1. The New Statistics Required Background What is the New Statistics? Common Misinterpretations of p Values Problems with NHST Logic The Replication Crises Common Misuses of NHST The Replication Crisis Some Proposed Remedies for NHST Problems Review of Confidence Intervals Effect Size Brief Introduction to Meta-Analysis Recommendations for Better Research and Analysis Summary 2. Advanced Data Screening: Outliers and Missing Values Introduction Variable Names and File Management Sources of Bias Screening Sample Data Possible Remedy for Skewness: Nonlinear Data Transformations Identification of Outliers Handling Outliers Testing Linearity Assumptions Evaluation of Other Assumptions Specific to Analyses Describing Amount of Missing Data How Missing Data Arise Patterns in Missing Data Empirical Example: Detecting Type a Missingness Possible Remedies for Missing Data Empirical Example: Multiple Imputation to Replace Missing Values Data Screening Checklist Reporting Guidelines Summary Appendix 2 A Brief Note About Zero Inflated Binomial or Poisson Regression 3. Statistical Control: How an X, Y Association Can Change When a Control Variable is Added What is Statistical Control? First Research Example: Controlling for a Categorical X2 Variable Assumptions for Partial Correlation Between X1 and Y, Controlling for X2 Notation for Partial Correlation Computing Partial Correlation: Use of Bivariate Regressions to Remove Variance Predictable by X2 from Both X1 and Y Partial Correlation Makes No Sense if There is An X1 x X2 Interaction Computation of Partial r From Bivariate Pearson Correlations Significance Tests, Confidence Intervals, and Statistical Power for Partial Correlations Comparing Outcomes for ry1.2 and ry1 Introduction to Path Models Possible Paths Among X1, Y, and X2 One Possible Model: X1 and Y are Not Related Whether You Control for X2 or Not Possible Model: Correlation Between X1 and Y is the Same Whether X2 is Statistically Controlled or Not (X2 is Irrelevant to the X1, Y Relationship) When You Control for X2, Correlation Between X1 and Y Drops to 0 When You Control for X2, the Correlation Between X1 and Y Becomes Smaller (But Does not Drop to 0 or Change Sign) Some Forms of Suppression: When You Control for X2, r1y.2 Becomes Larger Than r1y or Opposite in Sign to r1y. None of the Above Results Section Summary 4. Partition of Variance in Regression Introduction Hypothetical Research Example Graphic Representation of Regression Plane Semipartial (or Part) Correlation Partition of Variance In Y in Regression with Two Predictors Assumptions for Regression With Two Predictors Formulas for Regression With Two Predictors SPSS Regression Conceptual Basis: Factors that Affect the Magnitude and Sign of ? and b in Regression With Two Predictors Tracing Rules for Path Models Comparison of Equations for ?, b, pr, and sr Nature of Predictive Relationships Effect Size Information in Regression with Two Predictors Statistical Power Issues in Planning a Study Results Summary 5. Multiple Regression Research Questions Empirical Example Screening for Violations of Assumptions Issues in Planning a Study Computation of Regression Coefficients with k Predictor Variables Methods of Entry for Predictor Variables Variance Partitioning in Standard Regression Versus Hierarchical and Statistical Regression Significance Test for an Overall Regression Model Significance Tests for Individual Predictors in Multiple Regression Effect Size Changes in F and R as Additional Predictors Are Added to a Model in Sequential or Statistical Regression Statistical Power Nature of the Relationship Between Each X Predictor and Y (Controlling for Other Predictors) Assessment of Multivariate Outliers in Regression SPSS Examples and Results Summary Appendix 5 A Use of Matrix Algebra to Estimate Regression Coefficients for Multiple Predictors Appendix 5 B Tables for Wilkinson and Dallal (1981) Test of Significance of Multiple R2 in Forward Statistical Regression 6. Dummy Predictor Variables in Multiple Regression What Dummy Variables Are and When They Are Used Empirical Example Screening for Violations of Assumptions Issues in Planning a Study Parameter Estimates and Significance Tests for Regressions with Dummy Predictor Variables Group Mean Comparisons Using One-Way Between-S ANOVA Three Methods of Coding for Dummy Variables Regression Models That Include Both Dummy and Quantitative Predictor Variables Effect Size and Statistical Power Nature of the Relationship and/or