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This book describes the methods and techniques used in the design and analysis of experiments. It emphasizes the connection between the experiment and the model that the experimenter can develop from the results of the experiment and features a new chapter on experiments with random factors.

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CONTENTS
Chapter 1. Introduction = 1
  1-1 Strategy of Experimentation = 1
  1-2 Some Typical Applincations of Experimental Design = 7
  1-3 Basic Principles = 12
  1-4 Guidelines for Designing Experiments = 14
  1-5 Historical Perspective = 17
  1-6 Summary : Using Statistical Techniques in Experimentation = 18
Chapter 2. Simple Comparative Experiments = 20
  2-1 Introduction = 20
  2-2 Basic Statisical Concepts = 21
  2-3 Sampling and Sampling Distributions = 26
  2-4 Inferences About the Differences in Means Randomized Designs = 33
    2-4.1 Hypothesis Testing = 34
    2-4.2 Choice of Sample Size = 41
    2-4.3 Confidence Intervals = 43
    2-4.4 The Case Where σ1 2 ≠ σ2 2 = 45
    2-4.5 The Case Where σ1 2 and σ2 2 Are Known = 46
    2-4.6 Comparing a Single Mean to Specified Value = 46
    2-4.7 Summary = 48
  2-5 Inferences About the Differences in Means, Paired Comparison Designs = 48
    2-5.1 The Paired Comparison Problem = 48
    2-5.2 Advantages of the Paired Comparison Dasign = 53
  2-6 Inferences About the Varances of Normal Distributions = 54
  2-7 Problems = 56
Chapter 3. Experiments with a Single Factor : The Analysis of Varance = 63
  3-1 An Example = 63
  3-2 The Analysis of Variance = 67
  3-3 Analysis of the Fixes Effexts Model = 68
    3-3.1 Decomposition of the Total Sum of Squares = 69
    3-3.2 Statistical Analysis = 72
    3-3.3 Estimation of the Model Paramerters = 78
    3-3.4 Unbalanced Data = 79
  3-4 Model Adequarcy Checking = 79
    3-4.1 The Normality Assumpion = 80
    3-4.2 Plot of Residuals in Time Sequence = 83
    3-4.3 Plot of Residuals Versus Fitted Values = 84
    3-4.4 Selecting a Variance-Stabilizing Transformation = 87
    3-4.5 Plots of Residuals Versus Other Variables = 92
  3-5 Practical Interpretation of Results = 93
    3-5.1 A Regression Model = 93
    3-5.2 Cmparisons Among Treatment Means = 95
    3-5.3 Graphical Comparisons of Means = 95
    3-5.4 Contrasts = 96
    3-5.5 Orthogonal Contrasts = 98
    3-5.6 Scheff e' 's Method for Comparing All Contrasts = 100
    3-5.7 Comparing Pairs of Treatment Means = 101
    3-5.8 Comparing Treatment Means with a Control = 107
  3-6 Sample Computer Output = 108
  3-7 The Random Effects Model = 110
  3-8 Problems = 117
Chapter 4. More About Single-Factor Experiments = 126
  4-1 Choice of Sample Size = 126
    4-1.1 Operating Characteristic Curves = 126
    4-1.2 Specifying a Standard Deviation Increase = 130
    4-1.3 Confidence Interval Estimation Method = 131
  4-2 Discovering Dispersion Effects = 132
  4-3 Fitting Response Curves in the Single-Factor Model = 134
  4-4 The Regression Approach to the Analysis of Variance = 137
    4-4.1 Least Squares Extimation of the Model Parameters = 137
    4-4.2 The General Regression Significance Test = 138
  4-5 Nonparametric Methods in the Analysis of Variance = 143
    4-5.1 The Kruskal-Wallis Test = 143
    4-5.2 General Comments on the Rank Transforamtion = 145
  4-6 Repearted Measures = 146
  4-7 The Analysis of Covariance = 149
    4-7.1 Description of the Procedure = 150
    4-7.2 Computer Solution = 161
    4-7.3 Development by the General Regression Signifiance Test = 164
  4-8 Problems = 166
Chapter 5. Randomized Blocks, Latin Squares, and Related Designs = 171
