Yates analysis

Abstract: Basic Principles and Experiments with a Single Factor. Experiments With More Than One Factor. Full Factorial Experiments at Two Levels. Fractional Factorial Experiments at Two Levels. Full Factorial and Fractional Factorial Experiments at Three Levels. Other Design and Analysis Techniques for Experiments at More Than Two Levels. Nonregular Designs: Construction and Properties. Experiments with Complex Aliasing. Response Surface Methodology. Introduction to Robust Parameter Design. Robust Parameter Design for Signal-Response Systems. Experiments for Improving Reliability. Experiments With Nonnormal Data. Appendices. Indexes.

Abstract: 1. The Experiment, the Design, and the Analysis 1.1 Introduction 1.2 The Experiment 1.3 The Design 1.4 The Analysis 1.5 Examples 1.6 Summary in Outline Further Reading Problems 2. Review of Statistical Inference 2.1 Introduction 2.2 Estimation 2.3 Tests of hypothesis 2.4 The Operating Characterisitc Curve 2.5 How Large a Sample? 2.6 Application to Tests on Variances 2.7 Application to Tests on Means 2.8 Assessing Normality 2.9 Applications to Tests on Proportions 2.10 Analysis of Experiments with SAS Further Reading Problems 3. Single-Factor Experiments with No Restrictions on Randomization 3.1 Introduction 3.2 Analysis of Variance Rationale 3.3 After ANOVA-What? 3.4 Tests of Means 3.5 Confidence Limits on Means 3.6 Components of Variance 3.7 Checking the Model 3.8 SAS Programs for ANOVA and Tests after ANOVA 3.9 Summary Further Reading Problems 4. Single-Factor Experiments -- Randomized Block and Latin Square Designs 4.1 Introduction 4.2 Randomized Complete Block Design 4.3 ANOVA Rationale 4.4 Missing Values 4.5 Latin Squares 4.6 Interpretations 4.7 Assessing the Model 4.8 Graeco-Latin Squares 4.9 Extensions 4.10 SAS Programs for Randomized Blocks and Latin Squares 4.11 Summary Further Reading Problems 5. Factorial Experiments 5.1 Introduction 5.2 Factorial Experiments: An Example 5.3 Interpretations 5.4 The Model and Its Assessment 5.5 ANOVA Rationale 5.6 One Observation Per Treatment 5.7 SAS Programs for Factorial Experiments 5.8 Summary Further Reading Summary 6. Fixed, Random, and Mixed Models 6.1 Introduction 6.2 Single-Factor Models 6.3 Two-Factor Models 6.4 EMS Rule 6.5 EMS Derivations 6.6 The Pseudo-F Test 6.7 Expected Mean Squares Via Statistical Computing Packages 6.8 Remarks 6.9 Repeatability and Reproducibility for a Measurement System Further Reading Problems 7. Nested and Nested-Factorial Experiments 7.1 Introduction 7.2 Nested Experiments 7.3 ANOVA Rationale 7.4 Nested-Factorial Experiments 7.5 Repeated-Measures Design and Nested-Factorial Experiments 7.6 SAS Programs for Nested and Nested-Factorial Experiments 7.7 Summary Further Reading Problems 8. Experiments of Two or More Factors -- Restrictions and Randomization 8.1 Introductin 8.2 Factorial Experiment in a Randomized Block Design 8.3 Factorial Experiment in a Latin Square Design 8.4 Remarks 8.5 SAS Programs 8.6 Summary Further Reading Problems 9.2 2 Squared Factorial 9.3 2 Cubed Factorial 9.4 2f Factorial 9.5 The Yates Method 9.6 Analysis of 2f Factorials When n=1 9.8 Summary Further Reading Problems 10. 