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Analysis of Variance Designs

Book Description

ANOVA (Analysis Of Variance) is one of the most fundamental and ubiquitous univariate methodologies employed by psychologists and other behavioural scientists. Analysis of Variance Designs presents the foundations of this experimental design, including assumptions, statistical significance, strength of effect, and the partitioning of the variance. Exploring the effects of one or more independent variables on a single dependent variable as well as two-way and three-way mixed designs, this textbook offers an overview of traditionally advanced topics for advanced undergraduates and graduate students in the behavioural and social sciences. Separate chapters are devoted to multiple comparisons (post hoc and planned/weighted), ANCOVA, and advanced topics. Each of the design chapters contains conceptual discussions, hand calculations, and procedures for the omnibus and simple effects analyses in both SPSS and the new 'click and shoot' SAS Enterprise Guide interface.

Table of Contents

  1. Coverpage
  2. Analysis of Variance Designs
  3. Title page
  4. Copyright page
  5. Contents
  6. Preface
  7. Section 1. Research Foundations
    1. 1 Anova and Research Design
      1. 1.1 What Is Analysis of Variance?
      2. 1.2 A Brief History of ANOVA
      3. 1.3 Dependent and Independent Variables
      4. 1.4 The Importance of Variation
      5. 1.5 Exploratory Research and Hypothesis Testing
    2. 2 Measurement, Central Tendency, and Variability
      1. 2.1 Scales of Measurement
      2. 2.2 Central Tendency and Variability
      3. 2.3 The Mean as a Measure of Central Tendency
      4. 2.4 The Median as a Measure of Central Tendency
      5. 2.5 The Mode as a Measure of Central Tendency
      6. 2.6 Range as a Measure of Variability
      7. 2.7 Variance as a Measure of Variability
      8. 2.8 Standard Deviation as a Measure of Variability
      9. Chapter 2 Exercises
  8. Section 2. Foundations of Analysis of Variance
    1. 3 Elements of ANOVA
      1. 3.1 Partitioning of the Variance
      2. 3.2 A Simple Example Study
      3. 3.3 Sources of Variance
      4. 3.4 Sums of Squares
      5. 3.5 Degrees of Freedom
      6. 3.6 Mean Square
      7. 3.7 Where All This Leads
    2. 4 The Statistical Significance of F and Effect Strength
      1. 4.1 The F Ratio
      2. 4.2 The Sampling Distribution of F
      3. 4.3 The Area Under the Sampling Distribution
      4. 4.4 Statistical Significance
      5. 4.5 Explaining Variance: Strength of Effect
      6. 4.6 Reporting the Results
      7. 4.7 Statistical Power
      8. 4.8 The Limiting Case of ANOVA: The t Test
    3. 5 ANOVA Assumptions
      1. 5.1 Overview
      2. 5.2 Independence of Errors
      3. 5.3 Normality of Errors
      4. 5.4 Homogeneity of Variance
      5. 5.5 SPSS Applications: Assumption Violation Detection and Solution
      6. 5.6 SAS Applications: Assumption Violation Detection and Solution
      7. 5.7 Communicating the Results
      8. Chapter 5 Exercises
  9. Section 3. Between-Subjects Designs
    1. 6 One-Way Between-Subjects Design
      1. 6.1 Overview
      2. 6.2 A Numerical Example
      3. 6.3 Partitioning the Total Variance into Its Sources
      4. 6.4 Omnibus and Simplifying Analyses
      5. 6.5 Computing the Omnibus Analysis by Hand
      6. 6.6 Performing the Omnibus One-Way Between-Subjects ANOVA in SPSS
      7. 6.7 The Output of the Omnibus One-Way Between-Subjects ANOVA in SPSS
      8. 6.8 Performing the Omnibus One-Way Between-Subjects ANOVA in SAS
      9. 6.9 The Output of the Omnibus One-Way Between-Subjects ANOVA in SAS
      10. 6.10 Communicating the Results
      11. Chapter 6 Exercises
    2. 7 Multiple Comparison Procedures
      1. 7.1 Overview
      2. 7.2 Planned Versus Unplanned Comparisons
      3. 7.3 Pairwise Versus Composite Comparisons
      4. 7.4 Orthogonal Versus Nonorthogonal Comparisons
