图书简介

Preface 1 Preliminary Considerations 1.1 The Philosophical Bases of Knowledge: Rationalistic versus Empiricist Pursuits 1.2 What is a \"Model\"? 1.3 Social Sciences versus Hard Sciences 1.4 Is Complexity a Good Depiction of Reality? Are Multivariate Methods Useful? 1.5 Causality 1.6 The Nature of Mathematics: Mathematics as a Representation of Concepts 1.7 As a Scientist, How Much Mathematics Do You Need to Know? 1.8 Statistics and Relativity 1.9 Experimental versus Statistical Control 1.10 Statistical versus Physical Effects 1.11 Understanding What \"Applied Statistics\" Means Review Exercises 2 Introductory Statistics 2.1 Densities and Distributions 2.1.2 Binomial Distributions 2.1.3 Normal Approximation 2.1.4 Joint Probability Densities: Bivariate and Multivariate Distributions 2.2 Chi-Square Distributions and Goodness-of-Fit Test 2.2.1 Power for Chi-Square Test of Independence 2.3 Sensitivity and Specificity 2.4 Scales of Measurement: Nominal, Ordinal, and Interval, Ratio 2.4.1 Nominal Scale 2.4.2 Ordinal Scale 2.4.3 Interval Scale 2.4.4 Ratio Scale 2.5 Mathematical Variables versus Random Variables 2.6 Moments and Expectations 2.7 Estimation and Estimators 2.8 Variance 2.9 Degrees of Freedom 2.10 Skewness and Kurtosis 2.11 Sampling Distributions 2.11.1 Sampling Distribution of the Mean 2.12 Central Limit Theorem 2.13 Confidence Intervals 2.14 Maximum Likelihood 2.15 Akaike’s Information Criteria 2.16 Covariance and Correlation 2.17 Psychometric Validity, Reliability: A Common Use of Correlation Coefficients 2.18 Covariance and Correlation Matrices 2.19 Other Correlation Coefficients 2.20 Student’s t Distribution 2.20.1 t-Tests for One Sample 2.20.2 t-Tests for Two Samples 2.21 Statistical Power 2.21.1 Power Estimation Using R and G Power 2.21.2 Estimating Sample Size and Power for Independent Samples t-Test 2.22 Paired Samples t-Test: Statistical Test for Matched Pairs (Elementary Blocking) Designs 2.23 Blocking with Several Conditions 2.24 Composite Variables: Linear Combinations 2.25 Models in Matrix Form 2.26 Graphical Approaches 2.26.1 Box-and-Whisker Plots 2.27 What Makes a p-Value Small? A Critical Overview and Simple Demonstration of Null Hypothesis Significance Testing 2.27.1 Null Hypothesis Significance Testing: A History of Criticism 2.27.2 The Makeup of a p-Value: A Brief Recap and Summary 2.27.3 The Issue of Standardized Testing: Are Students in Your School Achieving More Than the National Average? 2.27.4 Other Test Statistics 2.27.5 The Solution 2.27.6 Statistical Distance: Cohen’s d 2.27.7 Why and Where the Significance Test Still Makes Sense 2.28 Chapter Summary and Highlights Review Exercises 3 Analysis of Variance: Fixed Effects Models 3.1 What is Analysis of Variance? Fixed versus Random Effects 3.1.1 Small Sample Example: Achievement as a Function of Teacher 3.2 How Analysis of Variance Works: A Big Picture Overview 3.2.1 Is the Observed Difference Likely? ANOVA as a Comparison (Ratio) of Variances 3.3 Logic and Theory of ANOVA: A Deeper Look 3.3.1 Independent Samples t-tests versus Analysis of Variance 3.3.2 The ANOVA Model: Explaining Variation 3.3.3 Breaking Down a Deviation 3.3.4 Naming the Deviations 3.3.5 The Sums of Squares of ANOVA 3.4 From Sums of Squares to Unbiased Variance Estimators: Dividing by Degrees of Freedom 3.5 Expected Mean Squares for One-Way Fixed Effects Model: Deriving the F-Ratio 3.6 The Null Hypothesis in ANOVA 3.7 Fixed Effects ANOVA: Model Assumptions 3.8 A Word on Experimental Design and Randomization 3.9 A Preview of the Concept of Nesting 3.10 Balanced versus Unbalanced Data in ANOVA Models 3.11 Measures of Association and Effect Size in ANOVA: Measures of Variance Explained 3.11.1 Eta-Squared 3.11.2 Omega-Squared 3.12 The F-Test and the Independent Samples t-Test 3.13 Contrasts and Post-Hocs 3.13.1 Independence of Contrasts 3.13.2 Independent Samples t-Test as a Linear Contrast 3.14 Post-Hoc Tests 3.14.1 Newman-Keuls and Tukey HSD 3.14.2 Tukey HSD 3.14.3 Scheffe Test 3.14.4 Contrast versus Post-Hoc? Which Should I Be Doing? 