Applied Statistics

Preface Acknowledgments Chapter 1. Review of Basic Concepts 1.1 Introduction 1.2 A Simple Example of a Research Problem 1.3 Discrepancies Between Real and Ideal Research Situations 1.4 Samples and Populations 1.5 Descriptive Versus Inferential Uses of Statistics 1.6 Levels of Measurement and Types of Variables 1.7 The Normal Distribution 1.8 Research Design 1.9 Parametric Versus Nonparametric Statistics 1.10 Additional Implicit Assumptions 1.11 Selection of an Appropriate Bivariate Analysis 1.12 Summary Comprehension Questions Chapter 2. Introduction to SPSS: Basic Statistics, Sampling Error, and Confidence Intervals 2.1 Introduction 2.2 Research Example: Description of a Sample of HR Scores 2.3 Sample Mean (M) 2.4 Sum of Squared Deviations and Sample Variance (s2) 2.5 Degrees of Freedom (df) for a Sample Variance 2.6 Why Is There Variance? 2.7 Sample Standard Deviation (s) 2.8 Assessment of Location of a Single X Score Relative to a Distribution of Scores 2.9 A Shift in Level of Analysis: The Distribution of Values of M Across Many Samples From the Same Population 2.10 An Index of Amount of Sampling Error: The Standard Error of the Mean (oM) 2.11 Effect of Sample Size (N) on the Magnitude of the Standard Error (oM ) 2.12 Sample Estimate of the Standard Error of the Mean (SEM) 2.13 The Family of t Distributions 2.14 Confidence Intervals 2.15 Summary Appendix on SPSS Comprehension Questions Chapter 3. Statistical Significance Testing 3.1 The Logic of Null Hypothesis Significance Testing (NHST) 3.2 Type I Versus Type II Error 3.3 Formal NHST Procedures: The z Test for a Null Hypothesis About One Population Mean 3.4 Common Research Practices Inconsistent With Assumptions and Rules for NHST 3.5 Strategies to Limit Risk of Type I Error 3.6 Interpretation of Results 3.7 When Is a t Test Used Instead of a z Test? 3.8 Effect Size 3.9 Statistical Power Analysis 3.10 Numerical Results for a One-Sample t Test Obtained From SPSS 3.11 Guidelines for Reporting Results 3.12 Summary Comprehension Questions Chapter 4. Preliminary Data Screening 4.1 Introduction: Problems in Real Data 4.2 Quality Control During Data Collection 4.3 Example of an SPSS Data Worksheet 4.4 Identification of Errors and Inconsistencies 4.5 Missing Values 4.6 Empirical Example of Data Screening for Individual Variables 4.7 Identification and Handling of Outliers 4.8 Screening Data for Bivariate Analyses 4.9 Nonlinear Relations 4.10 Data Transformations 4.11 Verifying That Remedies Had the Desired Effects 4.12 Multivariate Data Screening 4.13 Reporting Preliminary Data Screening 4.14 Summary and Checklist for Data Screening Comprehension Questions Chapter 5. Comparing Group Means Using the Independent Samples t Test 5.1 Research Situations Where the Independent Samples t Test Is Used 5.2 A Hypothetical Research Example 5.3 Assumptions About the Distribution of Scores on the Quantitative Dependent Variable 5.4 Preliminary Data Screening 5.5 Issues in Designing a Study 5.6 Formulas for the Independent Samples t Test 5.7 Conceptual Basis: Factors That Affect the Size of the t Ratio 5.8 Effect Size Indexes for t 5.9 Statistical Power and Decisions About Sample Size for the Independent Samples t Test 5.10 Describing the Nature of the Outcome 5.11 SPSS Output and Model Results Section 5.12 Summary Comprehension Questions Chapter 6. One-Way Between-Subjects Analysis of Variance 6.1 Research Situations Where One-Way Between-Subjects Analysis of Variance (ANOVA) Is Used 6.2 Hypothetical Research Example 6.3 Assumptions About Scores on the Dependent Variable for One-Way Between-S ANOVA 6.4 Issues in Planning a Study 6.5 Data Screening 6.6 Partition of Scores Into Components 6.7 Computations for the One-Way Between-S ANOVA 6.8 Effect Size Index for One-Way Between-S ANOVA 6.9 Statistical Power Analysis for One-Way Between-S ANOVA 6.10 Nature of Differences Among Group Means 6.11 SPSS Output and Model Results 6.12 Summary Comprehension Questions Chapter 7. Bivariate Pearson Correlation 7.1 Research Situations Where Pearson r Is Used 7.2 Hypothetical Research Example 7.3 Assumptions for Pearson r 7.4 Preliminary Data Screening 7.5 Design Issues in Planning Correlation Research 7.6 Computation of Pearson r 7.7 Statistical Significance Tests for Pearson r 7.8 Setting Up CIs for Correlations 