3f Factorial Experiments 10.1 Introduction 10.2 3 Squared Factorial 10.3 3 Cubed Factorial 10.4 Computer Programs 10.5 Summary Further Reading Problems 11. Factorial Experiment -- Split-Plot Design 11.1 Introduction 11.2 A Split-Plot Design 11.3 A Split-Split-Plot Design 11.4 Using SAS to Analyze a Split-Plot Experiment 11.5 Summary Further Reading Problems 12. Factorial Experiment -- Confounding in Blocks 12.1 Introduction 12.2 Confounding Systems 12.3 Block Confounding -- No Replication 12.4 Blcok Confounding with Replication 12.5 Confounding in 3F Factorials 12.6 SAS Progrms 12.7 Summary Further Reading Problems 13. Fractional Replication 13.1 Introduction 13.2 Aliases 13.3 2f Fractional Replication 13.4 Plackett-Burman Designs 14. Taguchi Approach to the Design of Experiments 14.1 Introduction 14.2 The L4 (2 Cubed) Orthogonal Array 14.3 Outer Arrays 14.4 Signal-To-Noise-Ratio 14.5 The L8 (2 7) Orthogonal Array 14.6 The L16 (2 15) Orthogonal Array 14.7 The L9 (3 4) Orthogonal Array 14.8 Some Other Taguchi Designs 14.9 Summary Futher Reading Problems 15. Regression 15.1 Introduction 15.2 Linear Regression 15.3 Curvilinear Regression 15.4 Orthogronal Polynomials 15.5 Multiple Regression 15.6 Summary Further Reading Summary 16. Miscellaneous Topics 16.1 Introduction 16.2 Covariance Analysis 16.3 Response-Surface Experimentation 16.4 Evolutionary Operation (EVOP) 16.5 Analysis of Attribute Data 16.6 Randomized Incomplete Blocks -- Restriction On Experimentation 16.7 Youden Squares Further Reading Problems SUMMARY AND SPECIAL PROBLEMS GLOSSARY OF TERMS REFERENCES STATISTICAL TABLES Table A Areas Under the Normal Curve Table B Student's t Distribution Table C Cumulative Chi-Square Distribution Table D Cumulative F Distribution Table E.1 Upper 5 Percent of Studentized Range q Table E.2 Upper 1 Percent of Studentized Range q Table F Coefficients of Orthogonal Polynomials ANSWERS TO SELECTED PROBLEMS INDEX

Abstract: Preface. PART I: FUNDAMENTAL STATISTICAL CONCEPTS. Statistics in Engineering and Science. Fundamentals of Statistical Inference. Inferences on Means and Standard Deviations. PART II: DESIGN AND ANALYSIS WITH FACTORIAL STRUCTURE. Statistical Principles in Experimental Design. Factorial Experiments in Completely Randomized Designs. Analysis of Completely Randomized Designs. Fractional Factorial Experiments. Analysis of Fractional Factorial Experiments. PART III: DESIGN AND ANALYSIS WITH RANDOM EFFECTS. Experiments in Randomized Block Designs. Analysis of Designs with Random Factor Levels. Nested Designs. Special Designs for Process Improvement. Analysis of Nested Designs and Designs for Process Improvement. PART IV: DESIGN AND ANALYSIS WITH QUANTITATIVE PREDICTORS AND FACTORS. Linear Regression with One Predicator Variables. Linear Regression with Several Predicator Variables. Linear Regression with Factors and Covariates as Predictors. Designs and Analyses for Fitting Re sponse Surfaces. Model Assessment. Variable Selection Techniques. Appendix: Statistical Tables. Index.