  5-1 The Randomized Complete Block Design = 171
    5-1.1 Statisical Analysis = 173
    5-1.2 Adequarcy Checking = 182
    5-1.3 Some Other Aspects of the Randomizes Complete Block Design = 185
    5-1.4 Estimating Model Parameters and the General Regression Significance Test = 191
  5-2 The Latin Square Design = 194
  5-3 The Graeco-Latin Square Design = 205
  5-4 Balanced Incomplete Block Designs = 208
    5-4.1 Statistical Analysis = 208
    5-4.2 Least Squares Estimation of the Parametrs = 216
    5-4.3 Recovery of Interblock Information in the Balanced Incomplete Block Design = 217
  5-5 Problem
Chapter 6. Introduction to Factorial Designs = 228
  6-1 Basic Definitions and Principles = 228
  6-2 The Advantage of Factorials = 233
  6-3 The Two-Factor Factorial Design= 234
    6-3.1 An Example = 234
    6-3.2 Statistical Analysis of the Fixed Effects Model = 237
    6-3.3 Model Adequacy Checking = 243
    6-3.4 Estimating the Model Parameters = 245
    6-3.5 Choice of Sample Size = 249
    6-3.6 The Assumption of No Interaction in a Two-Factor Model = 251
    6-3.7 One Observation per Cell = 252
  6-4 The General Factorial Design = 255
  6-5 Fitting Response Curves and Surfaces = 263
  6-6 Blocking in a Factorial Design = 271
  6-7 Unbalanced Data in a Factorial Design = 276
    6-7.1 Proportional Data : An Easy Case = 277
    6-7.2 Approxmate Methods = 279
    6-7.3 The Exact Methods = 281
  6-8 Problems = 281
Chapter 7. The \mathop 2k Factorial Design = 290
  7-1 Introduction = 290
  7-2 The 2² Design = 291
  7-3 The 2³ Design = 301
  7-4 The General \mathop 2k Design = 315
  7-5 ASingle REplicate of the \mathop 2k Design = 318
  7-6 The addition of Center Points to the \mathop 2k Design = 336
  7-7 Yates' Algorithm for the \mathop 2k Design = 340
  7-8 Problems = 341
Chapter 8. Blocking and Confounding in the \mathop 2k Factorial Design = 354
  8-1 Introduction = 354
  8-2 Blocking a Replicated \mathop 2k Factorial Design = 354
  8-3 Confounding in the \mathop 2k Factorial Design = 356
  8-4 Confounding in the \mathop 2k Factorial Design in Two Blocks = 356
  8-5 Confounding in the \mathop 2k Factorial Design in four Blocks = 363
  8-6 Confounding in the \mathop 2k Factorial Design in \mathop 2p Blocks = 365
  8-7 Partial Confounding = 367
  8-8 Problems = 370
Chapter 9. Two-Level Factional Factorial Design = 372
  9-1 Introduction = 372
  9-2 The One-Half Fraction of the \mathop 2k Design = 373
  9-3 The One-Quarter Faction of the \mathop 2k Design = 389
  9-4 The General \mathop 2k -p Fractional Factorial Design = 398
  9-5 Resolution Ⅲ Designs = 409
  9-6 Resolution Ⅳ and Ⅴ Designs = 420
  9-7 Summary = 421
  9-8 Problems = 422
Chapter 10. Three-Level and Mixed-Level Factorial and Fractional Factorial Designs = 436
  10-1 the \mathop 3k Factorial Design = 436
    10-1.1 Nortation and Motivation for the \mathop 3k Design = 436
    10-1.2 The 3² Design = 438
    10-1.3 The 3³ Design = 441
    10-1.4 The General \mathop 3k Design = 447
    10-1.5 Yates' Algorithm for the \mathop 3k Design = 448
  10-2 Confounding in the \mathop 3k Factorial Design = 449
    10-2.1 The \mathop 3k Factorial Design in Three Blocks = 449
    10-2.2 The \mathop 3k Factorial Design in Nine Blocks = 454
    10-2.3 The \mathop 3k Factorial Design in \mathop 3p Blocks = 455
  10-3 Fractional Replication of the \mathop 3k Factorial Designs = 456
    10-3.1 The One-Third Fraction of the 3^k Factorial Design = 456
    10-3.2 Other \mathop 3k -p Fractional Factorial Designs = 460
  10-4 Factorials with Mixed Levels = 461
    10-4.1 Factors at Two and Three Levels = 462
    10-4.2 Factors at Two and Four Levels = 464
  10-5 Problems = 466