7.9 Factors That Influence the Magnitude and Sign of Pearson r 7.10 Pearson r and r2 as Effect Size Indexes 7.11 Statistical Power and Sample Size for Correlation Studies 7.12 Interpretation of Outcomes for Pearson r 7.13 SPSS Output and Model Results Write-Up 7.14 Summary Comprehension Questions Chapter 8. Alternative Correlation Coefficients 8.1 Correlations for Different Types of Variables 8.2 Two Research Examples 8.3 Correlations for Rank or Ordinal Scores 8.4 Correlations for True Dichotomies 8.5 Correlations for Artificially Dichotomized Variables 8.6 Assumptions and Data Screening for Dichotomous Variables 8.7 Analysis of Data: Dog Ownership and Survival After a Heart Attack 8.8 Chi-Square Test of Association (Computational Methods for Tables of Any Size) 8.9 Other Measures of Association for Contingency Tables 8.10 SPSS Output and Model Results Write-Up 8.11 Summary Comprehension Questions Chapter 9. Bivariate Regression 9.1 Research Situations Where Bivariate Regression Is Used 9.2 A Research Example: Prediction of Salary From Years of Job Experience 9.3 Assumptions and Data Screening 9.4 Issues in Planning a Bivariate Regression Study 9.5 Formulas for Bivariate Regression 9.6 Statistical Significance Tests for Bivariate Regression 9.7 Setting Up Confidence Intervals Around Regression Coefficients 9.8 Factors That Influence the Magnitude and Sign of b 9.9 Effect Size/Partition of Variance in Bivariate Regression 9.10 Statistical Power 9.11 Raw Score Versus Standard Score Versions of the Regression Equation 9.12 Removing the Influence of X From the Y Variable by Looking at Residuals From Bivariate Regression 9.13 Empirical Example Using SPSS 9.14 Summary Comprehension Questions Chapter 10. Adding a Third Variable: Preliminary Exploratory Analyses 10.1 Three-Variable Research Situations 10.2 First Research Example 10.3 Exploratory Statistical Analyses for Three-Variable Research Situations 10.4 Separate Analysis of X1, Y Relationship for Each Level of the Control Variable X2 10.5 Partial Correlation Between X1 and Y Controlling for X2 10.6 Understanding Partial Correlation as the Use of Bivariate Regression to Remove Variance Predictable by X2 From Both X1 and Y 10.7 Computation of Partial r From Bivariate Pearson Correlations 10.8 Intuitive Approach to Understanding Partial r 10.9 Significance Tests, Confidence Intervals, and Statistical Power for Partial Correlations 10.10 Interpretation of Various Outcomes for rY1.2 and rY1 10.11 Two-Variable Causal Models 10.12 Three-Variable Models: Some Possible Patterns of Association Among X1, Y, and X2 10.13 Mediation Versus Moderation 10.14 Model Results 10.15 Summary Comprehension Questions Chapter 11. Multiple Regression With Two Predictor Variables 11.1 Research Situations Involving Regression With Two Predictor Variables 11.2 Hypothetical Research Example 11.3 Graphic Representation of Regression Plane 11.4 Semipartial (or "Part") Correlation 11.5 Graphic Representation of Partition of Variance in Regression With Two Predictors 11.6 Assumptions for Regression With Two Predictors 11.7 Formulas for Regression Coefficients, Significance Tests, and Confidence Intervals 11.8 SPSS Regression Results 11.9 Conceptual Basis: Factors That Affect the Magnitude and Sign of B and b Coefficients in Multiple Regression With Two Predictors 11.10 Tracing Rules for Causal Model Path Diagrams 11.11 Comparison of Equations for B, b, pr, and sr 11.12 Nature of Predictive Relationships 11.13 Effect Size Information in Regression With Two Predictors 11.14 Statistical Power 11.15 Issues in Planning a Study 11.16 Use of Regression With Two Predictors to Test Mediated Causal Models 11.17 Results 11.18 Summary Comprehension Questions Chapter 12. Dummy Predictor Variables and Interaction Terms in Multiple Regression 12.1 Research Situations Where Dummy Predictor Variables Can Be Used 12.2 Empirical Example 12.3 Screening for Violations of Assumptions 12.4 Issues in Planning a Study 12.5 Parameter Estimates and Significance Tests for Regressions With Dummy Variables 12.6 Group Mean Comparisons Using One-Way Between-S ANOVA 12.7 Three Methods of Coding for Dummy Variables 12.8 Regression Models That Include Both Dummy and Quantitative Predictor Variables 12.9 Tests for Interaction (or Moderation) 12.10 Interaction Terms That