CONTENTS
1. Introduction = 1
1-1 The Role of Experimental Design = 1
1-2 Basic Principles = 2
1-3 Historical Perspective = 5
1-4 How to Use Statistical Techniques in Experimentation = 6
2. Simple Comparative Experiments = 9
2-1 Introduction = 9
2-2 Basic Statistical Concepts = 10
2-3 Sampling and Sampling Distributions = 13
2-4 Inferences About the Differences in Means, Randomized Designs = 21
2-4.1 Hypothesis Testing = 21
2-4.2 Choice of Sample Size = 24
2-4.3 Confidence Intervals = 26
2-4.4 The Case Where = 28
2-4.5 The Case Where Are Known = 29
2-4.6 Comparing a Single Mean to a Specified Value = 29
2-4.7 Summary = 32
2-5 Inferences About the Difference in Means, Paired Comparison Designs = 32
2-5.1 The Paired Comparison Problem = 32
2-5.2 Advantages of the Paired Comparison Design = 35
2-6 Inferences About Variances of Normal Distributions = 36
2-7 Problems = 39
3. Experiments to Compare Several Treatments: The Analysis of Variance = 43
3-1 Introduction = 43
3-2 The One-Way Classification Analysis of Variance = 44
3-3 Analysis of the Fixed Effects Model = 45
3-3.1 Decomposition of the Total Sum of Squares = 46
3-3.2 Statistical Analysis = 49
3-3.3 Estimation of the Model Parameters = 55
3-3.4 Model Adequacy Checking: Preview = 57
3-3.5 The Unbalanced Case = 58
3-4 Comparison of Individual Treatment Means = 59
3-4.1 Orthogonal Contrasts = 60
3-4.2 Scheffes Method for Comparing All Contrasts = 62
3-4.3 Comparing Pairs of Treatment Means = 64
3-4.4 Comparing Treatments with a Control = 70
3-5 The Random Effects Model = 71
3-6 Sample Computer Output = 78
3-7 Problems = 80
4. More About the One-Way Model = 85
4-1 Model Adequacy Checking = 85
4-1.1 The Normality Assumption = 86
4-1.2 Plot of Residuals in Time Sequence = 89
4-1.3 Plot of Residuals Versus Fitted Values = 90
4-1.4 Selecting a Variance Stabilizing Transformation = 93
4-1.5 Plot of Residuals Versus Other Variables = 98
4-2 Choice of Sample Size = 99
4-2.1 Operating Characteristic Curves = 99
4-2.2 Specifying a Standard Deviation Increase = 103
4-2.3 Confidence Interval Estimation Method = 104
4-3 Fitting Response Curves in the One-Way Model = 105
4-3.1 General Regression Approach = 105
4-3.2 Orthogonal Polynomials = 107
4-4 The Regression Approach to Analysis of Variance = 110
4-5 Nonparametric Methods in the Analysis of Variance = 116
4-5.1 The Kruskal-Wallis Test = 116
4-5.2 General Comments on the Rank Transformation = 117
4-6 Repeated Measures = 118
4-7 Problems = 121
5. Randomized Blocks, Latin Squares, and Related Designs = 123
5-1 The Randomized Complete Block Design = 123
5-1.1 Statistical Analysis = 124
5-1.2 Model Adequacy Checking = 136
5-1.3 Estimating Missing Values = 139
5-1.4 Estimating Model Parameters and the General Regression Significance Test = 141
5-1.5 Sample Computer Output = 144
5-2 The Latin Square Design = 146
5-3 The Graeco-Latin Square Design = 156
5-4 Problems = 160
6. Incomplete Block Designs = 165
6-1 Introduction = 165
6-2 Balanced Incomplete Block Designs = 165
6-2.1 Statistical Analysis = 166
6-2.2 Least Squares Estimation of the Parameters = 173
6-3 Recovery of Interblock Information in the Balanced Incomplete Block Design = 174
6-4 Partially Balanced Incomplete Block Designs = 177
6-5 Youden Squares = 180
6-6 Lattice Designs = 183
6-7 Problems = 184
7. Introduction to Factorial Designs = 189
7-1 Basic Definitions and Principles = 189
7-2 The Advantage of Factorials = 192
7-3 The Two-Factor Factorial Design = 192
7-3.1 Statistical Analysis of the Fixed Effects Model = 194
7-3.2 Model Adequacy Checking = 201
7-3.3 Estimating the Model Parameters = 206
7-3.4 Choice of Sample Size = 208
7-3.5 The Assumption of No Interaction in a Two-Factor Model = 210
7-3.6 One Observation per Cell = 211
7-4 Random and Mixed Models = 215
7-4.1 The Random Effects Model = 215
7-4.2 Mixed Models = 218
7-4.3 Choice of Sample Size = 223
7-5 The General Factorial Design = 223
7-6 Fitting Response Curves and Surfaces = 229
7-7 Dealing with Unbalanced Data = 236
7-7.1 Proportional Data: An Easy Case = 237
7-7.2 Approximate Methods = 238
7-7.3 The Exact Method = 240
7-8 Problems = 241
8. Rules for Sums of Squares and Expected Mean Squares = 247
