Preface xix About the Companion Website xxxiii 1 Preliminary Considerations 1 1.1 The Philosophical Bases of Knowledge: Rationalistic versus Empiricist Pursuits 1 1.2 What is a "Model"? 4 1.3 Social Sciences versus Hard Sciences 6 1.4 Is Complexity a Good Depiction of Reality? Are Multivariate Methods Useful? 8 1.5 Causality 9 1.6 The Nature of Mathematics: Mathematics as a Representation of Concepts 10 1.7 As a Social Scientist How Much Mathematics Do You Need to Know? 11 1.

8 Statistics and Relativity 12 1.9 Experimental versus Statistical Control 13 1.10 Statistical versus Physical Effects 14 1.11 Understanding What "Applied Statistics" Means 15 Review Exercises 15 2 Mathematics and Probability Theory 18 2.1 Set Theory 20 2.2 Cartesian Product A × B 24 2.3 Sets of Numbers 26 2.4 Set Theory Into Practice: Samples, Populations, and Probability 27 2.

5 Probability 28 2.6 Interpretations of Probability: Frequentist versus Subjective 35 2.7 Bayes'' Theorem: Inverting Conditional Probabilities 39 2.8 Statistical Inference 44 2.9 Essential Mathematics: Precalculus, Calculus, and Algebra 48 2.10 Chapter Summary and Highlights 72 Review Exercises 74 3 Introductory Statistics 78 3.1 Densities and Distributions 79 3.2 Chi-Square Distributions and Goodness-of-Fit Test 91 3.

3 Sensitivity and Specificity 98 3.4 Scales of Measurement: Nominal, Ordinal, and Interval, Ratio 98 3.5 Mathematical Variables versus Random Variables 101 3.6 Moments and Expectations 103 3.7 Estimation and Estimators 106 3.8 Variance 108 3.9 Degrees of Freedom 110 3.10 Skewness and Kurtosis 111 3.

11 Sampling Distributions 113 3.12 Central Limit Theorem 116 3.13 Confidence Intervals 117 3.14 Bootstrap and Resampling Techniques 119 3.15 Likelihood Ratio Tests and Penalized Log-Likelihood Statistics 121 3.16 Akaike''s Information Criteria 122 3.17 Covariance and Correlation 123 3.18 Other Correlation Coefficients 128 3.

19 Student''s t Distribution 131 3.20 Statistical Power 139 3.21 Paired Samples t -Test: Statistical Test for Matched Pairs (Elementary Blocking) Designs 146 3.22 Blocking with Several Conditions 149 3.23 Composite Variables: Linear Combinations 149 3.24 Models in Matrix Form 151 3.25 Graphical Approaches 152 3.26 What Makes a p -Value Small? A Critical Overview and Simple Demonstration of Null Hypothesis Significance Testing 155 3.

27 Chapter Summary and Highlights 164 Review Exercises 167 4 Analysis of Variance: Fixed Effects Models 173 4.1 What is Analysis of Variance? Fixed versus Random Effects 174 4.2 How Analysis of Variance Works: A Big Picture Overview 178 4.3 Logic and Theory of ANOVA: A Deeper Look 180 4.4 From Sums of Squares to Unbiased Variance Estimators: Dividing by Degrees of Freedom 189 4.5 Expected Mean Squares for One-Way Fixed Effects Model: Deriving the F -Ratio 190 4.6 The Null Hypothesis in ANOVA 196 4.7 Fixed Effects ANOVA: Model Assumptions 198 4.

8 A Word on Experimental Design and Randomization 201 4.9 A Preview of the Concept of Nesting 201 4.10 Balanced versus Unbalanced Data in ANOVA Models 202 4.11 Measures of Association and Effect Size in ANOVA: Measures of Variance Explained 202 4.12 The F -Test and the Independent Samples t -Test 205 4.13 Contrasts and Post-Hocs 205 4.14 Post-Hoc Tests 212 4.15 Sample Size and Power for ANOVA: Estimation with R and G∗Power 218 4.

16 Fixed Effects One-Way Analysis of Variance in R: Mathematics Achievement as a Function of Teacher 222 4.17 Analysis of Variance Via R''s lm 226 4.18 Kruskal-Wallis Test in R 227 4.19 ANOVA in SPSS: Achievement as a Function of Teacher 228 4.20 Chapter Summary and Highlights 230 Review Exercises 232 5 Factorial Analysis of Variance: Modeling Interactions 237 5.1 What is Factorial Analysis of Variance? 238 5.2 Theory of Factorial ANOVA: A Deeper Look 239 5.3 Comparing One-Way ANOVA to Two-Way ANOVA: Cell Effects in Factorial ANOVA versus Sample Effects in One-Way ANOVA 245 5.

4 Partitioning the Sums of Squares for Factorial ANOVA: The Case of Two Factors 246 5.5 Interpreting Main Effects in the Presence of Interactions 253 5.6 Effect Size Measures 253 5.7 Three-Way Four-Way and Higher-Order Models 254 5.8 Simple Main Effects 254 5.9 Nested Designs 256 5.10 Achievement as a Function of Teacher and Textbook: Example of Factorial ANOVA in R 258 5.11 Interaction Contrasts 266 5.