Involve Two Quantitative Predictors 12.11 Effect Size and Statistical Power 12.12 Nature of the Relationship and/or Follow-Up Tests 12.13 Results 12.14 Summary Comprehension Questions Chapter 13. Factorial Analysis of Variance 13.1 Research Situations and Research Questions 13.2 Screening for Violations of Assumptions 13.3 Issues in Planning a Study 13.4 Empirical Example: Description of Hypothetical Data 13.5 Computations for Between-S Factorial ANOVA 13.6 Conceptual Basis: Factors That Affect the Size of Sums of Squares and F Ratios in Factorial ANOVA 13.7 Effect Size Estimates for Factorial ANOVA 13.8 Statistical Power 13.9 Nature of the Relationships, Follow-Up Tests, and Information to Include in the Results 13.10 Factorial ANOVA Using the SPSS GLM Procedure 13.11 Summary Appendix: Nonorthogonal Factorial ANOVA (ANOVA With Unbalanced Numbers of Cases in the Cells or Groups) Comprehension Questions Chapter 14. Multiple Regression With More Than Two Predictors 14.1 Research Questions 14.2 Empirical Example 14.3 Screening for Violations of Assumptions 14.4 Issues in Planning a Study 14.5 Computation of Regression Coefficients With k Predictor Variables 14.6 Methods of Entry for Predictor Variables 14.7 Variance Partitioning in Regression for Standard or Simultaneous Regression Versus Regressions That Involve a Series of Steps 14.8 Significance Test for an Overall Regression Model 14.9 Significance Tests for Individual Predictors in Multiple Regression 14.10 Effect Size 14.11 Changes in F and R as Additional Predictors Are Added to a Model in Sequential or Statistical Regression 14.12 Statistical Power 14.13 Nature of the Relationship Between Each X Predictor and Y (Controlling for Other Predictors) 14.14 Assessment of Multivariate Outliers in Regression 14.15 SPSS Example and Results 14.16 Summary Appendix 14.A: A Review of Matrix Algebra Notation and Operations and Application of Matrix Algebra to Estimation of Slope Coefficients for Regression With More Than k Predictor Variables Appendix 14.B: Tables for Wilkinson and Dallal (1981) Test of Significance of Multiple R2 in Method = Forward Statistical Regression Comprehension Questions Chapter 15. Analysis of Covariance 15.1 Research Situations and Research Questions 15.2 Empirical Example 15.3 Screening for Violations of Assumptions 15.4 Variance Partitioning in ANCOVA 15.5 Issues in Planning a Study 15.6 Formulas for ANCOVA 15.7 Computation of Adjusted Effects and Adjusted Y* Means 15.8 Conceptual Basis: Factors That Affect the Magnitude of SSAadj and SSresidual and the Pattern of Adjusted Group Means 15.9 Effect Size 15.10 Statistical Power 15.11 Nature of the Relationship and Follow-Up Tests: Information to Include in the Results Section 15.12 SPSS Analysis and Model Results 15.13 Additional Discussion of ANCOVA Results 15.14 Summary Appendix: Alternative Methods for the Analysis of Pretest/Posttest Data Comprehension Questions Chapter 16. Discriminant Analysis 16.1 Research Situations and Research Questions 16.2 Introduction of an Empirical Example 16.3 Screening for Violations of Assumptions 16.4 Issues in Planning a Study 16.5 Equations for Discriminant Analysis 16.6 Conceptual Basis: Factors That Affect the Magnitude of Wilks's Lambda 16.7 Effect Size 16.8 Statistical Power and Sample Size Recommendations 16.9 Follow-Up Tests to Assess What Pattern of Scores Best Differentiates Groups 16.10 Results 16.11 One-Way ANOVA on Scores on Discriminant Functions 16.12 Summary Appendix: Eigenvalue/Eigenvector Problem Comprehension Questions Chapter 17. Multivariate Analysis of Variance 17.1 Research Situations and Research Questions 17.2 Introduction of the Initial Research Example: A One-Way MANOVA 17.3 Why Include Multiple Outcome Measures? 