      5. 7.5 Statistical Power
      6. 7.6 Alpha Inflation
      7. 7.7 General Categories of Multiple Comparison Procedures
      8. 7.8 Post Hoc Tests
      9. 7.9 Computing a Tukey HSD Test by Hand
      10. 7.10 Performing a Tukey HSD Test in SPSS
      11. 7.11 The Tukey HSD Output from SPSS
      12. 7.12 Performing a Tukey HSD Test in SAS
      13. 7.13 The Tukey HSD Output from SAS
      14. 7.14 Communicating the Tukey Results
      15. 7.15 Preset Contrasts in SPSS
      16. 7.16 Performing Simple Contrasts in SPSS
      17. 7.17 The Simple Contrasts Output from SPSS
      18. 7.18 Performing Simple Contrasts in SAS
      19. 7.19 The Simple Contrasts Output from SAS
      20. 7.20 Communicating the Simple Contrast Results
      21. 7.21 Polynomial Contrasts (Trend Analysis)
      22. 7.22 Performing a Trend Analysis by Hand
      23. 7.23 Performing Polynomial Contrasts (Trend Analysis) in SPSS
      24. 7.24 Output for Polynomial Contrasts (Trend Analysis) in SPSS
      25. 7.25 Communicating the Results of the Trend Analysis
      26. 7.26 User-Defined Contrasts
      27. 7.27 Performing User-Defined (Planned) Comparisons by Hand
      28. 7.28 Performing User-Defined Contrasts in SPSS
      29. 7.29 Output from User-Defined Contrasts Analysis in SPSS
      30. 7.30 Communicating the Results of the Contrasts Analyses
      31. 7.31 Performing User-Defined Contrasts (Planned Comparisons) in SAS
      32. 7.32 Output for Planned Comparisons in SAS
      33. 7.33 Communicating the Results of the Planned Comparisons
      34. 7.34 Performing Polynomial Contrasts (Trend Analysis) in SAS
      35. 7.35 Output for Polynomial Contrasts (Trend Analysis) in SAS
      36. 7.36 Communicating the Results of the Polynomial Contrasts
      37. Chapter 7 Exercises
    3. 8 Two-Way Between-Subjects Design
      1. 8.1 Combining Two Independent Variables Factorially
      2. 8.2 A Numerical Example
      3. 8.3 Partitioning the Variance into Its Sources
      4. 8.4 Effects of Interest in This Design
      5. 8.5 The Interaction Effect
      6. 8.6 Precedence of Effects: Interactions Supercede Main Effects
      7. 8.7 Computing an Omnibus Two-Factor Between-Subjects ANOVA by Hand
      8. 8.8 Computing Simple Effects by Hand
      9. 8.9 Performing the Omnibus Analysis in SPSS
      10. 8.10 SPSS Output for the Omnibus Analysis
      11. 8.11 Performing the Post-ANOVA Analyses in SPSS
      12. 8.12 SPSS Output for the Post-ANOVA Analyses
      13. 8.13 Performing the Omnibus Analysis in SAS Enterprise Guide
      14. 8.14 SAS Output for the Omnibus Analysis
      15. 8.15 Performing the Post-ANOVA Analyses in SAS
      16. 8.16 SAS Output for the Post-ANOVA Analyses
      17. 8.17 Communicating the Results
      18. Chapter 8 Exercises
    4. 9 Three-Way Between-Subjects Design
      1. 9.1 A Numerical Example of a Three-Way Design
      2. 9.2 Partitioning the Variance into Its Sources
      3. 9.3 Computing the Portions of the Summary Table
      4. 9.4 Precedence of Effects: Higher-Order Interactions, Lower-Order Interactions, Main Effects
      5. 9.5 Computing by Hand the Omnibus Three-Way Between-Subject Analysis
      6. 9.6 Performing the Omnibus Analysis in SPSS
      7. 9.7 SPSS Output for the Omnibus Analysis
      8. 9.8 Performing the Post-ANOVA Analyses in SPSS
      9. 9.9 SPSS Output for the Post-ANOVA Analyses in SPSS
      10. 9.10 Performing the Omnibus Analysis in SAS Enterprise Guide
      11. 9.11 SAS Output for the Omnibus Analysis
      12. 9.12 Performing the Post-ANOVA Analyses in SAS
      13. 9.13 SAS Output for the Post-ANOVA Analyses in SAS
      14. 9.14 Communicating the Results
      15. Chapter 9 Exercises
  10. Section 4. Within-Subjects Designs
    1. 10 One-Way Within-Subjects Design
      1. 10.1 The Concept of Within-Subjects Variance
      2. 10.2 Nomenclature
      3. 10.3 Nature of Within-Subjects Variables
      4. 10.4 The Issue of Carry-Over Effects