12 Chapter Summary and Highlights 267 Review Exercises 268 6 Introduction to Random Effects and Mixed Models 270 6.1 What is Random Effects Analysis of Variance? 271 6.2 Theory of Random Effects Models 272 6.3 Estimation in Random Effects Models 273 6.4 Defining Null Hypotheses in Random Effects Models 276 6.5 Comparing Null Hypotheses in Fixed versus Random Effects Models: The Importance of Assumptions 278 6.6 Estimating Variance Components in Random Effects Models: ANOVA, ML, REML Estimators 279 6.7 Is Achievement a Function of Teacher? One-Way Random Effects Model in R 282 6.

8 R Analysis Using REML 285 6.9 Analysis in SPSS: Obtaining Variance Components 286 6.10 Factorial Random Effects: A Two-Way Model 287 6.11 Fixed Effects versus Random Effects: A Way of Conceptualizing Their Differences 289 6.12 Conceptualizing the Two-Way Random Effects Model: The Makeup of a Randomly Chosen Observation 289 6.13 Sums of Squares and Expected Mean Squares for Random Effects: The Contaminating Influence of Interaction Effects 291 6.14 You Get What You Go in with: The Importance of Model Assumptions and Model Selection 293 6.15 Mixed Model Analysis of Variance: Incorporating Fixed and Random Effects 294 6.

16 Mixed Models in Matrices 298 6.17 Multilevel Modeling as a Special Case of the Mixed Model: Incorporating Nesting and Clustering 299 6.18 Chapter Summary and Highlights 300 Review Exercises 301 7 Randomized Blocks and Repeated Measures 303 7.1 What is a Randomized Block Design? 304 7.2 Randomized Block Designs: Subjects Nested Within Blocks 304 7.3 Theory of Randomized Block Designs 306 7.4 Tukey Test for Nonadditivity 311 7.5 Assumptions for the Variance-Covariance Matrix 311 7.

6 Intraclass Correlation 313 7.7 Repeated Measures Models: A Special Case of Randomized Block Designs 314 7.8 Independent versus Paired Samples t -Test 315 7.9 The Subject Factor: Fixed or Random Effect? 316 7.10 Model for One-Way Repeated Measures Design 317 7.11 Analysis Using R: One-Way Repeated Measures: Learning as a Function of Trial 318 7.12 Analysis Using SPSS: One-Way Repeated Measures: Learning as a Function of Trial 322 7.13 SPSS: Two-Way Repeated Measures Analysis of Variance: Mixed Design: One Between Factor, One Within Factor 326 7.

14 Chapter Summary and Highlights 330 Review Exercises 331 8 Linear Regression 333 8.1 Brief History of Regression 334 8.2 Regression Analysis and Science: Experimental versus Correlational Distinctions 336 8.3 A Motivating Example: Can Offspring Height Be Predicted? 337 8.4 Theory of Regression Analysis: A Deeper Look 339 8.5 Multilevel Yearnings 342 8.6 The Least-Squares Line 342 8.7 Making Predictions Without Regression 343 8.

8 More About εi 345 8.9 Model Assumptions for Linear Regression 346 8.10 Estimation of Model Parameters in Regression 349 8.11 Null Hypotheses for Regression 351 8.12 Significance Tests and Confidence Intervals for Model Parameters 353 8.13 Other Formulations of the Regression Model 355 8.14 The Regression Model in Matrices: Allowing for More Complex Multivariable Models 356 8.15 Ordinary Least-Squares in Matrices 359 8.

16 Analysis of Variance for Regression 360 8.17 Measures of Model Fit for Regression: How Well Does the Linear Equation Fit? 363 8.18 Adjusted R 2 364 8.19 What "Explained Variance" Means: And More Importantly What It Does Not Mean 364 8.20 Values Fit by Regression 365 8.21 Least-Squares Regression in R: Using Matrix Operations 365 8.22 Linear Regression Using R 368 8.23 Regression Diagnostics: A Check on Model Assumptions 370 8.

24 Regression in SPSS: Predicting Quantitative from Verbal 379 8.25 Power Analysis for Linear Regression in R 383 8.26 Chapter Summary and Highlights 384 Review Exercises 385 9 Multiple Linear Regression 389 9.1 Theory of Partial Correlation and Multiple Regression 390 9.2 Semipartial Correlations 392 9.3 Multiple Regression 393 9.4 Some Perspective on Regression Coefficients: "Experimental Coefficients"? 394 9.5 Multiple Regression Model in Matrices 395 9.

6 Estimation of Parameters 396 9.7 Conceptualizing Multiple R 396 9.8 Interpreting Regression Coefficients: The Case of Uncorrelated Predictors 397 9.9 Anderson''s IRIS Data: Predicting Sepal Length from Petal Length and Petal Width 397 9.10 Fitting Other Functional Forms: A Brief Look at Polynomial Regression 402 9.11 Measures of Collinearity in Regr.