Preface.
1. Introduction.
1.1 Strategy of Experimentation.
1.2 Some Typical Applications of Experimental Design.
1.3 Basic Principles.
1.4 Guidelines for Designing Experiments.
1.5 A Brief History of Statistical Design.
1.6 Summary: Using Statistical Techniques in Experimentation.
1.7 Problems.
2. Simple Comparative Experiments.
2.1 Introduction.
2.2 Basic Statistical Concepts.
2.3 Sampling and Sampling Distributions.
2.4 Inferences About the Differences in Means, Randomized Designs.
2.4.1 Hypothesis Testing.
2.4.2 Choice of Sample Size.
2.4.3 Confidence Intervals.
2.4.4 The Case Where.
2.4.5 The Case Where and Are Known.
2.4.6 Comparing a Single Mean to a Specified Value.
2.4.7 Summary.
2.5 Inferences About the Differences in Means, Paired Comparison Designs.
2.5.1 The Paired Comparison Problem.
2.5.2 Advantages of the Paired Comparison Design.
2.6 Inferences About the Variances of Normal Distributions.
2.7 Problems.
3. Experiments with a Single Factor: The Analysis of Variance.
3.1 An Example.
3.2 The Analysis of Variance.
3.3 Analysis of the Fixed Effects Model.
3.3.1 Decomposition of the Total Sum of Squares.
3.3.2 Statistical Analysis.
3.3.3 Estimation of the Model Parameters.
3.3.4 Unbalanced Data.
3.4 Model Adequacy Checking.
3.4.1 The Normality Assumption.
3.4.2 Plot of Residuals in Time Sequence.
3.4.3 Plot of Residuals Versus Fitted Values.
3.4.4 Plots of Residuals Versus Other Variables.
3.5 Practical Interpretation of Results.
3.5.1 A Regression Model.
3.5.2 Comparisons Among Treatment Means.
3.5.3 Graphical Comparisons of Means.
3.5.4 Contrasts.
3.5.5 Orthogonal Contrasts.
3.5.6 Scheffé’s Method for Comparing All Contrasts.
3.5.7 Comparing Pairs of Treatment Means.
3.5.8 Comparing Treatment Means with a Control.
3.6 Sample Computer Output.
3.7 Determining Sample Size
3.7.1 Operating Characteristic Curves.
3.7.2 Specifying a Standard Deviation Increase.
3.7.3 Confidence Interval Estimation Method.
3.8 A Real Economy Application of a Designed Experiment.
3.9 Discovering Dispersion Effects.
3.10 The Regression Approach to the Analysis of Variance.
3.10.1 Least Squares Estimation of the Model Parameters.
3.10.2 The General Regression Significance Test.
3.11 Nonparametric Methods in the Analysis of Variance.
3.11.1 The Kruskal–Wallis Test.
3.11.2 General Comments on the Rank Transformation.
3.12 Problems.
4. Randomized Blocks, Latin Squares, and Related Designs.
4.1 The Randomized Complete Block Design.
4.1.1 Statistical Analysis of the RCBD.
4.1.2 Model Adequacy Checking.
4.1.3 Some Other Aspects of the Randomized Complete Block Design.
4.1.4 Estimating Model Parameters and the General Regression Significance Test.
4.2 The Latin Square Design.
4.3 The Graeco-Latin Square Design.
4.4 Balanced Incomplete Block Designs.
4.4.1 Statistical Analysis of the BIBD.
4.4.2 Least Squares Estimation of the Parameters.
4.4.3 Recovery of Interblock Information in the BIBD.
4.5 Problems.
5. Introduction to Factorial Designs.
5.1 Basic Definitions and Principles.
5.2 The Advantage of Factorials.
5.3 The Two-Factor Factorial Design.
5.3.1 An Example.
5.3.2 Statistical Analysis of the Fixed Effects Model.
5.3.3 Model Adequacy Checking.
5.3.4 Estimating the Model Parameters.
5.3.5 Choice of Sample Size.
5.3.6 The Assumption of No Interaction in a Two-Factor Model.
5.3.7 One Observation per Cell.
5.4 The General Factorial Design.
5.5 Fitting Response Curves and Surfaces.
5.6 Blocking in a Factorial Design.
5.7 Problems.
6. The 2^{k}Factorial Design.
6.1 Introduction.
6.2 The 2^{2}Design.
6.3 The 2^{3}Design.
6.4 The General 2^{k}Design.
6.5 A Single Replicate of the 2^{k}Design.
6.6 Additional Examples of Unreplicated 2^{k}Design.
6.7 2^{k}Designs are Optimal Designs.
