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Preface | |
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Introduction | |
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Role of Statistics in Experiment Design | |
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Organization of This Book | |
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Representativeness and Experimental Units | |
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Replication and Handling Unexplained Variability | |
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Randomization: Why and How | |
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Ethical Considerations | |
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Review Exercises | |
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Completely Randomized Design | |
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Introduction | |
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Completely Randomized Design | |
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Assumption of Additivity | |
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Factorial Treatment Combinations | |
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Nested Factors | |
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Review Exercises | |
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Linear Models for Designed Experiments | |
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Introduction | |
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Linear Model | |
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Principle of Least Squares | |
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Parameterizations for Row--Column Models | |
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Review Exercises | |
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Linear Combinations of Random Variables | |
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Simulating Random Samples | |
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Testing Hypotheses and Determining Sample Size | |
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Introduction | |
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Testing Hypotheses in Linear Models with Normally Distributed Errors | |
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Kruskal--Wallis Test | |
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Randomization Tests | |
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Power and Sample Size | |
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Sample Size for Binomial Proportions | |
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Confidence Interval Width and Sample Size | |
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Alternative Analysis: Selecting and Screening | |
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Review Exercises | |
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Methods of Reducing Unexplained Variation | |
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Randomized Complete Block Design | |
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Blocking | |
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Formal Statistical Analysis for the RCBD | |
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Models and Assumptions: Detailed Examination | |
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Statistical Analysis When Data Are Missing in an RCBD | |
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Analysis of Covariance | |
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Review Exercises | |
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Interaction of a Random Block Effect and a Fixed Treatment Effect | |
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Latin Squares | |
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Introduction | |
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Formal Structure of Latin Squares | |
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Combining Latin Squares | |
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Graeco--Latin Squares and Orthogonal Latin Squares | |
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Some Special Latin Squares and Variations on Latin Squares | |
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Frequency Squares | |
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Youden Square | |
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Review Exercises | |
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Some Standard Latin Squares | |
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Mutually Orthogonal Latin Squares | |
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Possible Youden Squares | |
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Split-Plot and Related Designs | |
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Introduction | |
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Background Material | |
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Examples of Situations That Lead to Split-Plots | |
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Statistical Analysis of Split-Plot Experiments | |
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Split-Split-Plot Experiments | |
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Strip-Plot Experiments | |
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Comments on Further Variations | |
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Analysis of Covariance in Split-Plots | |
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Repeated Measures | |
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Review Exercises | |
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Incomplete Block Designs | |
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Introduction | |
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Efficiency of Incomplete Block Designs | |
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Distribution-Free Analysis for Incomplete Block Designs | |
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Balanced Incomplete Block Designs | |
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Lattice Designs | |
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Cyclic Designs | |
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[alpha]-Designs | |
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Other Incomplete Block Designs | |
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Review Exercises | |
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Catalog of Incomplete Block Designs | |
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Repeated Treatments Designs | |
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Introduction | |
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Repeated Treatments Design Model | |
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Construction of Repeated Treatments Designs | |
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Statistical Analysis of Repeated Treatments Design Data | |
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Carryover Design for Two Treatments | |
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Correlated Errors | |
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Designs for More Complex Models | |
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Review Exercises | |
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Factorial Experiments: The 2[superscript N] System | |
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Introduction | |
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2[superscript N] Factorials | |
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General Notation for the 2[superscript N] System | |
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Analysis of Variance for 2[superscript N] Factorials | |
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Factorial Experiments: The 3[superscript N] System | |
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Introduction | |
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3 X 3 Factorial | |
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General System of Notation for the 3[superscript N] System | |
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Analysis of Experiments without Designed Error Terms | |
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Introduction | |
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Techniques That Look for Location Parameters | |
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Analysis for Dispersion Effects | |
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Review Exercises | |
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Confounding Effects with Blocks | |
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Introduction | |
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Confounding 2[superscript 3] Factorials | |
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General Confounding Patterns | |
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Double Confounding | |
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3[superscript N] System | |
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Detailed Numerical Example: 3[superscript 3] Factorial in Blocks of Nine | |
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Confounding Schemes for the 3[superscript 4] System | |
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Review Exercises | |
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Fractional Factorial Experiments | |
