Denis D.J. Applied Univariate, Bivariate, and Multivariate Statistics

John Wiley & Sons, Inc., 2015. — 760 p. — ISBN: 1118632338, 9781118632338A clear and efficient balance between theory and application of statistical modeling techniques in the social and behavioral sciences.
Written as a general and accessible introduction, Applied Univariate, Bivariate, and Multivariate Statistics provides an overview of statistical modeling techniques used in fields in the social and behavioral sciences. Blending statistical theory and methodology, the book surveys both the technical and theoretical aspects of good data analysis.
Featuring applied resources at various levels, the book includes statistical techniques such as t-tests and correlation as well as more advanced procedures such as MANOVA, factor analysis, and structural equation modeling. To promote a more in-depth interpretation of statistical techniques across the sciences, the book surveys some of the technical arguments underlying formulas and equations. Applied Univariate, Bivariate, and Multivariate Statistics also featuresDemonstrations of statistical techniques using software packages such as R and SPSS
Examples of hypothetical and real data with subsequent statistical analyses
Historical and philosophical insights into many of the techniques used in modern social science
A companion website that includes further instructional details, additional data sets, solutions to selected exercises, and multiple programming optionsAn ideal textbook for courses in statistics and methodology at the upper- undergraduate and graduate-levels in psychology, political science, biology, sociology, education, economics, communications, law, and survey research, Applied Univariate, Bivariate, and Multivariate Statistics is also a useful reference for practitioners and researchers in their field of application.Preliminary Considerations
The Philosophical Bases of Knowledge: Rationalistic versus Empiricist Pursuits
What is a “Model”?
Social Sciences versus Hard Sciences
Is Complexity a Good Depiction of Reality? Are Multivariate Methods Useful?
Causality
The Nature of Mathematics: Mathematics as a Representation of Concepts
As a Social Scientist, How Much Mathematics Do You Need to Know?
Statistics and Relativity
Experimental versus Statistical Control
Statistical versus Physical Effects
Understanding What “Applied Statistics” Means
Review Exercises
Mathematics and Probability Theory
Set Theory
Cartesian Product A х B
Sets of Numbers
Set Theory Into Practice: Samples, Populations, and Probability
Probability
Interpretations of Probability: Frequentist versus Subjective
Bayes’ Theorem: Inverting Conditional Probabilities
Statistical Inference
Essential Mathematics: Precalculus, Calculus, and Algebra
Chapter Summary and Highlights
Review Exercises
Introductory Statistics
Densities and Distributions
Chi-Square Distributions and Goodness-of-Fit Test
Sensitivity and Specificity
Scales of Measurement: Nominal, Ordinal, and Interval, Ratio
Mathematical Variables versus Random Variables
Moments and Expectations
Estimation and Estimators
Variance
Degrees of Freedom
Skewness and Kurtosis
Sampling Distributions
Central Limit Theorem
Confidence Intervals
Bootstrap and Resampling Techniques
Likelihood Ratio Tests and Penalized Log-Likelihood Statistics
Akaike’s Information Criteria
Covariance and Correlation
Other Correlation Coefficients
Student’s t Distribution
Statistical Power
Paired Samples t-Test: Statistical Test for Matched Pairs (Elementary Blocking) Designs
Blocking with Several Conditions
Composite Variables: Linear Combinations
Models in Matrix Form
Graphical Approaches
What Makes a p-Value Small? A Critical Overview and Simple Demonstration of Null Hypothesis Significance Testing
Chapter Summary and Highlights
Review Exercises
Analysis of Variance: Fixed Effects Models
What is Analysis of Variance? Fixed versus Random Effects
How Analysis of Variance Works: A Big Picture Overview
Logic and Theory of ANOVA: A Deeper Look
From Sums of Squares to Unbiased Variance Estimators: Dividing by Degrees of Freedom
Expected Mean Squares for One-Way Fixed Effects Model: Deriving the F-Ratio
The Null Hypothesis in ANOVA
Fixed Effects ANOVA: Model Assumptions
A Word on Experimental Design and Randomization
A Preview of the Concept of Nesting
Balanced versus Unbalanced Data in ANOVA Models
Measures of Association and Effect Size in ANOVA: Measures of Variance Explained
The F-Test and the Independent Samples t-Test
Contrasts and Post-Hocs
Post-Hoc Tests
Sample Size and Power for ANOVA: Estimation with R and G∗Power
Fixed Effects One-Way Analysis of Variance in R: Mathematics Achievement as a Function of Teacher
Analysis of Variance Via R’s lm
Kruskal–Wallis Test in R
ANOVA in SPSS: Achievement as a Function of Teacher
Chapter Summary and Highlights
Review Exercises
Factorial Analysis of Variance: Modeling Interactions
What is Factorial Analysis of Variance?