      5. 10.5 Between- Versus Within-Subjects Variance
      6. 10.6 A Numerical Example of a One-Way Within-Subjects Design
      7. 10.7 Effect of Interest in This Design
      8. 10.8 The Error Term in a One-Way Within-Subjects Design
      9. 10.9 Computing the Omnibus Analysis by Hand
      10. 10.10 Performing User-Defined (Planned) Comparisons by Hand
      11. 10.11 Performing the Omnibus Analysis in SPSS
      12. 10.12 SPSS Output for the Omnibus Analysis
      13. 10.13 Performing the Post-ANOVA Analysis in SPSS
      14. 10.14 SPSS Output for the Post-ANOVA Analysis
      15. 10.15 SPSS and SAS Data File Structures
      16. 10.16 Performing the Omnibus Analysis in SAS
      17. 10.17 SAS Output for the Omnibus Analysis
      18. 10.18 Performing the Post-ANOVA Analysis in SAS
      19. 10.19 SAS Output for the Post-ANOVA Analysis
      20. 10.20 Communicating the Results
      21. Chapter 10 Exercises
    2. 11 Two-Way Within-Subjects Design
      1. 11.1 Combining Two Within-Subjects Factors
      2. 11.2 A Numerical Example of a Two-Way Within-Subjects Design
      3. 11.3 Partitioning the Variance into Its Sources
      4. 11.4 Effects of Interest in This Design
      5. 11.5 The Error Terms in a Two-Way Within-Subjects Design
      6. 11.6 Computing the Omnibus Two-Factor Within-Subjects ANOVA by Hand
      7. 11.7 Performing the Omnibus Analysis in SPSS
      8. 11.8 SPSS Output for the Omnibus Analysis
      9. 11.9 Performing the Post-ANOVA Analysis in SPSS
      10. 11.10 SPSS Output for the Post-ANOVA Analysis
      11. 11.11 Performing the Omnibus Analysis in SAS
      12. 11.12 SAS Output from the Omnibus Analysis
      13. 11.13 Performing the Simple Effects Analysis in SAS
      14. 11.14 SAS Output from the Simple Effects Analysis
      15. 11.15 Performing the Post Hoc Analysis in SAS
      16. 11.16 SAS Output from the Post Hoc Analysis
      17. 11.17 Communicating the Results
      18. Chapter 11 Exercises
    3. 12 Three-Way Within-Subjects Design
      1. 12.1 A Numerical Example of a Three-Way Within-Subjects Design
      2. 12.2 Partitioning the Variance into Its Sources
      3. 12.3 Effects of Interest in This Design
      4. 12.4 The Error Terms in a Three-Way Within-Subjects Design
      5. 12.5 Computing the Omnibus Analysis
      6. 12.6 Performing the Omnibus Analysis in SPSS
      7. 12.7 SPSS Output for the Omnibus Analysis
      8. 12.8 Performing the Post-ANOVA Analysis in SPSS
      9. 12.9 SPSS Output for the Post-ANOVA Analysis
      10. 12.10 Performing the Omnibus Analysis in SAS
      11. 12.11 SAS Output from the Omnibus Analysis
      12. 12.12 Performing the Simple Effects Analysis in SAS
      13. 12.13 SAS Output from the Simple Effects Analysis
      14. 12.14 Performing the Post Hoc Analysis in SAS
      15. 12.15 SAS Output from the Post Hoc Analysis
      16. 12.16 Communicating the Results
      17. Chapter 12 Exercises
  11. Section 5. Mixed Designs
    1. 13 Simple Mixed Design
      1. 13.1 Combining Between-Subjects and Within-Subjects Factors
      2. 13.2 A Numerical Example of a Simple Mixed Design
      3. 13.3 Effects of Interest
      4. 13.4 Computing the Omnibus Analysis by Hand
      5. 13.5 Performing the Omnibus Analysis in SPSS
      6. 13.6 SPSS Output of the Omnibus Analysis
      7. 13.7 Performing the Post-ANOVA Analysis in SPSS
      8. 13.8 Output for the Post-ANOVA Analysis in SPSS
      9. 13.9 Performing the Omnibus Analysis in SAS
      10. 13.10 SAS Output of the Omnibus Analysis
      11. 13.11 Performing the Simple Effects Analysis in SAS
      12. 13.12 SAS Output from the Simple Effects Analysis
      13. 13.13 Performing the Post Hoc Analysis in SAS
      14. 13.14 SAS Output from the Post Hoc Analysis
      15. 13.15 Communicating the Results
      16. Chapter 13 Exercises
    2. 14 Complex Mixed Design: Two Between-Subjects Factors and One Within-Subjects Factor