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Introduction | |
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Organization of This Chapter | |
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Fractional Replication in the 2[superscript N] System | |
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Resolution | |
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Constructing Fractional Replicates by Superimposing Factors | |
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Foldover Technique | |
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Franklin-Bailey Algorithm for Constructing Fractions | |
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Irregular Fractions of the 2[superscript N] System | |
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Fractional Factorials with Compromised Resolution | |
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A Caution About Minimum Aberration | |
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Direct Enumeration Approach to Constructing Plans | |
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Blocking in Small 2[superscript N-k] Plans | |
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Fractional Replication in the 3[superscript N] System | |
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Review Exercises | |
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Minimum Aberration Fractions without Blocking | |
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Minimum Aberration Fractions with Blocking | |
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Response Surface Designs | |
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Introduction | |
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Basic Formulation | |
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Some Basic Designs | |
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Rotatability | |
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Statistical Analyses of Data from Response Surface Designs | |
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Blocking in Response Surface Designs | |
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Mixture Designs | |
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Optimality Criteria and Parametric Modeling | |
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Response Surfaces in Irregular Regions | |
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Searching the Operability Region for an Optimum | |
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Examination of an Experimental Problem | |
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Review Exercise | |
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Plackett-Burman Hadamard Plans | |
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Introduction | |
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Hadamard Matrix | |
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Plackett-Burman Plans | |
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Hadamard Plans and Interactions | |
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Statistical Analyses | |
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Weighing Designs | |
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Projection Properties of Hadamard Plans | |
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Very Large Factorial Experiments | |
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General p[superscript N] and Nonstandard Factorials | |
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Introduction | |
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Organization of This Chapter | |
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p[superscript N] System with p Prime | |
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4[superscript N] System | |
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4[superscript N] System Using Pseudofactors at Two Levels | |
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6[superscript N] Factorial System | |
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Asymmetrical Factorials | |
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2[superscript N] X 3[superscript M] Plans | |
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Plans for Which Run Order Is Important | |
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Introduction | |
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Preliminary Concepts | |
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Trend-Resistant Plans | |
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Generating Run Orders for Fractions | |
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Extreme Number of Level Changes | |
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Trend-Free Plans from Hadamard Matrices | |
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Extensions to More Than Two Levels | |
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Small One-at-a-Time Plans | |
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Comments | |
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Sequences of Fractions of Factorials | |
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Introduction | |
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Motivating Example | |
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Foldover Techniques Examined | |
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Augmenting a 2[superscript 4-1] Fraction | |
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Sequence Starting from a Seven-Factor Main Effect Plan | |
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Augmenting a One-Eighth Fraction of 4[superscript 3] | |
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Adding Levels of a Factor | |
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Double Semifold | |
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Planned Sequences | |
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Sequential Fractions | |
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Factorial Experiments with Quantitative Factors: Blocking and Fractions | |
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Introduction | |
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Factors at Three Levels | |
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Factors at Four Levels Based on the 2[superscript N] System | |
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Pseudofactors and Hadamard Plans | |
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Box-Behnken Plans | |
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Review Exercises | |
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Box-Behnken Plans | |
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Supersaturated Plans | |
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Introduction | |
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Plans for Small Experiments | |
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Supersaturated Plans That Include an Orthogonal Base | |
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Model-Robust Plans | |
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Multistage Experiments | |
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Introduction | |
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Factorial Structures in Split-Plot Experiments | |
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Splitting on Interactions | |
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Factorials in Strip-Plot or Strip-Unit Designs | |
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General Comments on Strip-Unit Experiments | |
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Split-Lot Designs | |
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Fractional Factorial Plans for Split-Plot Designs | |
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Orthogonal Arrays and Related Structures | |
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Introduction | |
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Orthogonal Arrays and Fractional Factorials | |
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Other Construction Methods | |
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Nearly Orthogonal Arrays | |
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Large Orthogonal Arrays | |
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Summary | |
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Factorial Plans Derived via Orthogonal Arrays | |
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Introduction | |
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Preliminaries | |
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Product Array Designs | |
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Block Crossed Arrays | |
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Compound Arrays | |
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Experiments on the Computer | |
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Introduction | |
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Stratified and Latin Hypercube Sampling | |
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Using Orthogonal Arrays for Computer Simulation Studies | |
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Demonstration Simulations | |
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References | |
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Index | |