Chapter 11. Factorial Experiments with Random Factors = 470
  11-1 The Rwo Factor Factorial with Random Factors = 471
  11-2 The Rwo Factor Mixed Model = 475
  11-3 Use of Operating Characteristic Curver in Models with Random Factors = 480
  11-4 for Expected Mean Squares = 480
  11-5 Approximate F Tests = 486
  11-6 Some Additional Topics on Estimation of Variance Cmponents = 491
    11-6.1 Approximate Confidence Intervalson Variance Components = 491
    11-6.2 The Modified Large-Sample Method = 494
    11-6.3 Maximum Likelihood Estimation of Variance Components = 496
  11-7 problems = 502
Chapter 12. Nerted and Split-Plot Designs = 506
  12-1 The Two-Stage Nested Design = 506
    12-1.1 Statistical Analysis = 507
    12-1.2 Dianostic Checking = 512
    12-1.3 Variance Components = 514
    12-1.4 Staggered Nested Designs = 515
  12-2 The General m-Stage Nested Design = 516
  12-3 Designs with Both Nested and Factorial Factors = 519
  12-4 The Split-Plot Design = 521
  12-5 The Split-Split-Plot Design = 526
  12-6 Problems = 529
Chapter 13. Fitting Regression Models = 536
  13-1 Introduction = 536
  13-2 Liner Regression Models = 537
  13-3 Estimation of the Parameters in Linear Regression Models = 538
  13-4 Hypothesis Testing in Multiple Regression = 554
    13-4.1 Test for Significance of Regression = 555
    13-4.2 Tests on Individual Regression Coefficients and Groups of Coefficients = 557
  13-5 Confidence Intervals in Multiple Regression = 561
    13-5.1 Confidence Intervals on the Individual Reression Coefficients = 561
    13-5.2 Confidence Interval on the Mean Response = 562
  13-6 Preduiction of new Response Observations = 562
  13-7 Regression Model Diagnostics = 563
    13-7.1 Scaled Residuals and PRESS = 563
    13-7.2 Influence Diagnostics = 563
  13-8 Testing for Lake of Fit = 566
  13-9 Problems = 569
Chapter 14. Response Surface Methods and Other Approaches to Process Optimization = 575
  14-1 Introduction to Response Surface Methodology = 575
  14-2 The Method of Steepest Ascent = 578
  14-3 Analysis of a Second-Order Response Surface = 585
    14-3.1 Location of the the Stationary Point = 585
    14-3.2 Characterizing the Response Surface = 587
    14-3.3 Ridge Systems = 595
    14-3.4 Multiple Responses = 596
  14-4 Expermental Designs for Fitting Response Surfaces = 599
    14-4.1 Design for Fitting the First-Order Model = 600
    14-4.2 Designs for Fitting the Second-Order Model = 601
    14-4.3 Blocking in Response Surface Desings = 606
  14-5 Mixture Experiments = 611
  14-6 Evolutionary Operation = 616
  14-7 Taguchi's Contributions to Experimental Design and Quality Engineering = 622
    14-7.1 The Taguchi Philosophy = 623
    14-7.2 The Taguchi Approach to Parameter Design = 625
  14-8 Problems = 642
Bibliography = 652
Appendix = 656
  Table Ⅰ. Cumulative Standard Normal Distribution = 657
  Table Ⅱ. Percentage Points of the t Distribution = 659
  Table Ⅲ. Percentage Points of the X²Distribution = 660
  Table Ⅳ. Percentage Points of the F Distribution = 661
  Table Ⅴ. Operating Characteistic Curves for the Fixed Effects Model Analysis of Variance = 666
  Table Ⅵ. PerceOperating Charctterstic Curves for the Random Effects Model Analysis of Variance = 670
  Table Ⅶ. Significant Ranges for Duncan's Multiple Range Test = 674
  Table Ⅷ. Percentage Points of Studentized Range Statistic = 675
  Table Ⅸ. Critical Values for Dunnett' s Test for Comparing Treatments with a Control = 677
  Table Ⅹ. Coefficients of Orthogonal Polynomials = 680
  Table XI. Random Numbers = 681
  Table XII. Alias Relationships for \mathop 2k -p Fractional Factorial Designs with k≤15 and n≤64 = 682
Index = 699