17.4 Equivalence of MANOVA and DA 17.5 The General Linear Model 17.6 Assumptions and Data Screening 17.7 Issues in Planning a Study 17.8 Conceptual Basis of MANOVA and Some Formulas for MANOVA 17.9 Multivariate Test Statistics 17.10 Factors That Influence the Magnitude of Wilks's Lambda 17.11 Effect Size for MANOVA 17.12 Statistical Power and Sample Size Decisions 17.13 SPSS Output for a One-Way MANOVA: Career Group Data From Chapter 16 17.14 A 2 x 3 Factorial MANOVA of the Career Group Data 17.15 A Significant Interaction in a 3 x 6 MANOVA 17.16 Comparison of Univariate and Multivariate Follow-Up Analyses for MANOVA 17.17 Summary Comprehension Questions Chapter 18. Principal Components and Factor Analysis 18.1 Research Situations 18.2 Path Model for Factor Analysis 18.3 Factor Analysis as a Method of Data Reduction 18.4 Introduction of an Empirical Example 18.5 Screening for Violations of Assumptions 18.6 Issues in Planning a Factor Analytic Study 18.7 Computation of Loadings 18.8 Steps in the Computation of Principal Components or Factor Analysis 18.9 Analysis 1: Principal Components Analysis of Three Items Retaining All Three Components 18.10 Analysis 2: Principal Component Analysis of Three Items Retaining Only the First Component 18.11 Principal Components Versus Principal Axis Factoring 18.12 Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation 18.13 Geometric Representation of Correlations Between Variables and Correlations Between Components or Factors 18.14 The Two Multiple Regressions 18.15 Analysis 4: PAF With Varimax Rotation 18.16 Questions to Address in the Interpretation of Factor Analysis 18.17 Results Section for Analysis 4: PAF With Varimax Rotation 18.18 Factor Scores Versus Unit-Weighted Composites 18.19 Summary of Issues in Factor Analysis 18.20 Optional: Brief Introduction to Concepts in Structural Equation Modeling Appendix: The Matrix Algebra of Factor Analysis Comprehension Questions Chapter 19. Reliability, Validity, and Multiple-Item Scales 19.1 Assessment of Measurement Quality 19.2 Cost and Invasiveness of Measurements 19.3 Empirical Examples of Reliability Assessment 19.4 Concepts From Classical Measurement Theory 19.5 Use of Multiple-Item Measures to Improve Measurement Reliability 19.6 Three Methods for the Computation of Summated Scales 19.7 Assessment of Internal Homogeneity for Multiple-Item Measures 19.8 Correlations Among Scores Obtained Using Different Methods of Summing Items 19.9 Validity Assessment 19.10 Typical Scale Development Study 19.11 Summary Appendix: The CESD Scale Comprehension Questions Chapter 20. Analysis of Repeated Measures 20.1 Introduction 20.2 Empirical Example: Experiment to Assess Effect of Stress on Heart Rate 20.3 Discussion of Sources of Within-Group Error in Between-S Versus Within-S Data 20.4 The Conceptual Basis for the Paired Samples t Test and One-Way Repeated Measures ANOVA 20.5 Computation of a Paired Samples t Test to Compare Mean HR Between Baseline and Pain Conditions 20.6 SPSS Example: Analysis of Stress/HR Data Using a Paired Samples t Test 20.7 Comparison Between Independent Samples t Test and Paired Samples t Test 20.8 SPSS Example: Analysis of Stress/HR Data Using a Univariate One-Way Repeated Measures ANOVA 20.9 Using the SPSS GLM Procedure for Repeated Measures ANOVA 20.10 Screening for Violations of Assumptions in Univariate Repeated Measures 20.11 The Greenhouse-Geisser e and Huynh Feldt e Correction Factors 20.12 MANOVA Approach to Analysis of Repeated Measures Data 20.13 Effect Size 20.14 Statistical Power 20.15 Planned Contrasts 20.16 Results 20.17 Design Problems in Repeated Measures Studies 20.18 More Complex Designs 20.19 Alternative Analyses for Pretest and Posttest Scores 20.20 Summary Comprehension Questions Chapter 21. Binary Logistic Regression 21.1 Research Situations 21.2 Simple Empirical Example: Dog Ownership and Odds of Death 21.3 Conceptual Basis for Binary Logistic Regression Analysis 21.4 Definition and Interpretation of Odds 21.5 A New Type of Dependent Variable: The Logit 21.6 Terms Involved in Binary Logistic Regression Analysis 21.7 Analysis of Data for First Empirical Example: Dog Ownership/Death Study 21.8 Issues in Planning and Conducting a Study 21.9 More Complex Models 21.10 Binary Logistic Regression for Second Empirical Analysis: Drug Dose and Gender as Predictors of Odds of Death 21.11 Comparison of Discriminant Analysis to Binary Logistic Regression 21.12 Summary Comprehension Questions Appendix A: Proportions of Area Under Standard Normal Curve Appendix B: Critical Values for t Distribution Appendix C: Critical Values of F Appendix D: Critical Values of Chi-Square Appendix E: Critical Values of the Correlation Coefficient Appendix F: Critical Values of the Studentized Range Statistic Appendix G: Transformation of r (Pearson Correlation) to Fisher Z Glossary References Index About the Author