About: Factorial experiment is a research topic. Over the lifetime, 2648 publications have been published within this topic receiving 59610 citations. The topic is also known as: factorial design & fully crossed design.
Papers published on a yearly basis
01 Jan 1982
TL;DR: Within-subject and mixed designs of Factorial Design have been studied in this article, where the Principal Two-Factor Within-Factor Effects and Simple Effects have been used to estimate the effect size and power of interaction components.
Abstract: I. INTRODUCTION. 1. Experimental Design. II. SINGLE FACTOR EXPERIMENTS. 2. Sources of Variability and Sums of Squares. 3. Variance Estimates and F Ratio. 4. Analytical Comparisons Among Means. 5. Analysis of Trend. 6. Simultaneous Comparisons. 7. The Linear Model and Its Assumptions. 8. Effect Size and Power. 9. Using Statistical Software. III. FACTORIAL EXPERIMENTS WITH TWO FACTORS. 10. Introduction to the Factorial Design. 11. The Principal Two-Factor Effects. 12. Main Effects and Simple Effects. 13. The Analysis of Interaction Components. IV. NONORTHOGONALITY AND THE GENERAL LINEAR MODEL. 14. General Linear Model. 15. The Analysis of Covariance. V. WITHIN-SUBJECT DESIGNS. 16. The Single-Factor Within-Subject Design. 17. Further Within-Subject Topics. 18. The Two-Factor Within-Subject Design. 19. The Mixed Design: Overall Analysis. 20. The Mixed Design: Analytical Analyses. VI. HIGHER FACTORIAL DESIGNS AND OTHER EXTENSIONS. 21. The Overall Three-Factor Design. 22. The Three-Way Analytical Analysis. 23. Within-Subject and Mixed Designs. 24. Random Factors and Generalization. 25. Nested Factors. 26. Higher-Order Designs. Appendix A: Statistical Tables.
01 Jan 1978
TL;DR: This paper used external reference distribution to compare two means and compared more than two treatment means, and compared the effects of different means and treatments in the United States of America, using the Declaration of Independence as an example.
Abstract: Science and Statistics. COMPARING TWO TREATMENTS. Use of External Reference Distribution to Compare Two Means. Random Sampling and the Declaration of Independence. Randomization and Blocking with Paired Comparisons. Significance Tests and Confidence Intervals for Means, Variances, Proportions and Frequences. COMPARING MORE THAN TWO TREATMENTS. Experiments to Compare k Treatment Means. Randomized Block and Two--Way Factorial Designs. Designs with More Than One Blocking Variable. MEASURING THE EFFECTS OF VARIABLES. Empirical Modeling. Factorial Designs at Two Levels. More Applications of Factorial Designs. Fractional Factorial Designs at Two Levels. More Applications of Fractional Factorial Designs. BUILDING MODELS AND USING THEM. Simple Modeling with Least Squares (Regression Analysis). Response Surface Methods. Mechanistic Model Building. Study of Variation. Modeling Dependence: Times Series. Appendix Tables. Index.
01 Jan 2000
TL;DR: This book discusses Factorial and Fractional Factorial Experiments at Three Levels, Robust Parameter Design for Signal-Response Systems, and other Design and Analysis Techniques for Experiments for Improving Reliability.
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.
TL;DR: In this article, the authors present an approach to the design of a randomized block and a split-split-plot model for estimating the mean square of a given set of points.
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
TL;DR: In this article, a tutorial is given to give a simple and easily understandable introduction to experimental design and optimization and the screening methods described in the paper are factorial and fractional factorial designs and identification of significant variables are performed by normal distribution plots as well as by confidence intervals.
Abstract: The aim with this tutorial is to give a simple and easily understandable introduction to experimental design and optimization. The screening methods described in the paper are factorial and fractional factorial designs. Identification of significant variables are performed by normal distribution plots as well as by confidence intervals. Refinements of the models are also discussed. For optimization, the simplex method, central composite designs and the Doehlert design are discussed. The paper also gives an introduction to mixture designs. The paper contains 14 hands-on examples and if anyone needs the answers on these it is just to contact the authors.