3.15 Sample Size and Power for ANOVA: Estimation with R and G Power 3.15.1 Power for ANOVA in R and G Power 3.16 Fixed Effects One-Way Analysis of Variance in R: Mathematics Achievement as a Function of Teacher 3.17 Analysis of Variance Via R’s lm 3.18 Kruskal-Wallis Test in R and the Motivation Behind Nonparametric Tests 3.19 ANOVA in SPSS: Achievement as a Function of Teacher 3.20 Chapter Summary and Highlights Review Exercises 4 Factorial Analysis of Variance: Modeling Interactions 4.1 What is Factorial Analysis of Variance? 4.2 Theory of Factorial ANOVA: A Deeper Look 4.2.1 Deriving the Model for Two-Way Factorial ANOVA 4.2.2 Cell Effects 4.2.3 Interaction Effects 4.2.4 A Model for the Two-Way Fixed Effects ANOVA 4.3 Comparing One-Way ANOVA to Two-Way ANOVA: Cell Effects in Factorial ANOVA versus Sample Effects in One-Way ANOVA 4.4 Partitioning the Sums of Squares for Factorial ANOVA: The Case of Two Factors 4.4.1 SS Total: A Measure of Total Variation 4.4.2 Model Assumptions: Two-Way Factorial Model 4.4.3 Expected Mean Squares for Factorial Design 4.5 Interpreting Main Effects in the Presence of Interactions 4.6 Effect Size Measures 4.7 Three-Way, Four-Way, and Higher-Order Models 4.8 Simple Main Effects 4.9 Nested Designs 4.9.1 Varieties of Nesting: Nesting of Levels versus Subjects 4.10 Achievement as a Function of Teacher and Textbook: Example of Factorial ANOVA in R 4.10.1 Simple Main Effects for Achievement Data: Breaking Down Interaction Effects 4.11 Interaction Contrasts 4.12 Chapter Summary and Highlights Review Exercises 5 Introduction to Random Effects and Mixed Models 5.1 What is Random Effects Analysis of Variance? 5.2 Theory of Random Effects Models 5.3 Estimation in Random Effects Models 5.3.1 Transitioning from Fixed Effects to Random Effects 5.3.2 Expected Mean Squares for MS Between and MS Within 5.4 Defining Null Hypotheses in Random Effects Models 5.4.1 F-Ratio for Testing 5.5 Comparing Null Hypotheses in Fixed versus Random Effects Models: The Importance of Assumptions 5.6 Estimating Variance Components in Random Effects Models: ANOVA, ML, REML Estimators 5.6.1 ANOVA Estimators of Variance Components 5.6.2 Maximum Likelihood and Restricted Maximum Likelihood 5.7 Is Achievement a Function of Teacher? One-Way Random Effects Model in R 5.7.1 Proportion of Variance Accounted for by Teacher 5.8 R Analysis Using REML 5.9 Analysis in SPSS: Obtaining Variance Components 5.10 Factorial Random Effects: A Two-Way Model 5.11 Fixed Effects versus Random Effects: A Way of Conceptualizing Their Differences 5.12 Conceptualizing the Two-Way Random Effects Model: The Makeup of a Randomly Chosen Observation 5.13 Sums of Squares and Expected Mean Squares for Random Effects: The Contaminating Influence of Interaction Effects 5.13.1 Testing Null Hypotheses 5.14 You Get What You Go in with: The Importance of Model Assumptions and Model Selection 5.15 Mixed Model Analysis of Variance: Incorporating Fixed and Random Effects 5.15.1 Mixed Model in R 5.16 Mixed Models in Matrices 5.17 Multilevel Modeling as a Special Case of the Mixed Model: Incorporating Nesting and Clustering 5.18 Chapter Summary and Highlights Review Exercises 6 Randomized Blocks and Repeated Measures 6.1 What Is a Randomized Block Design? 