6.8 The Addition of Center Points to the 2^{k}Design.
6.9 Why We Work with Coded Design Variables.
6.10 Problems.
7. Blocking and Confounding in the 2^{k}Factorial Design.
7.1 Introduction.
7.2 Blocking a Replicated 2^{k}Factorial Design.
7.3 Confounding in the 2^{k}Factorial Design.
7.4 Confounding the 2^{k}Factorial Design in Two Blocks.
7.5 Another Illustration of Why Blocking Is Important.
7.6 Confounding the 2^{k}Factorial Design in Four Blocks.
7.7 Confounding the 2^{k}Factorial Design in 2^{p}Blocks.
7.8 Partial Confounding.
7.9 Problems.
8. Two-Level Fractional Factorial Designs.
8.1 Introduction.
8.2 The One-Half Fraction of the 2^{k}Design.
8.2.1 Definitions and Basic Principles.
8.2.2 Design Resolution.
8.2.3 Construction and Analysis of the One-Half Fraction.
8.3 The One-Quarter Fraction of the 2^{k}Design.
8.4 The General 2^{k–p}Fractional Factorial Design.
8.4.1 Choosing a Design.
8.4.2 Analysis of 2^{k–p}Fractional Factorials.
8.4.3 Blocking Fractional Factorials.
8.5 Alias Structures in Fractional Factorials and other Designs.
8.6 Resolution III Designs.
8.6.1 Constructing Resolution III Designs.
8.6.2 Fold Over of Resolution III Fractions to Separate Aliased Effects.
8.6.3 Plackett-Burman Designs.
8.7 Resolution IV and V Designs.
8.7.1 Resolution IV Designs.
8.7.2 Sequential Experimentation with Resolution IV Designs.
8.7.3 Resolution V Designs.
8.8 Supersaturated Designs.
8.9 Summary.
8.10 Problems.
9. Three-Level and Mixed-Level Factorial and Fractional Factorial Designs.
9.1 The 3^{k}Factorial Design.
9.1.1 Notation and Motivation for the 3^{k}Design.
9.1.2 The 3^{2}Design.
9.1.3 The 3^{3}Design.
9.1.4 The General 3^{k}Design.
9.2 Confounding in the 3^{k}Factorial Design.
9.2.1 The 3^{k}Factorial Design in Three Blocks.
9.2.2 The 3^{k}Factorial Design in Nine Blocks.
9.2.3 The 3^{k}Factorial Design in 3^{p}Blocks.
9.3 Fractional Replication of the 3^{k}Factorial Design.
9.3.1 The One-Third Fraction of the 3^{k}Factorial Design.
9.3.2 Other 3^{k–p}Fractional Factorial Designs.
9.4 Factorials with Mixed Levels.
9.4.1 Factors at Two and Three Levels.
9.4.2 Factors at Two and Four Levels.
10. Fitting Regression Models.
10.1 Introduction.
10.2 Linear Regression Models.
10.3 Estimation of the Parameters in Linear Regression Models.
10.4 Hypothesis Testing in Multiple Regression.
10.4.1 Test for Significance of Regression.
10.4.2 Tests on Individual Regression Coefficients and Groups of Coefficients.
10.5 Confidence Intervals in Multiple Regression.
10.5.1 Confidence Intervals on the Individual Regression Coefficients.
10.5.2 Confidence Interval on the Mean Response.
10.6 Prediction of New Response Observations.
10.7 Regression Model Diagnostics.
10.7.1 Scaled Residuals and PRESS.
10.7.2 Influence Diagnostics.
10.8 Testing for Lack of Fit.
10.9 Problems.
11. Response Surface Methods and Designs.
11.1 Introduction to Response Surface Methodology.
11.2 The Method of Steepest Ascent.
11.3 Analysis of a Second-Order Response Surface.