8-1 Rules for Sums of Squares = 247
8-2 Rules for Expected Mean Squares = 250
8-3 Approximate FTests = 254
8-4 Problems = 259
9. 2k and 3k Factorial Designs = 261
9-1 Introduction = 261
9-2 Analysis of the 2k Factorial Design = 261
9-2.1 The 22 Design = 262
9-2.2 The 23 Design = 266
9-2.3 The General 2k Design = 271
9-2.4 A Single Replicate of the 2k Design = 273
9-2.5 Yates' Algorithm for the 2k Design = 280
9-3 Analysis of the 3k Factorial Design = 281
9-3.1 Notation for the 3k Series = 281
9-3.2 The 32 Design = 281
9-3.3 The 33 Design = 284
9-3.4 The General 3k Design = 289
9-3.5 Yates' Algorithm for the 3k Design = 290
9-4 Problems = 292
10. Confounding = 299
10-1 Introduction = 299
10-2 Confounding in the 2k Factorial Design = 299
10-2.1 The 2k Factorial Design in Two Blocks = 300
10-2.2 The 2k Factorial Design in Four Blocks = 306
10-2.3 The 2k Factorial Design in 2p Blocks = 308
10-3 Confounding in the 3k Factorial Design = 311
10-3.1 The 3k Factorial Design in Three Blocks = 311
10-3.2 The 3k Factorial Design in Nine Blocks = 315
10-3.3 The 3k Factorial Design in 3p Blocks = 317
10-4 Partial Confounding = 317
10-5 Other Confounding Systems = 321
10-6 Problems = 323
11. Fractional Factorial Designs = 325
11-1 Introduction = 325
11-2 Fractional Replication of the 2k Factorial Design = 325
11-2.1 The One-Half Fraction of the 2k Design = 326
11-2.2 The One-Quarter Fraction of the 2k Design = 335
11-2.3 The General 2k-p Fractional Factorial Design = 337
11-2.4 Designs of Resolution Ⅲ = 340
11-2.5 Designs of Resolution Ⅳ and Ⅴ = 347
11-3 Fractional Replication of the 3k Factorial Design = 349
11-3.1 The One-Third Fraction of the 3k Design = 349
11-3.2 Other 3k-p Fractional Factorial Designs = 352
11-4 Problems = 354
12. Nested or Hierarchial Designs = 357
12-1 Introduction = 357
12-2 The Two-Stage Nested Design = 358
12-2.1 Statistical Analysis = 358
12-2.2 Estimation of the Model Parameters = 363
12-2.3 Diagnostic Checking = 366
12-3 The General m-Stage Nested Design = 368
12-4 Designs with Nested and Crossed Factors = 370
12-5 Problems = 374
13. Multifactor Experiments with Randomization Restrictions = 379
13-1 Randomized Blocks and Latin Squares as Multifactor Designs = 379
13-2 The Split-Plot Design = 386
13-3 The Split-Split Plot Design = 391
13-4 Problems = 395
14. Regression Analysis = 399
14-1 Introduction = 399
14-2 Simple Linear Regression = 400
14-3 Hypothesis Testing in Simple Linear Regression = 407
14-4 Interval Estimation in Simple Linear Regression = 410
14-5 Model Adequacy Checking = 414
14-5.1 Residual Analysis = 414
14-5.2 The Lack-of-Fit Test = 416
14-5.3 The Coefficient of Determination = 419
14-6 Multiple Linear Regression = 420
14-7 Hypothesis Testing in Multiple Linear Regression = 429
14-8 Other Linear Regression Models = 435
14-9 Sample Computer Printout = 438
14-10 Problems = 440
15. Response Surface Methodology = 445
15-1 Introduction = 445
15-2 The Method of Steepest Ascent = 447
15-3 Analysis of Quadratic Models = 453
15-4 Response Surface Designs = 460
15-4.1 Designs for Fitting the First-Order Model = 460
15-4.2 Designs for Fitting the Second-Order Model = 462
15-5 Evolutionary Operation = 463
15-6 Problems = 470
16. Analysis of Covariance = 475
16-1 Introduction = 475
16-2 One-Way Classification with a Single Covariate = 476
16-3 Development by the General Regression Significance Test = 490
16-4 Other Covariance Models = 493
16-5 Problems = 495
Bibliography = 499
Appendix = 505
Table Ⅰ. Cumulative Standard Normal Distribution = 506
Table Ⅱ. Percentage Points of the t Distribution = 508
Table Ⅲ. Percentage Points of the X2 Distribution = 509
Table Ⅳ. Percentage Points of the F Distribution = 510
Table Ⅴ. Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance = 515
Table Ⅵ. Operating Characteristic Curves for the Random Effects Model Analysis of Variance = 519
Table Ⅶ. Significant Ranges for Duncan's Multiple Range Test = 523
Table Ⅷ. Percentage Points of the Studentized Range Statistic = 525
Table Ⅸ. Critical Values for Dunnett's Test for Comparing Treatments with a Control = 527
Table Ⅹ. Coefficients of Orthogonal Polynomials = 531
Table XI. Random Numbers = 532
Index = 535
