Experimental Units......Page 29
1.6 More About Responses......Page 31
2 Randomization and Design......Page 34
2.1 Randomization Against Confounding......Page 35
2.2 Randomizing Other Things......Page 37
2.3 Performing a Randomization......Page 38
2.4 Randomization for Inference......Page 40
2.4.1 The paired t-test......Page 41
2.4.2 Two-sample t-test......Page 46
2.4.3 Randomization inference and standard inference......Page 47
2.5 Further Reading and Extensions......Page 48
2.6 Problems......Page 49
3.1 Structure of a CRD......Page 52
3.2 Preliminary Exploratory Analysis......Page 54
3.3 Models and Parameters......Page 55
3.4 Estimating Parameters......Page 60
3.5 Comparing Models: The Analysis of Variance......Page 65
3.6 Mechanics of ANOVA......Page 66
3.8 Back to Model Comparison......Page 73
3.9 Side-by-Side Plots......Page 75
3.10 Dose-Response Modeling......Page 76
3.11 Further Reading and Extensions......Page 79
3.12 Problems......Page 81
4.1 Contrast Basics......Page 86
4.2 Inference for Contrasts......Page 89
4.3 Orthogonal Contrasts......Page 92
4.4 Polynomial Contrasts......Page 94
4.6 Problems......Page 96
5 Multiple Comparisons......Page 98
5.1 Error Rates......Page 99
5.2 Bonferroni-Based Methods......Page 102
5.3 The Scheffé Method for All Contrasts......Page 106
5.4 Pairwise Comparisons......Page 108
5.4.1 Displaying the results......Page 109
5.4.2 The Studentized range......Page 110
5.4.3 Simultaneous confidence intervals......Page 111
5.4.4 Strong familywise error rate......Page 113
5.4.5 False discovery rate......Page 117
5.4.6 Experimentwise error rate......Page 118
5.4.9 Pairwise comparisons methods that do not control combined Type I error rates......Page 119
5.4.10 Confident directions......Page 121
5.5.1 Comparison with a control......Page 122
5.5.2 Comparison with the best......Page 125
5.6 Reality Check on Coverage Rates......Page 126
5.8 Some Controversy......Page 127
5.9 Further Reading and Extensions......Page 128
5.10 Problems......Page 129
6.1 Assumptions......Page 132
6.2 Transformations......Page 134
6.3 Assessing Violations of Assumptions......Page 135
6.3.1 Assessing nonnormality......Page 136
6.3.2 Assessing nonconstant variance......Page 139
6.3.3 Assessing dependence......Page 141
6.4.1 Accommodating nonnormality......Page 145
6.4.2 Accommodating nonconstant variance......Page 147
6.4.3 Accommodating dependence......Page 154
6.5.1 Effects of nonnormality......Page 155
6.5.2 Effects of nonconstant variance......Page 157
6.5.3 Effects of dependence......Page 159
6.6 Implications for Design......Page 161
6.7 Further Reading and Extensions......Page 162
6.8 Problems......Page 164
7.1 Approaches to Sample Size Selection......Page 170
7.2 Sample Size for Confidence Intervals......Page 172
7.3 Power and Sample Size for ANOVA......Page 174
7.5 More about Units and Measurement Units......Page 179
7.6 Allocation of Units for Two Special Cases......Page 181
7.7 Further Reading and Extensions......Page 182
7.8 Problems......Page 183
8.1 Factorial Structure......Page 186
8.2 Factorial Analysis: Main Effect and Interaction......Page 188
8.3 Advantages of Factorials......Page 191
8.4 Visualizing Interaction......Page 192
8.5 Models with Parameters......Page 196
8.6 The Analysis of Variance for Balanced Factorials......Page 200
8.7 General Factorial Models......Page 203
8.8 Assumptions and Transformations......Page 206
8.9 Single Replicates......Page 207
8.10 Pooling Terms into Error......Page 212
8.11 Hierarchy......Page 213
8.12 Problems......Page 218
9.1 Contrasts for Factorial Data......Page 224
9.2.1 Interaction plots......Page 230
9.2.2 One-cell interaction......Page 231
9.2.3 Quantitative factors......Page 233
9.2.4 Tukey one-degree-of-freedom for nonadditivity......Page 238
9.3 Further Reading and Extensions......Page 241
9.4 Problems......Page 243
10.1 Unbalanced Data......Page 246
10.1.1 Sums of squares in unbalanced data......Page 247
10.1.2 Building models......Page 248
10.1.3 Testing hypotheses......Page 251
10.1.4 Empty cells......Page 254
10.2 Multiple Comparisons......Page 255
10.3 Power and Sample Size......Page 256
10.4 Two-Series Factorials......Page 257
10.4.1 Contrasts......Page 258
10.4.2 Single replicates......Page 261
10.5 Further Reading and Extensions......Page 265
10.6 Problems......Page 266
11.1 Models for Random Effects......Page 274
11.2 Why Use Random Effects?......Page 277
11.3 ANOVA for Random Effects......Page 278
11.4 Approximate Tests......Page 281
11.5 Point Estimates of Variance Components......Page 285
11.6 Confidence Intervals for Variance Components......Page 288
11.7 Assumptions......Page 292
11.8 Power......Page 293
11.9 Further Reading and Extensions......Page 295
11.10 Problems......Page 296
