Research Design and Statistical Analysis; Fourth Edition

This fully updated fourth edition of Research Design and Statistical Analysis provides comprehensive coverage of the design principles and statistical concepts necessary to make sense of real data. The guiding philosophy is to provide a strong conceptual foundation so that readers can generalize to new situations they encounter in their research, including new developments in data analysis. Key features include: Emphasis on basic concepts such as sampling distributions, design efficiency, and expected mean squares, relating the research designs and data analyses to the statistical models that underlie the analyses. Detailed instructions on performing analysis using both R and SPSS. Pedagogical exercises mapped to key topic areas to support students as they review their understanding and strive to reach their higher learning goals. Incorporating the analyses of both experimental and observational data, and with coverage that is broad and deep enough to serve a two-semester sequence, this textbook is suitable for researchers, graduate students and advanced undergraduates in psychology, education, and other behavioral, social, and health sciences. The book is supported by a robust set of digital resources, including data files and exercises from the book in an Excel format for easy import into R or SPSS; R scripts for running example analysis and generating figures; and a solutions manual. Cover Endorsements Half Title Title Copyright Contents Preface Acknowledgments Part 1 Foundations of Research Design and Data Analysis 1 Planning the Research 1.1 Overview 1.2 The Independent Variable 1.3 The Dependent Variable 1.4 The Participant Population 1.5 Nuisance Variables 1.6 Research Design 1.7 Statistical Analyses 1.8 Generalizing Conclusions 1.9 Summary 2 Describing the Data 2.1 Overview 2.2 Graphical Summaries of the Data 2.3 Numerical Summaries of the Data 2.4 Standardized (z) Scores 2.5 Measures of the Shape of a Distribution: Skewness and Kurtosis 2.6 Comparing Two Data Sets 2.7 Relationships Among Quantitative Variables 2.8 Summary 3 Basic Concepts in Probability 3.1 Overview 3.2 Basic Concepts for Analyzing the Structure of Events 3.3 Computing Probabilities 3.4 Probability Distributions 3.5 Connecting Probability Theory to Data 3.6 Summary 4 Developing the Fundamentals of Hypothesis Testing Using the Binomial Distribution 4.1 Overview 4.2 What Do We Need to Know to Test a Hypothesis? 4.3 The Binomial Distribution 4.4 Hypothesis Testing 4.5 The Power of a Statistical Test 4.6 When Assumptions Fail 4.7 Summary 5 Further Development of the Foundations of Statistical Inference 5.1 Overview 5.2 Using Sample Statistics to Estimate Population Parameters 5.3 The Sampling Distribution of the Sample Mean 5.4 The Normal Distribution 5.5 Inferences About Population Means 5.6 The Power of the z Test 5.7 Validity of Assumptions 5.8 Summary 6 The t Distribution and Its Applications 6.1 Overview 6.2 Design Considerations: Independent Groups or Correlated Scores? 6.3 The t Distribution 6.4 Data Analyses in the Independent-Groups Design 6.5 Data Analyses in the Correlated-Scores Design 6.6 Assumptions Underlying the Application of the t Distribution 6.7 Measuring the Standardized Effect Size: Cohen’s d 6.8 Deciding on Sample Size 6.9 Post Hoc Power 6.10 Summary 7 Integrated Analysis I 7.1 Overview 7.2 Introduction to the Research 7.3 Method 7.4 Exploring the Data 7.5 Confidence Intervals and Hypothesis Tests 7.6 The Standardized Effect Size (Cohen’s d) 7.7 Reanalysis: Alternative Approaches 7.8 Discussion