Follow-Up Tests Results Summary 7. Moderation: Interaction in Multiple Regression Terminology Interaction Between Two Categorical Predictors: Factorial ANOVA Interaction Between One Categorical and One Quantitative Predictor Preliminary Data Screening: One Categorical and One Quantitative Predictor Scatterplot for Preliminary Assessment of Possible Interaction Between Categorical and Quantitative Predictor Regression to Assess Statistical Significance of Interaction Between One Categorical and One Quantitative Predictor Interaction Analysis With More Than Three Categories Example With Different Data: Significant Sex by Years Interaction Follow-Up: Analysis of Simple Main Effects Interaction Between Two Quantitative Predictors SPSS Example of Interaction Between Two Quantitative Predictors Results for Interaction of Age and Habits as Predictors of Symptoms Graphing Interaction for Two Quantitative Predictors Results Section for Interaction of Two Quantitative Predictors Additional Issues and Summary Appendix 7 A Graphing Interactions Between Quantitative Variables By Hand 8. Analysis of Covariance Research Situations for ANCOVA Empirical Example Screening for Violations of Assumptions Variance Partitioning in ANCOVA Issues in Planning a Study Formulas for ANCOVA Computation of Adjusted Effects and Adjusted Y* Means Conceptual Basis: Factors that Affect the Magnitude of SSAadj and SSresidual and the Pattern of Adjusted Group Means Effect Size Statistical Power Nature of the Relationship and Follow-Up Tests: Information to Include in the Results Section SPSS Analysis and Results Additional Discussion of ANCOVA Results Summary Appendix 8 A Alternative Methods for the Analysis of Pretest/Posttest Data 9. Mediation Definition of Mediation Hypothetical Research Example Limits of Causal Models Questions in a Mediation Analysis Issues in Designing a Mediation Analysis Study Assumptions in Mediation Analysis and Preliminary Data Screening Path Coefficient Estimation Conceptual Issues: Assessment of Direct Versus Indirect Paths Evaluating Statistical Significance Effect Size Information Sample Size and Statistical Power Additional Examples of Mediation Note About Use of Structural Equation Modeling Programs to Test Mediation Hypotheses Results Section Summary 10. Discriminant Analysis Research Situations and Research Questions Introduction to Empirical Example Screening for Violations of Assumptions Issues in Planning a Study Equations for Discriminant Analysis Conceptual Basis: Factors That Affect the Magnitude of Wilks's L Effect Size Statistical Power and Sample Size Recommendations Follow-Up Tests to Assess What Pattern of Scores Best Differentiates Groups Results One-Way ANOVA on Scores on Discriminant Functions Summary Appendix 10 A The Eigenvalue/ Eigenvector Problem Appendix 10 B Additional Equations for Discriminant Analysis 11. Multivariate Analysis of Variance (MANOVA) Research Situations and Research Questions First Research Example: One-Way MANOVA Why Include Multiple Outcome Measures? Equivalence of MANOVA and DA The General Linear Model Assumptions and Data Screening Issues in Planning a Study Conceptual Basis of MANOVA Multivariate Test Statistics Factors that Influence the Magnitude of Wilks's Lambda Effect Size for MANOVA Statistical Power and Sample Size Decisions One Way MANOVA: Career Group Data 2 x 3 Factorial MANOVA: Career Group Data Significant Interaction in a 3 x 6 MANOVA Comparison of Univariate Versus Multivariate Follow Up Analyses Summary 12. Exploratory Factor Analysis Research Situations Path Model for Factor Analysis Factor Analysis as a Method of Data Reduction Introduction of Empirical Example Screening for Violations of Assumptions Issues in Planning a Factor-Analytic Study Computation of Factor Loadings Steps in the Computation of Principal Components and Factor Analysis Analysis One: Principal Components Analysis of Three Items Retaining All Three Components Analysis Two: Principal Component Analysis of Three Items Retaining Only the First Component Principal Components Versus Principal Axis Factoring Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation Geometric Representation of Factor Rotation Factor Analysis as Two Sets of Multiple Regressions Final Analysis/ Analysis 4: PAF With Varimax Rotation Questions to Address in the Interpretation of Factor Analysis Results Section for Analysis 4: PAF With Varimax Rotation Factor Scores Versus Unit-Weighted Composites Summary of Issues in Factor Analysis