Rebecca M. M. Warner 
Applied Statistics II [PDF ebook] 
Multivariable and Multivariate Techniques

Preface
Acknowledgments
About the Author
1. The New Statistics
Required Background
What Is the “New Statistics”?
Common Misinterpretations of p Values
Problems With NHST Logic
Common Misuses of NHST
The Replication Crisis
Some Proposed Remedies for Problems With NHST
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 2A: Brief Note About Zero-Inflated Binomial or Poisson Regression
3. Statistical Control: What Can Happen When You Add a Third Variable?
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
Understanding 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 × 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 Zero
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. Regression Analysis and Statistical Control
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 ß and b Coefficients in Multiple Regression With Two Predictors
Tracing Rules for Path Models
Comparison of Equations for ß, 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 With Multiple Predictors
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
Summary
Appendix 5A: Use of Matrix Algebra to Estimate Regression Coefficients for Multiple Predictors
Appendix 5B: Tables for Wilkinson and Dallal (1981) Test of Significance of Multiple R2 in Forward Statistical Regression
Appendix 5C: Confidence Interval for R2
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 7A: Graphing Interactions Between Quantitative Variables “by Hand”
8. Analysis of Covariance
Research Situations for Analysis of Covariance
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 Model Results
Additional Discussion of ANCOVA Results
Summary
Appendix 8A: Alternative Methods for the Analysis of Pretest–Posttest Data
9. Mediation
Definition of Mediation
Hypothetical Research Example
Limitations 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 Models
Note About Use of Structural Equation Modeling Programs to Test Mediation Models
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’ Lambda
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 10A: The Eigenvalue/Eigenvector Problem
Appendix 10B: Additional Equations for Discriminant Analysis
11. Multivariate Analysis of Variance
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’ Lambda
Effect Size for MANOVA
Statistical Power and Sample Size Decisions
One-Way MANOVA: Career Group Data
2 × 3 Factorial MANOVA: Career Group Data
Significant Interaction in a 3 × 6 MANOVA
Comparison of Univariate and 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 PC and Factor Analysis
Analysis 1: PC Analysis of Three Items Retaining All Three Components
Analysis 2: PC Analysis of Three Items Retaining Only the First Component
PC Versus PAF
Analysis 3: PAF of Nine Items, Two Factors Retained, No Rotation
Geometric Representation of Factor Rotation
Factor Analysis as Two Sets of Multiple Regressions
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 12A: The Matrix Algebra of Factor Analysis
Appendix 12B: A Brief Introduction to Latent Variables in SEM
13. Reliability, Validity, and Multiple-Item Scales
Assessment of Measurement Quality
Cost and Invasiveness of Measurements
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 Reliability Coefficient
Validity Assessment
Typical Scale Development Process
A Brief Note About Modern Measurement Theories
Reporting Reliability
Summary
Appendix 13A: The CES-D
Appendix 13B: Web Resources on Psychological Measurement
14. More About Repeated Measures
Introduction
Review of Assumptions for Repeated-Measures ANOVA
First Example: Heart Rate and Social Stress
Test for Participant-by-Time or Participant-by-Treatment Interaction
One-Way Repeated-Measures Results for Heart Rate and Social Stress Data
Testing the Sphericity Assumption
MANOVA for Repeated Measures
Results for Heart Rate 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®
Screening and Preparing Data for SEM
Specifying the SEM Model (Variable Names and Paths)
Specify 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
Comparing Structural Equation Models
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 With 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
Glossary
References
Index

Rebecca M. Warner received a B.A. from Carnegie-Mellon University in Social Relations in 1973 and a Ph.D. in Social Psychology from Harvard in 1978. She has taught statistics for more than 25 years: from Introductory and Intermediate Statistics to advanced topics seminars in Multivariate Statistics, Structural Equation Modeling, and Time Series Analysis. She is currently a Full Professor in the Department of Psychology at the University of New Hampshire. She is a Fellow in the Association for Psychological Science and a member of the American Psychological Association, the International Association for Relationships Research, the Society of Experimental Social Psychology, and the Society for Personality and Social Psychology. She has consulted on statistics and data management for the World Health Organization in Geneva and served as a visiting faculty member at Shandong Medical University in China.