6.2 Randomized Block Designs: Subjects Nested Within Blocks 6.3 Theory of Randomized Block Designs 6.3.1 Nonadditive Randomized Block Design 6.3.2 Additive Randomized Block Design 6.4 Tukey Test for Nonadditivity 6.5 Assumptions for the Variance-Covariance Matrix 6.6 Intraclass Correlation 6.7 Repeated Measures Models: A Special Case of Randomized Block Designs 6.8 Independent versus Paired Samples t-Test 6.9 The Subject Factor: Fixed or Random Effect? 6.10 Model for One-Way Repeated Measures Design 6.10.1 Expected Mean Squares for Repeated Measures Models 6.11 Analysis Using R: One-Way Repeated Measures: Learning as a Function of Trial 6.12 Analysis Using SPSS: One-Way Repeated Measures: Learning as a Function of Trial 6.12.1 Which Results Should Be Interpreted? 6.13 SPSS: Two-Way Repeated Measures Analysis of Variance: Mixed Design: One Between Factor, One Within Factor 6.13.1 Another Look at the Between-Subjects Factor 6.14 Chapter Summary and Highlights Review Exercises 7 Linear Regression 7.1 Brief History of Regression 7.2 Regression Analysis and Science: Experimental versus Correlational Distinctions 7.3 A Motivating Example: Can Offspring Height Be Predicted? 7.4 Theory of Regression Analysis: A Deeper Look 7.5 Multilevel Yearnings 7.6 The Least-Squares Line 7.7 Making Predictions Without Regression 7.8 More About 7.9 Model Assumptions for Linear Regression 7.9.1 Model Specification 7.9.2 Measurement Error 7.10 Estimation of Model Parameters in Regression 7.10.1 Ordinary Least-Squares 7.11 Null Hypotheses for Regression 7.12 Significance Tests and Confidence Intervals for Model Parameters 7.13 Other Formulations of the Regression Model 7.14 The Regression Model in Matrices: Allowing for More Complex Multivariable Models 7.15 Ordinary Least-Squares in Matrices 7.16 Analysis of Variance for Regression 7.17 Measures of Model Fit for Regression: How Well Does the Linear Equation Fit? 7.18 Adjusted 7.19 What \"Explained Variance\" Means: And More Importantly, What It Does Not Mean 7.20 Values Fit by Regression 7.21 Least-Squares Regression in R: Using Matrix Operations 7.22 Linear Regression Using R 7.23 Regression Diagnostics: A Check on Model Assumptions 7.23.1 Understanding How Outliers Influence a Regression Model 7.23.2 Examining Outliers and Residuals 7.24 Regression in SPSS: Predicting Quantitative from Verbal 7.25 Power Analysis for Linear Regression in R 7.26 Chapter Summary and Highlights Review Exercises 8 Multiple Linear Regression 8.1 Theory of Partial Correlation 8.2 Semipartial Correlations 8.3 Multiple Regression 8.4 Some Perspective on Regression Coefficients: \"Experimental Coefficients\"? 8.5 Multiple Regression Model in Matrices 8.6 Estimation of Parameters 8.7 Conceptualizing Multiple R 8.8 Interpreting Regression Coefficients: Correlated Versus Uncorrelated Predictors 8.9 Anderson’s Iris Data: Predicting Sepal Length from Petal Length and Petal Width 8.10 Fitting Other Functional Forms: A Brief Look at Polynomial Regression 8.11 Measures of Collinearity in Regression: Variance Inflation Factor and Tolerance 8.12 R-Squared as a Function of Partial and Semipartial Correlations: The Stepping Stones to Forward and Stepwise Regression 8.13 Model-Building Strategies: Simultaneous, Hierarchichal, Forward, and Stepwise 8.13.1 Simultaneous, Hierarchical, and Forward 8.13.2 Stepwise Regression 8.13.3 Selection Procedures in R 8.13.4 Which Regression Procedure Should Be Used? Concluding Comments and Recommendations Regarding Model-Building 8.14 