Theory of Factorial ANOVA: A Deeper Look
Comparing One-Way ANOVA to Two-Way ANOVA: Cell Effects in Factorial ANOVA versus Sample Effects in One-Way ANOVA
Partitioning the Sums of Squares for Factorial ANOVA: The Case of Two Factors
Interpreting Main Effects in the Presence of Interactions
Effect Size Measures
Three-Way, Four-Way, and Higher-Order Models
Simple Main Effects
Nested Designs
Achievement as a Function of Teacher and Textbook: Example of Factorial ANOVA in R Interaction Contrasts
Chapter Summary and Highlights
Review Exercises
Introduction to Random Effects and Mixed Models
What is Random Effects Analysis of Variance?
Theory of Random Effects Models
Estimation in Random Effects Models
Defining Null Hypotheses in Random Effects Models
Comparing Null Hypotheses in Fixed versus Random Effects Models: The Importance of Assumptions
Estimating Variance Components in Random Effects Models: ANOVA, ML, REML Estimators
Is Achievement a Function of Teacher? One-Way Random Effects Model in R
R Analysis Using REML
Analysis in SPSS: Obtaining Variance Components
Factorial Random Effects: A Two-Way Model
Fixed Effects versus Random Effects: A Way of Conceptualizing Their Differences
Conceptualizing the Two-Way Random Effects Model: The Make up of a Randomly Chosen Observation
Sums of Squares and Expected Mean Squares for Random Effects: The Contaminating Influence of Interaction Effects
You Get What You Go in with: The Importance of Model Assumptions and Model Selection
Mixed Model Analysis of Variance: Incorporating Fixed and Random Effects
Mixed Models in Matrices
Multilevel Modeling as a Special Case of the Mixed Model: Incorporating Nesting and Clustering
Chapter Summary and Highlights
Review Exercises
Randomized Blocks and Repeated Measures
What Is a Randomized Block Design?
Randomized Block Designs: Subjects Nested Within Blocks
Theory of Randomized Block Designs
Tukey Test for Nonadditivity
Assumptions for the Variance–Covariance Matrix
Intraclass Correlation
Repeated Measures Models: A Special Case of Randomized Block Designs
Independent versus Paired Samples t-Test
The Subject Factor: Fixed or Random Effect?
Model for One-Way Repeated Measures Design
Analysis Using R: One-Way Repeated Measures: Learning as a Function of Trial
Analysis Using SPSS: One-Way Repeated Measures: Learning as a Function of Trial
SPSS: Two-Way Repeated Measures Analysis of Variance: Mixed Design: One Between Factor, One Within Factor
Chapter Summary and Highlights
Review Exercises
Linear Regression
Brief History of Regression
Regression Analysis and Science: Experimental versus Correlational Distinctions
A Motivating Example: Can Offspring Height Be Predicted?
Theory of Regression Analysis: A Deeper Look
Multilevel Yearnings
The Least-Squares Line
Making Predictions Without Regression
More About εi
Model Assumptions for Linear Regression
Estimation of Model Parameters in Regression
Null Hypotheses for Regression
Significance Tests and Confidence Intervals for Model Parameters
Other Formulations of the Regression Model
The Regression Model in Matrices: Allowing for More Complex Multivariable Models
Ordinary Least-Squares in Matrices
Analysis of Variance for Regression
Measures of Model Fit for Regression: How Well Does the Linear Equation Fit?