      1. 14.1 Combining Between- and Within-Subjects Factors
      2. 14.2 A Numerical Example of a Complex Mixed Design
      3. 14.3 Effects of Interest
      4. 14.4 Computing the Omnibus Complex Mixed Design by Hand
      5. 14.5 Performing the Omnibus Analysis in SPSS
      6. 14.6 SPSS Output of the Omnibus Analysis
      7. 14.7 Performing the Post-ANOVA Analysis in SPSS
      8. 14.8 SPSS Output of the Omnibus Analysis
      9. 14.9 Performing the Omnibus Analysis in SAS
      10. 14.10 SAS Output of the Omnibus Analysis
      11. 14.11 Performing the Simple Effects Analysis in SAS
      12. 14.12 SAS Output from the Simple Effects Analysis
      13. 14.13 Communicating the Results
      14. Chapter 14 Exercises
    3. 15 Complex Mixed Design: One Between-Subjects Factor and Two Within-Subjects Factors
      1. 15.1 A Numerical Example of a Complex Mixed Design
      2. 15.2 Effects of Interest
      3. 15.3 Computing the Omnibus Complex Mixed Design by Hand
      4. 15.4 Performing the Omnibus Analysis in SPSS
      5. 15.5 SPSS Output of the Omnibus Analysis
      6. 15.6 Performing the Post-ANOVA Analysis in SPSS
      7. 15.7 Output for the Post-ANOVA Analysis in SPSS
      8. 15.8 Performing the Omnibus Analysis in SAS
      9. 15.9 SAS Output of the Omnibus Analysis
      10. 15.10 Performing the Post-ANOVA Analysis in SAS
      11. 15.11 Output for the Post-ANOVA Analysis in SAS
      12. 15.12 Communicating the Results
      13. Chapter 15 Exercises
  12. Section 6. Advanced Topics
    1. 16 Analysis of Covariance
      1. 16.1 Experimental and Statistical Control
      2. 16.2 A Simple Illustration of Covariance
      3. 16.3 The Effect of a Covariate on Group Differences
      4. 16.4 The Process of Performing ANCOVA
      5. 16.5 Assumptions of ANCOVA
      6. 16.6 Numerical Example of a One-Way ANCOVA
      7. 16.7 Performing the ANOVA in SPSS
      8. 16.8 Evaluating the ANCOVA Assumptions in SPSS
      9. 16.9 Performing the ANCOVA in SPSS
      10. 16.10 Performing the ANOVA in SAS
      11. 16.11 Evaluating the ANCOVA Assumptions in SAS
      12. 16.12 Performing the ANCOVA in SAS
      13. 16.13 Communicating the Results
      14. Chapter 16 Exercises
    2. 17 Advanced Topics in Analysis of Variance
      1. 17.1 Interaction Comparisons
      2. 17.2 Fixed and Random Factors
      3. 17.3 Nested Designs
      4. 17.4 Latin Squares
      5. 17.5 Unequal Sample Size
      6. 17.6 Multivariate Analysis of Variance (MANOVA)
  13. Appendixes
    1. Appendix A. Primer on SPSS
      1. A.1 Historical Overview
      2. A.2 Different Kinds of Files and Their Extensions
      3. A.3 Opening SPSS
      4. A.4 Saving SPSS Files
      5. A.5 Setting Preferences
      6. A.6 Creating New Data Files in SPSS
      7. A.7 Variable View of the Data File
      8. A.8 Data View of the Data File
      9. A.9 Reading Data from an Excel Worksheet
      10. A.10 Reading Data from a Text File
      11. A.11 Opening Saved Data Files
      12. A.12 The Main SPSS Menu
      13. A.13 Performing Statistical Procedures in SPSS
      14. A.14 Saving Output Files
    2. Appendix B. Primer on SAS
      1. B.1 Historical Overview
      2. B.2 Installing Enterprise Guide on Your Computer
      3. B.3 Opening SAS Enterprise Guide
      4. B.4 Entering Data Directly into SAS Enterprise Guide
      5. B.5 Saving a Project
      6. B.6 Constructing Your Data File in Excel
      7. B.7 Importing Data from Excel
      8. B.8 The Main SAS Menu
      9. B.9 Performing Statistical Procedures in SAS Enterprise Guide
      10. B.10 SAS Enterprise Guide Output
      11. B.11 Saving the SAS Output File as a PDF Document
      12. B.12 Additional Resources
    3. Appendix C. Table of Critical F Values
    4. Appendix D. Deviational Formula for Sums of Squares
    5. Appendix E. Coefficients OF Orthogonal Polynomials
    6. Appendix F. Critical Values of the Studentized Range Statistic
  14. References
  15. Author Index
  16. Subject Index