Power Analysis for Multiple Regression 8.15 Introduction to Statistical Mediation: Concepts and Controversy 8.15.1 Statistical versus True Mediation: Some Philosophical Pitfalls in the Interpretation of Mediation Analysis 8.16 Brief Survey of Ridge and Lasso Regression: Penalized Regression Models and the Concept of Shrinkage 8.17 Chapter Summary and Highlights Review Exercises 9 Interactions in Multiple Linear Regression: Dichotomous, Polytomous, and Continuous Moderators 9.1 The Additive Regression Model with Two Predictors 9.2 Why the Interaction is the Product Term : Drawing an Analogy to Factorial ANOVA 9.3 A Motivating Example of Interaction in Regression: Crossing a Continuous Predictor with a Dichotomous Predictor 9.4 Analysis of Covariance 9.5 Continuous Moderators 9.6 Summing Up the Idea of Interactions in Regression 9.7 Do Moderators Really \"Moderate\" Anything? Some Philosophical Considerations 9.8 Interpreting Model Coefficients in the Context of Moderators 9.9 Mean-Centering Predictors: Improving the Interpretability of Simple Slopes 9.10 Multilevel Regression: Another Special Case of the Mixed Model 9.11 Chapter Summary and Highlights Review Exercises 10 Logistic Regression and the Generalized Linear Model 10.1 Nonlinear Models 10.2 Generalized Linear Models 10.2.1 The Logic of the Generalized Linear Model: How the Link Function Transforms Nonlinear Response Variables 10.3 Canonical Links 10.3.1 Canonical Link for Gaussian Variable 10.4 Distributions and Generalized Linear Models 10.4.1 Logistic Models 10.4.2 Poisson Models 10.5 Dispersion Parameters and Deviance 10.6 Logistic Regression: A Generalized Linear Model for Binary Responses 10.6.1 Model for Single Predictor 10.7 Exponential and Logarithmic Functions 10.7.1 Logarithms 10.7.2 The Natural Logarithm 10.8 Odds and the Logit 10.9 Putting It All Together: The Logistic Regression Model 10.9.1 Interpreting the Logit: A Survey of Logistic Regression Output 10.10 Logistic Regression in R: Challenger O-ring Data 10.11 Challenger Analysis in SPSS 10.11.1 Predictions of New Cases 10.12 Sample Size, Effect Size, and Power 10.13 Further Directions 10.14 Chapter Summary and Highlights Review Exercises 11 Multivariate Analysis of Variance 11.1 A Motivating Example: Quantitative and Verbal Ability as a Variate 11.2 Constructing the Composite 11.3 Theory of MANOVA 11.4 Is the Linear Combination Meaningful? 11.5 Multivariate Hypotheses 11.6 Assumptions of MANOVA 11.7 Hotelling’s : The Case of Generalizing from Univariate to Multivariate 11.8 The Covariance Matrix 11.9 From Sums of Squares and Cross-Products to Variances and Covariances 11.10 Hypothesis and Error Matrices of MANOVA 11.11 Multivariate Test Statistics 11.11.1 Pillai’s Trace 11.11.2 Lawley-Hotelling’s Trace 11.12 Equality of Variance-Covariance Matrices 11.13 Multivariate Contrasts 11.14 MANOVA in R and SPSS 11.14.1 Univariate Analyses 11.15 MANOVA of Fisher’s Iris Data 11.16 Power Analysis and Sample Size for MANOVA 11.17 Multivariate Analysis of Covariance and Multivariate Models: A Bird’s Eye View of Linear Models 11.18 Chapter Summary and Highlights Review Exercises 12 Discriminant Analysis 12.1 What is Discriminant Analysis? The Big Picture on the Iris Data 12.2 Theory of Discriminant Analysis 12.2.1 Discriminant Analysis for Two Populations 12.3 LDA in R and SPSS 12.4 Discriminant Analysis for Several Populations 12.4.1 Theory for Several Populations 12.5 Discriminating Species of Iris: Discriminant Analyses for Three Populations 12.6 A Note on Classification and Error Rates 12.7 Discriminant Analysis and Beyond 12.8 Canonical