Adjusted R²
What “Explained Variance” Means: And More Importantly, What It Does Not Mean
Values Fit by Regression
Least-Squares Regression in R: Using Matrix Operations
Linear Regression Using R
Regression Diagnostics: A Check on Model Assumptions
Regression in SPSS: Predicting Quantitative from Verbal
Power Analysis for Linear Regression in R
Chapter Summary and Highlights
Review Exercises
Multiple Linear Regression
Theory of Partial Correlation and Multiple Regression
Semipartial Correlations
Multiple Regression
Some Perspective on Regression Coefficients: “Experimental Coefficients”?
Multiple Regression Model in Matrices
Estimation of Parameters
Conceptualizing Multiple R
Interpreting Regression Coefficients: The Case of Uncorrelated Predictors
Anderson’s IRIS Data: Predicting Sepal Length from Petal Length and Petal Width
Fitting Other Functional Forms: A Brief Look at Polynomial Regression
Measures of Collinearity in Regression: Variance Inflation Factor and Tolerance
R-Squared as a Function of Partial and Semipartial Correlations: The Stepping Stones to Forward and Stepwise Regression
Model-Building Strategies: Simultaneous, Hierarchichal, Forward, and Stepwise
Power Analysis for Multiple Regression
Introduction to Statistical Mediation: Concepts and Controversy
Chapter Summary and Highlights
Review Exercises
Interactions in Multiple Linear Regression: Dichotomous, Polytomous, and Continuous Moderators
The Additive Regression Model with Two Predictors
Why the Interaction is the Product Term xizi: Drawing an Analogy to Factorial ANOVA
A Motivating Example of Interaction in Regression: Crossing a Continuous Predictor with a Dichotomous Predictor
Theory of Interactions in Regression
Simple Slopes for Continuous Moderators
A Simple Numerical Example: How Slopes Can Change as a Function of the Moderator
Calculating Simple Slopes: A Useful Algebraic Derivation
Summing Up the Idea of Interactions in Regression
Do Moderators Really “Moderate” Anything? Some Philosophical Considerations
Interpreting Model Coefficients in the Context of Moderators
Mean-Centering Predictors: Improving the Interpretability of Simple Slopes
The Issue of Multicollinearity: A Second Reason to Like Mean-Centering
Interaction of Continuous and Polytomous Predictors in R
Multilevel Regression: Another Special Case of the Mixed Model
Chapter Summary and Highlights
Review Exercises
Logistic Regression and the Generalized Linear Model
Nonlinear Models
Generalized Linear Models
Canonical Links
Distributions and Generalized Linear Models
Dispersion Parameters and Deviance
Logistic Regression: A Generalized Linear Model for Binary Responses
Exponential and Logarithmic Functions
Odds, Odds Ratio, and the Logit
Putting It All Together: The Logistic Regression Model
Logistic Regression in R: Challenger O-Ring Data
Challenger Analysis in SPSS
Sample Size, Effect Size, and Power
Further Directions
Chapter Summary and Highlights
Review Exercises
Multivariate Analysis of Variance
A Motivating Example: Quantitative and Verbal Ability as a Variate
Constructing the Composite
Theory of MANOVA
Is the Linear Combination Meaningful?