Appendix 12 A The Matrix Algebra of Factor Analysis Appendix 12 B A Brief Introduction to Latent Variables in Structural Equation Modeling 13. Reliability, Validity, and Multiple-Item Scales Assessment of Measurement Quality Cost and Invasiveness of Measures Empirical Examples of Reliability Assessment Concepts from Classical Measurement Theory Use of Multiple-Item Measures to Improve Measurement Reliability Computation of Summated Scales Assessment of Internal Homogeneity for Multiple-Item Measures: Cronbach's Alpha Reliabilit Coefficient Validity Assessment Typical Scale Development Process A Brief Note About Modern Measurement Theories Reporting Reliability Summary Appendix 13 A The CES-D Scale Appendix 13 B Web Resources About Psychological Measurement 14. Repeated Measures: Tests of Assumptions, Factorial Designs, and Order Effects Introduction Review of Assumptions for Repeated Measures ANOVA First Example: Heart Rate/ Social Stress Study Test for Participant by Time or Participant by Treatment Interaction One-Way Repeated Measures Results for HR/ Social Stress Data Testing the Sphericity Assumption MANOVA for Repeated Measures Results for HR and Social Stress Analysis Using MANOVA Doubly Multivariate Repeated Measures Mixed Model ANOVA: Between-S and Within-S Factors Order and Sequence Effects First Example: Order Effect as a Nuisance Second Example: Order Effect is of Interest Summary and Other Complex Designs 15. Structural Equation Modeling with AMOS: A Brief Introduction What is Structural Equation Modeling? Review of Path Models More Complex Path Models First Example: Mediation Structural Model Introduction to AMOS (R) Screening and Preparing Data for SEM Specifying the SEM Model (Variable Names and Paths) Specifying the Analysis Properties Running the Analysis and Examining Results Locating Bootstrapped CI Information Sample Results for the Mediation Analysis Selected SEM Model Terminology SEM Goodness of Fit Indexes Second Example: Confirmatory Factor Analysis Third Example: Model with Both Measurement and Structural Components Reporting SEM Summary 16. Binary Logistic Regression Research Situations First Example: Dog Ownership and Odds of Death Conceptual Basis for Binary Logistic Regression Analysis Definition and Interpretation of Odds A New Type of Dependent Variable: The Logit Terms Involved in Binary Logistic Regression Analysis Logistic Regression for First Example: Prediction of Death from Dog Ownership. Issues in Planning and Conducting a Study More Complex Models Binary Logistic Regression for Second Example: Drug Dose and Sex as Predictors of Odds of Death Comparison of Discriminant Analysis to Binary Logistic Regression Summary 17. Additional Statistical Techniques Introduction A Brief History of Developments in Statistics Survival Analysis Cluster Analyses Time Series Analyses Poisson and Binomial Regression for Zero-Inflated Count Data Bayes' Theorem Multilevel Modeling Some Final Words Second Example: Order Effect is of Interest Summary and Other Complex Designs What is Structural Equation Modeling? Review of Path Models More Complex Path Models First Example: Mediation Structural Model Introduction to AMOS (R) Screening and Preparing Data for SEM Specifying the SEM Model (Variable Names and Paths) Specifying the Analysis Properties Running the Analysis and Examining Results Locating Bootstrapped CI Information Sample Results for the Mediation Analysis Selected SEM Model Terminology SEM Goodness of Fit Indexes Second Example: Confirmatory Factor Analysis Third Example: Model with Both Measurement and Structural Components Reporting SEM Summary 19. Binary Logistic Regression Research Situations First Example: Dog Ownership and Odds of Death Conceptual Basis for Binary Logistic Regression Analysis Definition and Interpretation of Odds A New Type of Dependent Variable: The Logit Terms Involved in Binary Logistic Regression Analysis Logistic Regression for First Example: Prediction of Death from Dog Ownership. Issues in Planning and Conducting a Study More Complex Models Binary Logistic Regression for Second Example: Drug Dose and Sex as Predictors of Odds of Death Comparison of Discriminant Analysis to Binary Logistic Regression Summary 20. Additional Statistical Techniques Introduction A Brief History of Developments in Statistics Survival Analysis Cluster Analyses Time Series Analyses Poisson and Binomial Regression for Zero-Inflated Count Data Bayes' Theorem Multilevel Modeling Some Final Words
