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Preface | |
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About the Author | |
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Research Strategies and the Control of Nuisance Variables | |
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Introduction | |
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Formulation of Plans for the Collection and Analysis of Data | |
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Research Strategies | |
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Other Research Strategies | |
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Threats to Valid Inference Making | |
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Other Threats to Valid Inference Making | |
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Controlling Nuisance Variables and Minimizing Threats to Valid Inference Making | |
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Ethical Treatment of Subjects | |
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Review Exercises | |
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Experimental Designs: An Overview | |
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Introduction | |
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Overview of Some Basic Experimental Designs | |
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Classification of Analysis of Variance Designs | |
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Selecting an Appropriate Design | |
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Review of Statistical Inference | |
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Review Exercises | |
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Fundamental Assumptions in Analysis of Variance | |
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Sampling Distributions in Analysis of Variance | |
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Partition of the Total Sum of Squares | |
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Expectation of the Mean Squares | |
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The F Statistic in Analysis of Variance | |
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Effects of Failure to Meet Assumptions in Analysis of Variance | |
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Transformations | |
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Other Procedures for Dealing With Nonnormality, Unequal Variances, and Outliers | |
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Supplement for Section 3.3 | |
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Review Exercises | |
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Completely Randomized Design | |
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Description of the Design | |
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Exploratory Data Analysis | |
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Computational Example for CR-4 Design | |
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Measures of Strength of Association and Effect Size | |
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Power and the Determination of Sample Size | |
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Random-Effects Model | |
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Advantages and Disadvantages of CR-p Design | |
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Review Exercises | |
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Multiple Comparison Tests | |
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Introduction to Multiple Comparison Tests | |
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Procedures for Testing p - 1 a Priori Orthogonal Contrasts | |
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Procedures for Testing p - 1 Contrasts Involving a Control Group Mean | |
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Procedures for Testing C a Priori Nonorthogonal Contrasts | |
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Procedures for Testing All Pairwise Contrasts | |
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Testing All Contrasts Suggested by an Inspection of the Data | |
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Other Multiple Comparison Procedures | |
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Comparison of Multiple Comparison Procedures | |
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Review Exercises | |
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Trend Analysis | |
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Introduction to Tests for Trends | |
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Test for the Linear Trend Contrast | |
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Tests for Higher-Order Trend Contrasts | |
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Linear and Curvilinear Correlation | |
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Variance Accounted for by Mean Contrasts | |
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Review Exercises | |
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General Linear Model Approach to ANOVA | |
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Comparison of Analysis of Variance and Multiple Regression | |
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Operations With Vectors and Matrices | |
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General Linear Model | |
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Estimating the Parameters in a Regression Model | |
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Regression Model Approach to ANOVA | |
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Alternative Conception of the Test of �<sub>1</sub> = �<sub>2</sub> = … = �<sub>h-1</sub> = 0 | |
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Cell Means Model Approach to ANOVA | |
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Summary | |
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Review Exercises | |
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Randomized Block Designs | |
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Description of Randomized Block Design | |
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Computational Example for RB-p Design | |
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Alternative Models for RB-p Design | |
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Some Assumptions Underlying RB-p Design | |
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Procedures for Testing Differences Among Means | |
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Tests for Trends | |
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Relative Efficiency of Randomized Block Design | |
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Cell Mean Model Approach to the RB-p Design | |
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Generalized Randomized Block Design | |
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Advantages and Disadvantages of RB-p and GRB-p Designs | |
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Review Exercises | |
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Completely Randomized Factorial Design With Two Treatments | |
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Introduction to Factorial Designs | |
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Description of Completely Randomized Factorial Design | |
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Computational Example for CRF-pq Design | |
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Experimental Design Model for CRF-pq Design | |
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Procedures for Testing Differences Among Means | |
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More on the Interpretation of Interactions | |
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Tests for Trends | |
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Estimating Strength of Association, Effect Size, Power, and Sample Size | |
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Rules for Deriving Expected Values of Mean Squares | |
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Quasi F Statistics | |
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Preliminary Tests on the Model and Pooling Procedures | |
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Analysis of Completely Randomized Factorial Designs With n = 1 | |
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Cell Means Model Approach to Completely Randomized Factorial Design | |
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Analysis of Completely Randomized Factorial Designs With Missing Observations and Empty Cells | |
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Advantages and Disadvantages of Factorial Designs | |
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Review Exercises | |
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Completely Randomized Factorial Design With Three or More Treatments and Randomized Block Factorial Design | |
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Introduction to CRF-pqr Design | |
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Computational Example for CRF-pqr Design | |
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Patterns Underlying Sum-of-Squares Formulas | |
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Formulating Coefficient Matrices for the Cell Means Model | |
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Introduction to Randomized Block Factorial Design | |
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Computational Example for RBF-pq Design | |
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Expected Value of Mean Squares and the Sphericity Conditions | |
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Cell Means Model Approach to Randomized Block Factorial Design | |