Abstract: Preface to the Second Edition. Preface to the First Edition. Suggestions of Topics for Instructors. List of Experiments and Data Sets. 1 Basic Concepts for Experimental Design and Introductory Regression Analysis. 1.1 Introduction and Historical Perspective. 1.2 A Systematic Approach to the Planning and Implementation of Experiments. 1.3 Fundamental Principles: Replication, Randomization, and Blocking. 1.4 Simple Linear Regression. 1.5 Testing of Hypothesis and Interval Estimation. 1.6 Multiple Linear Regression. 1.7 Variable Selection in Regression Analysis. 1.8 Analysis of Air Pollution Data. 1.9 Practical Summary. 2 Experiments with a Single Factor. 2.1 One-Way Layout. 2.2 Multiple Comparisons. 2.3 Quantitative Factors and Orthogonal Polynomials. 2.4 Expected Mean Squares and Sample Size Determination. 2.5 One-Way Random Effects Model. 2.6 Residual Analysis: Assessment of Model Assumptions. 2.7 Practical Summary. 3 Experiments with More Than One Factor. 3.1 Paired Comparison Designs. 3.2 Randomized Block Designs. 3.3 Two-Way Layout: Factors With Fixed Levels. 3.4 Two-Way Layout: Factors With Random Levels. 3.5 Multi-Way Layouts. 3.6 Latin Square Designs: Two Blocking Variables. 3.7 Graeco-Latin Square Designs. 3.8 Balanced Incomplete Block Designs. 3.9 Split-Plot Designs. 3.10 Analysis of Covariance: Incorporating Auxiliary Information. 3.11 Transformation of the Response. 3.12 Practical Summary. 4 Full Factorial Experiments at Two Levels. 4.1 An Epitaxial Layer Growth Experiment. 4.2 Full Factorial Designs at Two Levels: A General Discussion. 4.3 Factorial Effects and Plots. 4.4 Using Regression to Compute Factorial Effects. 4.5 ANOVA Treatment of Factorial Effects. 4.6 Fundamental Principles for Factorial Effects: Effect Hierarchy, Effect Sparsity, and Effect Heredity. 4.7 Comparisons with the "One-Factor-at-a-Time" Approach. 4.8 Normal and Half-Normal Plots for Judging Effect Significance. 4.9 Lenth's Method: Testing Effect Significance for Experiments Without Variance Estimates. 4.10 Nominal-the-Best Problem and Quadratic Loss Function. 4.11 Use of Log Sample Variance for Dispersion Analysis. 4.12 Analysis of Location and Dispersion: Revisiting the Epitaxial Layer Growth Experiment. 4.13 Test of Variance Homogeneity and Pooled Estimate of Variance. 4.14 Studentized Maximum Modulus Test: Testing Effect Significance for Experiments with Variance Estimates. 4.15 Blocking and Optimal Arrangement of 2 k Factorial Designs in 2 q Blocks. 4.16 Practical Summary. 5 Fractional Factorial Experiments at Two Levels. 5.1 A Leaf Spring Experiment. 5.2 Fractional Factorial Designs: Effect Aliasing and the Criteria Of Resolution and Minimum Aberration. 5.3 Analysis of Fractional Factorial Experiments. 5.4 Techniques for Resolving the Ambiguities in Aliased Effects. 5.5 Selection of 2 k-p Designs Using Minimum Aberration and Related Criteria. 5.6 Blocking in Fractional Factorial Designs. 5.7 Practical Summary. 6 Full Factorial and Fractional Factorial Experiments at Three Levels. 6.1 A Seat-Belt Experiment. 6.2 Larger-the-Better and Smaller-the-Better Problems. 6.3 3 k Full Factorial Designs. 6.4 3 k-p Fractional Factorial Designs. 6.5 Simple Analysis Methods: Plots and Analysis of Variance. 6.6 An Alternative Analysis Method. 6.7 Analysis Strategies for Multiple Responses I: Out-of-Spec Probabilities. 6.8 Blocking in 3 k and 3 k-p Designs. 6.9 Practical Summary. 7 Other Design and Analysis Techniques for Experiments at More Than Two Levels. 7.1 A Router Bit Experiment Based on a Mixed Two-Level and Four-Level Design. 7.2 Method of Replacement and Construction of 2 m 4 n Designs. 7.3 Minimum Aberration 2 m 4 n Designs with n = 1, 2. 7.4 An Analysis Strategy for 2 m 4 n Experiments. 7.5 Analysis of the Router Bit Experiment. 7.6 A Paint Experiment Based on a Mixed Two-Level and Three-Level Design. 7.7 Design and Analysis of 36-Run Experiments at Two And Three Levels. 7.8 r k-p Fractional Factorial Designs for any Prime Number r . 7.9 Related Factors: Method of Sliding Levels, Nested Effects Analysis, and Response Surface Modeling. 7.10 Practical Summary. 8 Nonregular Designs: Construction and Properties. 