12.1 Nesting Versus Crossing......Page 300
12.3 Crossed and Nested Factors......Page 304
12.4 Mixed Effects......Page 306
12.5 Choosing a Model......Page 309
12.6 Hasse Diagrams and Expected Mean Squares......Page 310
12.6.1 Test denominators......Page 311
12.6.2 Expected mean squares......Page 314
12.6.3 Constructing a Hasse diagram......Page 317
12.7 Variances of Means and Contrasts......Page 319
12.8 Unbalanced Data and Random Effects......Page 325
12.9 Staggered Nested Designs......Page 327
12.10 Problems......Page 328
13.1 Blocking......Page 336
13.2 The Randomized Complete Block Design......Page 337
13.2.1 Why and when to use the RCB......Page 339
13.2.2 Analysis for the RCB......Page 340
13.2.3 How well did the blocking work?......Page 343
13.3 Latin Squares and Related Row/Column Designs......Page 345
13.3.1 The crossover design......Page 347
13.3.3 Analysis for the LS design......Page 348
13.3.4 Replicating Latin Squares......Page 351
13.3.5 Efficiency of Latin Squares......Page 356
13.3.6 Designs balanced for residual effects......Page 359
13.4 Graeco-Latin Squares......Page 364
13.5 Further Reading and Extensions......Page 365
13.6 Problems......Page 366
14 Incomplete Block Designs......Page 378
14.1 Balanced Incomplete Block Designs......Page 379
14.1.1 Intrablock analysis of the BIBD......Page 381
14.1.2 Interblock information......Page 385
14.2 Row and Column Incomplete Blocks......Page 389
14.3 Partially Balanced Incomplete Blocks......Page 391
14.4 Cyclic Designs......Page 393
14.5 Square, Cubic, and Rectangular Lattices......Page 395
14.6 Alpha Designs......Page 397
14.7 Further Reading and Extensions......Page 399
14.8 Problems......Page 400
15 Factorials in Incomplete Blocks—Confounding......Page 408
15.1 Confounding the Two-Series Factorial......Page 409
15.1.1 Two blocks......Page 410
15.1.2 Four or more blocks......Page 413
15.1.3 Analysis of an unreplicated confounded two-series......Page 418
15.1.4 Replicating a confounded two-series......Page 420
15.1.5 Double confounding......Page 423
15.2 Confounding the Three-Series Factorial......Page 424
15.2.1 Building the design......Page 425
15.2.2 Confounded effects......Page 428
15.2.3 Analysis of confounded three-series......Page 429
15.3 Further Reading and Extensions......Page 430
15.4 Problems......Page 431
16.1 What Is a Split Plot?......Page 438
16.2 Fancier Split Plots......Page 440
16.3 Analysis of a Split Plot......Page 441
16.4 Split-Split Plots......Page 449
16.5 Other Generalizations of Split Plots......Page 455
16.6 Repeated Measures......Page 459
16.8 Further Reading and Extensions......Page 462
16.9 Problems......Page 463
17 Designs with Covariates......Page 474
17.1 The Basic Covariate Model......Page 475
17.2 When Treatments Change Covariates......Page 481
17.3 Other Covariate Models......Page 483
17.5 Problems......Page 487
18.1 Why Fraction?......Page 492
18.2 Fractioning the Two-Series......Page 493
18.3 Analyzing a 2^(k−q)......Page 500
18.4 Resolution and Projection......Page 503
18.6 De-aliasing......Page 506
18.7 Fold-Over......Page 508
18.9 Fractioning the Three-Series......Page 510
18.10 Problems with Fractional Factorials......Page 513
18.11 Using Fractional Factorials in Off-Line Quality Control......Page 514
18.11.1 Designing an off-line quality experiment......Page 515
18.11.2 Analysis of off-line quality experiments......Page 516
18.12 Further Reading and Extensions......Page 519
18.13 Problems......Page 520
19.1 Visualizing the Response......Page 530
19.2 First-Order Models......Page 532
19.3 First-Order Designs......Page 533
19.4 Analyzing First-Order Data......Page 535
19.5 Second-Order Models......Page 538
19.6 Second-Order Designs......Page 543
19.7 Second-Order Analysis......Page 547
19.8 Mixture Experiments......Page 550
19.8.1 Designs for mixtures......Page 551
19.8.2 Models for mixture designs......Page 554
19.9 Further Reading and Extensions......Page 556
19.10 Problems......Page 557
20.1 Experimental Context......Page 564
20.2 Experiments by the Numbers......Page 565
20.3 Final Project......Page 569
Bibliography......Page 570
A.1 Models......Page 584
A.2 Least Squares......Page 587
A.3 Comparison of Models......Page 589
A.4 Projections......Page 591
A.5 Random Variation......Page 593
A.6 Estimable Functions......Page 597
A.7 Contrasts......Page 599
A.8 The Scheffé Method......Page 600
A.9 Problems......Page 601
B Notation......Page 604
C.1.1 Standard Latin Squares......Page 628
C.1.2 Orthogonal Latin Squares......Page 629
C.2 Balanced Incomplete Block Designs......Page 630
C.3 Efficient Cyclic Designs......Page 636
C.4 Alpha Designs......Page 637
C.5 Two-Series Confounding and Fractioning Plans......Page 638
D Tables......Page 642
Index......Page 668