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Minimizing Time and Location Effects by Using a Randomized Block Factorial Design | |
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Review Exercises | |
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Hierarchical Designs | |
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Introduction to Hierarchical Designs | |
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Computational Example for CKH-pq(A) Design | |
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Experimental Design Model for CRH-pq(A) Design | |
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Procedures for Testing Differences Among Means | |
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Estimating Strength of Association, Effect Size, Power, and Sample Size | |
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Description of Other Completely Randomized Hierarchical Designs | |
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Cell Means Model for Completely Randomized Hierarchical Design | |
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Cell Means Model for Randomized Block Hierarchical! Design | |
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Advantages and Disadvantages of Hierarchical Designs | |
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Review Exercises | |
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Split-Plot Factorial Design: Design With Group-Treatment Confounding | |
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Description of Split-Plot Factorial Design | |
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Computational Example for SW-p�q Design | |
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Experimental Design Model for SPF-p�q Design | |
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Some Assumptions Underlying SFF-p�q Design | |
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Procedures for Testing Differences Among Means | |
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Procedures for Testing Hypotheses About Simple Main Effects and Treatment-Contrast Interactions | |
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Relative Efficiency of Split-Plot Factorial Design | |
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Computational Procedures for SPF-pr�q Design | |
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Computational Procedures for SW-prt�q Design | |
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Computational Procedures for SPF-p�qr Design | |
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Computational Procedures for STF-p�qrt Design | |
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Computational Procedures for SW-pr�qt Design | |
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Evaluation of Sequence Effects | |
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Cell Means Model Approach to SPF-p�g Design | |
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Advantages and Disadvantages of Split-Plot Factorial Designs | |
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Review Exercises | |
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Analysis of Covariance | |
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Introduction to Analysis of Covariance | |
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Rationale Underlying Covariate Adjustment | |
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Layout and Computational Procedures for CRAC-p Design | |
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Some Assumptions Underlying CRAC-p Design | |
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Procedures for Testing Differences Among Means in CRAC-p Design | |
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Analysis With Two Covariates | |
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Analysis of Covariance for Randomized Block Design | |
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Analysis of Covariance for Factorial Designs | |
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Covariance Versus Stratification | |
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Regression Model Approach to Analysis of Covariance | |
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Cell Means Model Approach to Analysis of Covariance | |
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Advantages and Disadvantages of Analysis of Covariance | |
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Review Exercises | |
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Latin Square and Related Designs | |
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Description of Latin Square Design | |
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Construction and Randomization of Latin Squares | |
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Computational Example for Latin Square Design | |
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Computational Procedures for n = 1 | |
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Experimental Design Model for Latin Square Design | |
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Procedures for Testing Differences Among Means | |
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Relative Efficiency of Latin Square Design With n = 1 | |
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Analysis of Covariance for Latin Square Design | |
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Cell Means Model Approach to Latin Square Design | |
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Graeco-Latin Square Design | |
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Hyper-Graeco-Latin Square Designs | |
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Crossover Design | |
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Advantages and Disadvantages of Designs Based on a Latin Square | |
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Review Exercises | |
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Confounded Factorial Designs: Designs With Group-Interaction Confounding | |
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Group-Interaction Confounding | |
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Use of Modular Arithmetic in Constructing Confounded Designs | |
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Computational Procedures for RBCF-2<sup>2</sup> Design | |
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Experimental Design Model for RBCF-2<sup>2</sup> Design | |
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Layout and Analysis for RBCF-2<sup>3</sup> Design | |
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Complete Versus Partial Confounding | |
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Computational Procedures for RBPF-2<sup>3</sup> Design | |
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Computational Procedures for RBCF-3<sup>2</sup> and RBPF-3<sup>2</sup> Designs | |
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Analysis Procedures for Higher-Order Confounded Designs | |
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Alternative Notation and Computational Systems | |
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Computational Procedures for RBPF-32<sup>2</sup> Design | |
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Cell Means Model Approach to RBCF-p<sup>k</sup> Design | |
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Group-Interaction Confounding by Means of a Latin Square | |
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Advantages and Disadvantages of Confounding in Factorial Designs | |
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Review Exercises | |
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Fractional Factorial Designs: Designs With Treatment-Interaction Confounding | |
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Introduction to Fractional Factorial Designs | |
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General Procedures for Constructing Completely Randomized Fractional Factorial Designs | |
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Computational Procedures for CRFF-2<sup>4-1</sup> Design | |
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Computational Procedures for CRFF-3<sup>4-1</sup> Design | |
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Cell Means Model for CRFF-p<sup>k-i</sup> Design | |
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General Procedures for Constructing RBFF-p<sup>k-i</sup> Designs | |
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Other Types of CRFF and RBFF Designs | |
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Introduction to Latin Square Fractional Factorial Designs | |
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Computational Procedures for LSFF-p�p<sup>2</sup> Design | |
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Computational Procedures for LSFF-p<sup>3</sup>t Design | |
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Computational Procedures for LSFF-p<sup>4</sup>u Design | |
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Computational Procedures for GLSFF-p<sup>3</sup> Design | |
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Advantages and Disadvantages of Fractional Factorial Designs | |
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Review Exercises | |
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Rules of Summation | |
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Rules of Expectation, Variance, and Covariance | |
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Orthogonal Coefficients for Unequal Intervals and Unequal ns | |
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Matrix Algebra | |
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Tables | |
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Answers to Starred Exercises | |
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References | |
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Index | |