11.3.1 Location of the Stationary Point.
11.3.2 Characterizing the Response Surface.
11.3.3 Ridge Systems.
11.3.4 Multiple Responses.
11.4 Experimental Designs for Fitting Response Surfaces.
11.4.1 Designs for Fitting the First-Order Model.
11.4.2 Designs for Fitting the Second-Order Model.
11.4.3 Blocking in Response Surface Designs.
11.4.4 Computer-Generated (Optimal) Designs.
11.5 Experiments with Computer Models.
11.6 Mixture Experiments.
11.7 Evolutionary Operation.
11.8 Problems.
12. Robust Parameter Design and Process Robustness Studies.
12.1 Introduction.
12.2 Crossed Array Designs.
12.3 Analysis of the Crossed Array Design.
12.4 Combined Array Designs and the Response Model Approach.
12.5 Choice of Designs.
12.6 Problems.
13. Experiments with Random Factors.
13.1 The Random Effects Model.
13.2 The Two-Factor Factorial with Random Factors.
13.3 The Two-Factor Mixed Model.
13.4 Sample Size Determination with Random Effects.
13.5 Rules for Expected Mean Squares.
13.6 Approximate F Tests.
13.7 Some Additional Topics on Estimation of Variance Components.
13.7.1 Approximate Confidence Intervals on Variance Components.
13.7.2 The Modified Large-Sample Method.
13.7.3 Maximum Likelihood Estimation of Variance Components.
13.8 Problems.
14. Nested and Split-Plot Designs.
14.1 The Two-Stage Nested Design.
14.1.1 Statistical Analysis.
14.1.2 Diagnostic Checking.
14.1.3 Variance Components.
14.1.4 Staggered Nested Designs.
14.2 The General m-Stage Nested Design.
14.3 Designs with Both Nested and Factorial Factors.
14.4 The Split-Plot Design.
14.5 Other Variations of the Split-Plot Design.
14.5.1 Split-Plot Designs with More Than Two Factors.
14.5.2 The Split-Split-Plot Design.
14.5.3 The Strip-Split-Plot Design.
14.6 Problems.
15. Other Design and Analysis Topics.
15.1 Nonnormal Responses and Transformations.
15.1.1 Selecting a Transformation: The Box–Cox Method.
15.1.2 The Generalized Linear Model.
15.2 Unbalanced Data in a Factorial Design.
15.2.1 Proportional Data: An Easy Case.
15.2.2 Approximate Methods.
15.2.3 The Exact Method.
15.3 The Analysis of Covariance.
15.3.1 Description of the Procedure.
15.3.2 Computer Solution.
15.3.3 Development by the General Regression Significance Test.
15.3.4 Factorial Experiments with Covariates.
15.4 Repeated Measures.
15.5 Problems.
Appendix.
Table I. Cumulative Standard Normal Distribution.
Table II. Percentage Points of the t Distribution.
Table III. Percentage Points of the X^{2}Distribution.
Table IV. Percentage Points of the F Distribution.
Table V. Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance.
Table VI. Operating Characteristic Curves for the Random Effects Model Analysis of Variance.
Table VII. Percentage Points of the Studentized Range Statistic.
Table VIII. Critical Values for Dunnett’s Test for Comparing Treatments with a Control.
Table IX. Coefficients of Orthogonal Polynomials.
Table X. Alias Relationships for 2^{k–p}Fractional Factorial Designs with k 15 and n 64.
Bibliography.
Index.