of the Results 7.9 Summary Part 2 Between-Participants Designs 8 Between-Participants Designs 8.1 Overview 8.2 An Example of the Design 8.3 The Structural Model 8.4 The Analysis of Variance (ANOVA) 8.5 Measures of Importance 8.6 When Group Sizes Are Not Equal 8.7 Deciding on Sample Size: Power Analysis in the Between-Participants Design 8.8 Assumptions Underlying the F Test 8.9 Summary 9 Multi-Factor Between-Participants Designs 9.1 Overview 9.2 The Two-Factor Design: The Structural Model 9.3 Two-Factor Designs: The Analysis of Variance 9.4 Three-Factor Between-Participants Designs 9.5 More Than Three Independent Variables 9.6 Measures of Effect Size 9.7 A Priori Power Calculations 9.8 Unequal Cell Frequencies 9.9 Pooling in Factorial Designs 9.10 Advantages and Disadvantages of Between-Participants Designs 9.11 Summary 10 Contrasting Means in Between-Subjects Designs 10.1 Overview 10.2 Definitions and Examples of Contrasts 10.3 Calculations for Hypothesis Tests and Confidence Intervals on Contrasts 10.4 Extending Cohen’s d to Contrasts 10.5 The Proper Unit for the Control of Type 1 Error 10.6 Controlling the FWE for Families of K Planned Contrasts Using Methods Based on the Bonferroni Inequality 10.7 Testing All Pairwise Contrasts 10.8 Comparing a – 1 Treatment Means With a Control: Dunnett’s Test 10.9 Controlling the Familywise Error Rate for Post Hoc Contrasts 10.10 Controlling the Familywise Error Rate in Multi-Factor Designs 10.11 The Sum of Squares Associated With a Contrast 10.12 Summary 11 Integrated Analysis II 11.1 Overview 11.2 Introduction to the Experiment 11.3 Method 11.4 Results and Discussion 11.5 Summary Part 3 Repeated-Measures Designs 12 Comparing Experimental Designs and Analyses 12.1 Overview 12.2 Factors Influencing the Choice Among Designs 12.3 The Treatments × Blocks Design 12.4 The Analysis of Covariance 12.5 Repeated-Measures (RM) Designs 12.6 The Latin Square Design 12.7 Summary 13 One-Factor Repeated-Measures Designs 13.1 Overview 13.2 The Additive Model in the One-Factor Repeated-Measures Design 13.3 Fixed and Random Effects 13.4 The Additive Model 13.5 The Nonadditive Model for the S × A Design 13.6 The Sphericity Assumption 13.7 Measures of Effect Size 13.8 Deciding on Sample Size: Power Analysis in the Repeated-Measures Design 13.9 Testing Single df Contrasts 13.10 The Problem of Missing Data in Repeated-Measures Designs 13.11 Nonparametric Procedures for Repeated-Measures Designs 13.12 Summary 14 Multi-Factor Repeated-Measures and Mixed Designs 14.1 Overview 14.2 The S × A × B Design With A and B Fixed 14.3 Mixed Designs With A and B Fixed 14.4 Designs With More Than One Random-Effects Factor: The Fixed- vs Random-Effects Distinction Again 14.5 Rules for Generating Expected Mean Squares 14.6 Constructing Unbiased F Tests in Designs With Two Random Factors 14.7 Fixed or Random Effects? 14.8 Understanding the Pattern of Means in Repeated-Measures Designs 14.9 Effect Size 14.10 A Priori Power Calculations 14.11 Summary 15 Nested and Counterbalanced Variables in Repeated-Measures Designs 15.1 Overview 15.2 Nesting Stimuli Within Factor Levels 15.3 Adding a Between-Participants Variable to the Within-Participants Hierarchical Design 15.4 The Replicated Latin Square Design 15.5 Including Between-Participants Variables in the Replicated Square Design 15.6 Summary 16 Integrated Analysis III 16.1 Overview 16.2 Introduction to the Experiment 16.3 Method 16.4 Results and Discussion 16.5 An Alternative Design: The Latin Square 16.6 Summary Part 4 Correlation and Regression 17 An Introduction to Correlation and Regression 17.1 Introduction to the Correlation and Regression Chapters 17.2 Overview of Chapter 17 17.3 Some Examples of Bivariate Relationships 17.4 Linear Relationships 17.5 Introducing Correlation and Regression Using z Scores 17.6 Least-Squares Linear Regression for Raw Scores 17.7 More About Interpreting the Pearson Correlation Coefficient 17.8 What About Nonlinear Relationships? 