8.1 Two Experiments: Weld-Repaired Castings and Blood Glucose Testing. 8.2 Some Advantages of Nonregular Designs Over the 2 k-p and 3 k-p Series of Designs. 8.3 A Lemma on Orthogonal Arrays. 8.4 Plackett-Burman Designs and Hall's Designs. 8.5 A Collection of Useful Mixed-Level Orthogonal Arrays. 8.6 Construction of Mixed-Level Orthogonal Arrays Based on Difference Matrices. 8.7 Construction of Mixed-Level Orthogonal Arrays Through the Method of Replacement. 8.8 Orthogonal Main-Effect Plans Through Collapsing Factors. 8.9 Practical Summary. 9 Experiments with Complex Aliasing. 9.1 Partial Aliasing of Effects and the Alias Matrix. 9.2 Traditional Analysis Strategy: Screening Design and Main Effect Analysis. 9.3 Simplification of Complex Aliasing via Effect Sparsity. 9.4 An Analysis Strategy for Designs with Complex Aliasing. 9.5 A Bayesian Variable Selection Strategy for Designs with Complex Aliasing. 9.6 Supersaturated Designs: Design Construction and Analysis. 9.7 Practical Summary. 10 Response Surface Methodology. 10.1 A Ranitidine Separation Experiment. 10.2 Sequential Nature of Response Surface Methodology. 10.3 From First-Order Experiments to Second-Order Experiments: Steepest Ascent Search and Rectangular Grid Search. 10.4 Analysis of Second-Order Response Surfaces. 10.5 Analysis of the Ranitidine Experiment. 10.6 Analysis Strategies for Multiple Responses II: Contour Plots and the Use of Desirability Functions. 10.7 Central Composite Designs. 10.8 Box-Behnken Designs and Uniform Shell Designs. 10.9 Practical Summary. 11 Introduction to Robust Parameter Design. 11.1 A Robust Parameter Design Perspective of the Layer Growth and Leaf Spring Experiments. 11.2 Strategies for Reducing Variation. 11.3 Noise (Hard-to-Control) Factors. 11.4 Variation Reduction Through Robust Parameter Design. 11.5 Experimentation and Modeling Strategies I: Cross Array. 11.6 Experimentation and Modeling Strategies II: Single Array and Response Modeling. 11.7 Cross Arrays: Estimation Capacity and Optimal Selection. 11.8 Choosing Between Cross Arrays and Single Arrays. 11.9 Signal-to-Noise Ratio and Its Limitations for Parameter Design Optimization. 11.10 Further Topics. 11.11 Practical Summary. 12 Robust Parameter Design for Signal-Response Systems. 12.1 An Injection Molding Experiment. 12.2 Signal-Response Systems and their Classification. 12.3 Performance Measures for Parameter Design Optimization. 12.4 Modeling and Analysis Strategies. 12.5 Analysis of the Injection Molding Experiment. 12.6 Choice of Experimental Plans. 12.7 Practical Summary. 13 Experiments for Improving Reliability. 13.1 Experiments with Failure Time Data. 13.2 Regression Model for Failure Time Data. 13.3 A Likelihood Approach for Handling Failure Time Data with Censoring. 13.4 Design-Dependent Model Selection Strategies. 13.5 A Bayesian Approach to Estimation and Model Selection for Failure Time Data. 13.6 Analysis of Reliability Experiments with Failure Time Data. 13.7 Other Types of Reliability Data. 13.8 Practical Summary. 14 Analysis of Experiments with Nonnormal Data. 14.1 A Wave Soldering Experiment with Count Data. 14.2 Generalized Linear Models. 14.3 Likelihood-Based Analysis of Generalized Linear Models. 14.4 Likelihood-Based Analysis of the Wave Soldering Experiment. 14.5 Bayesian Analysis of Generalized Linear Models. 14.6 Bayesian Analysis of the Wave Soldering Experiment. 14.7 Other Uses and Extensions of Generalized Linear Models and Regression Models for Nonnormal Data. 14.8 Modeling and Analysis for Ordinal Data. 14.9 Analysis of Foam Molding Experiment. 14.10 Scoring: A Simple Method for Analyzing Ordinal Data. 14.11 Practical Summary. Appendix A Upper Tail Probabilities of the Standard Normal Distribution. Appendix B Upper Percentiles of the t Distribution. Appendix C Upper Percentiles of the chi 2 Distribution. Appendix D Upper Percentiles of the F Distribution. Appendix E Upper Percentiles of the Studentized Range Distribution. Appendix F Upper Percentiles of the Studentized Maximum Modulus Distribution. Appendix G Coefficients of Orthogonal Contrast Vectors. Appendix H Critical Values for Lenth's Method. Author Index. Subject Index.