Multivariate Hypotheses
Assumptions of MANOVA
Hotelling’s T²: The Case of Generalizing from Univariate to Multivariate
The Variance–Covariance Matrix S
From Sums of Squares and Cross-Products to Variances and Covariances
Hypothesis and Error Matrices of MANOVA
Multivariate Test Statistics
Equality of Variance–Covariance Matrices
Multivariate Contrasts
MANOVA in R and SPSS
MANOVA of Fisher’s Iris Data
Power Analysis and Sample Size for MANOVA
Multivariate Analysis of Covariance and Multivariate Models: A Bird’s Eye View of Linear Models
Chapter Summary and Highlights
Review Exercises
Discriminant Analysis
What is Discriminant Analysis? The Big Picture on the Iris Data
Theory of Discriminant Analysis
LDA in R and SPSS
Discriminant Analysis for Several Populations
Discriminating Species of Iris: Discriminant Analyses for Three Populations
A Note on Classification and Error Rates
Discriminant Analysis and Beyond
Canonical Correlation
Motivating Example for Canonical Correlation: Hotelling’s 1936 Data
Canonical Correlation as a General Linear Model
Theory of Canonical Correlation
Canonical Correlation of Hotelling’s Data
Canonical Correlation on the Iris Data: Extracting Canonical Correlation from Regression, MANOVA, LDA
Chapter Summary and Highlights
Review Exercises
Principal Components Analysis
History of Principal Components Analysis
Hotelling 1933
Theory of Principal Components Analysis
Eigenvalues as Variance
Principal Components as Linear Combinations
Extracting the First Component
Extracting the Second Component
Extracting Third and Remaining Components
The Eigenvalue as the Variance of a Linear Combination Relative to Its Length
Demonstrating Principal Components Analysis: Pearson’s 1901 Illustration
Scree Plots
Principal Components versus Least-Squares Regression Lines
Covariance versus Correlation Matrices: Principal Components and Scaling
Principal Components Analysis Using SPSS
Chapter Summary and Highlights
Review Exercises
Factor Analysis
History of Factor Analysis
Factor Analysis: At a Glance
Exploratory versus Confirmatory Factor Analysis
Theory of Factor Analysis: The Exploratory Factor-Analytic Model
The Common Factor-Analytic Model
Assumptions of the Factor-Analytic Model
Why Model Assumptions Are Important
The Factor Model as an Implication for the Covariance Matrix Σ
Again, Why is Σ=ΛΛ’ + ψ so Important a Result?
The Major Critique Against Factor Analysis: Indeterminacy and the Nonuniqueness of Solutions
Has Your Factor Analysis Been Successful?
Estimation of Parameters in Exploratory Factor Analysis
Estimation of Factor Scores
Principal Factor
Maximum Likelihood
The Concepts (and Criticisms) of Factor Rotation
Varimax and Quartimax Rotation
Should Factors Be Rotated? Is That Not “Cheating?”
Sample Size for Factor Analysis
Principal Components Analysis versus Factor Analysis: Two Key Differences
Principal Factor in SPSS: Principal Axis Factoring
Bartlett Test of Sphericity and Kaiser–Meyer–Olkin Measure of Sampling Adequacy (MSA)
Factor Analysis in R: Holzinger and Swineford (1939)
Cluster Analysis
What Is Cluster Analysis? The Big Picture
Measuring Proximity
Hierarchical Clustering Approaches
Nonhierarchical Clustering Approaches
K-Means Cluster Analysis in R
Guidelines and Warnings About Cluster Analysis
Chapter Summary and Highlights
Review Exercises
Path Analysis and Structural Equation Modeling
Path Analysis: A Motivating Example — Predicting IQ Across Generations
Path Analysis and “Causal Modeling”
Early Post-Wright Path Analysis: Predicting Child’sIQ (Burks, 1928)
Decomposing Path Coefficients
Path Coefficients and Wright’s Contribution
Path Analysis in R: A Quick Overview — Modeling Galton’s Data
Confirmatory Factor Analysis: The Measurement Model
Structural Equation Models
Direct, Indirect, and Total Effects
Theory of Statistical Modeling: A Deeper Look into Covariance Structures and General Modeling
Other Discrepancy Functions
The Discrepancy Function and Chi-Square
Identification
Disturbance Variables
Measures and Indicators of Model Fit
Overall Measures of Model Fit
Model Comparison Measures: Incremental Fit Indices
Which Indicator of Model Fit Is Best?
Structural Equation Model in R
How All Variables Are Latent: A Suggestion for Resolving the Manifest–Latent Distinction
The Structural Equation Model as a General Model: Some Concluding Thoughts on Statistics and Science
Chapter Summary and Highlights
Review Exercises
Appendix A: Matrix Algebra