17.9 Concluding Remarks 17.10 Summary 18 More About Correlation 18.1 Overview 18.2 Inference About Correlation 18.3 Partial and Semipartial (or Part) Correlations 18.4 Missing Data in Correlation 18.5 Other Measures of Correlation 18.6 Summary 19 More About Bivariate Regression 19.1 Overview 19.2 Inference in Linear Regression 19.3 Using Regression to Make Predictions 19.4 Regression Analysis in Nonexperimental Research 19.5 Consequences of Measurement Error in Bivariate Regression 19.6 Unstandardized vs Standardized Regression Coefficients 19.7 Checking for Violations of Assumptions 19.8 Locating Outliers and Influential Data Points 19.9 Limitations of Ordinary Least-Squares Regression 19.10 Summary 20 Introduction to Multiple Regression 20.1 Overview 20.2 An Example With Preliminary Analyses 20.3 The Multiple Regression Model 20.4 The Partitioning of Variability in Multiple Regression 20.5 Using Software for Multiple Regression and Cross-Validation 20.6 Multiple Regression Analyses of the TC Data 20.7 The Meaning of the Regression Coefficients 20.8 Suppression Effects in Multiple Regression 20.9 Summary 21 Inference, Assumptions, and Power in Multiple Regression 21.1 Overview 21.2 Inference Models and Assumptions 21.3 Testing Assumptions and Checking for Outliers and Influential Data Points 21.4 Testing Different Hypotheses in Multiple Regression 21.5 Controlling Type 1 Error in Multiple Regression 21.6 Inferences About the Predictions of Y 21.7 Power Calculations in Multiple Regression 21.8 Automated Procedures for Developing Prediction Equations 21.9 Summary 22 Additional Topics in Multiple Regression 22.1 Overview 22.2 Specification Errors and Their Consequences 22.3 Measurement Error in Multiple Regression 22.4 Missing Data in Multiple Regression 22.5 Multicollinearity 22.6 Regression With Direct and Mediated Effects 22.7 Testing for Curvilinearity in Regression 22.8 Including Interaction Terms in Multiple Regression 22.9 Limitations of Ordinary Least-Squares Regression 22.10 Summary 23 Regression With Qualitative and Quantitative Variables 23.1 Overview 23.2 One-Factor Designs 23.3 Regression Analyses and Factorial ANOVA Designs 23.4 Testing Homogeneity of Regression Slopes Using Multiple Regression 23.5 Coding Designs With Within-Participants Factors 23.6 Summary 24 ANCOVA as a Special Case of Multiple Regression 24.1 Overview 24.2 The ANCOVA Model 24.3 Adjusting the Group Means in Y for Differences in X and Testing Contrasts 24.4 Assumptions and Interpretation in ANCOVA 24.5 Using the Covariate to Assign Participants to Groups 24.6 Estimating Power in ANCOVA 24.7 Extensions of ANCOVA 24.8 Summary 25 Integrated Analysis IV 25.1 Overview 25.2 Introduction to the Study 25.3 Method 25.4 Procedure 25.5 Results and Discussion 25.6 A Hypothetical Experimental Test of the Effects of Leisure Activity on Depression 25.7 Summary and More Discussion Part 5 Epilogue 26 Some Final Thoughts, Suggestions, and Cautions 26.1 Designing the Research 26.2 The Initial Analyses 26.3 Interpreting the Results Appendices Appendix A Notation and Summation Operations Appendix B Expected Values and Their Applications Appendix C Statistical Tables Answers to Selected Exercises References Index