Correlation 12.9 Motivating Example for Canonical Correlation: Hotelling’s 1936 Data 12.10 Canonical Correlation as a General Linear Model 12.11 Theory of Canonical Correlation 12.12 Canonical Correlation of Hotelling’s Data 12.13 Canonical Correlation on the Iris Data: Extracting Canonical Correlation from Regression, MANOVA, LDA 12.14 Chapter Summary and Highlights Review Exercises 13 Principal Components Analysis 13.1 History of Principal Components Analysis 13.2 Hotelling 1933 13.3 Theory of Principal Components Analysis 13.3.1 The Theorem of Principal Components Analysis 13.4 Eigenvalues as Variance 13.5 Principal Components as Linear Combinations 13.6 Extracting the First Component 13.6.1 Sample Variance of a Linear Combination 13.7 Extracting the Second Component 13.8 Extracting Third and Remaining Components 13.9 The Eigenvalue as the Variance of a Linear Combination Relative to Its Length 13.10 Demonstrating Principal Components Analysis: Pearson’s 1901 Illustration 13.11 Scree Plots 13.12 Principal Components versus Least-Squares Regression Lines 13.13 Covariance versus Correlation Matrices: Principal Components and Scaling 13.14 Principal Components Analysis Using SPSS 13.15 Chapter Summary and Highlights Review Exercises 14 Factor Analysis 14.1 History of Factor Analysis 14.2 Factor Analysis: At a Glance 14.3 Exploratory vs. Confirmatory Factor Analysis 14.4 Theory of Factor Analysis: The Exploratory Factor-Analytic Model 14.5 The Common Factor-Analytic Model 14.6 Assumptions of the Factor-Analytic Model 14.7 Why Model Assumptions are Important 14.8 The Factor Model as an Implication for the Covariance Matrix 14.9 Again, Why is so Important a Result? 14.10 The Major Critique Against Factor Analysis: Indeterminacy and the Nonuniqueness of Solutions 14.11 Has Your Factor Analysis Been Successful? 14.12 Estimation of Parameters in Exploratory Factor Analysis 14.13 Principal Factor 14.14 Maximum Likelihood 14.15 The Concepts (and Criticisms) of Factor Rotation 14.16 Varimax and Quartimax Rotation 14.17 Should Factors Be Rotated? Is That Not \"Cheating?\" 14.18 Sample Size for Factor Analysis 14.19 Principal Components Analysis versus Factor Analysis: Two Key Differences 14.19.1 Hypothesized Model and Underlying Theoretical Assumptions 14.19.2 Solutions Are Not Invariant in Factor Analysis 14.20 Principal Factor in SPSS: Principal Axis Factoring 14.21 Bartlett Test of Sphericity and Kaiser-Meyer-Olkin Measure of Sampling Adequacy (MSA) 14.23 Factor Analysis in R: Holzinger and Swineford (1939) 14.23 Cluster Analysis 14.24 What Is Cluster Analysis? The Big Picture 14.25 Measuring Proximity 14.26 Hierarchical Clustering Approaches 14.27 Nonhierarchical Clustering Approaches 14.28 K-Means Cluster Analysis in R 14.29 Guidelines and Warnings About Cluster Analysis 14.30 A Brief Look at Multidimensional Scaling 14.31 Chapter Summary and Highlights Review Exercises 15 Path Analysis and Structural Equation Modeling 15.1 Path Analysis: A Motivating Example-Predicting IQ Across Generations 15.2 Path Analysis and \"Causal Modeling\" 15.3 Early Post-Wright Path Analysis: Predicting Child’s IQ (Burks, 1928) 15.4 Decomposing Path Coefficients 15.5 Path Coefficients and Wright’s Contribution 15.6 Path Analysis in R: A Quick Overview-Modeling Galton’s Data 15.7 Confirmatory Factor Analysis: The Measurement Model 15.7.1. Confirmatory Factor Analysis as a Means of Evaluating Construct Validity and Assessing Psychometric Qualities 15.8 Structural Equation Models 15.9 Direct, Indirect, and Total Effects 15.10 Theory of Statistical Modeling: A Deeper Look into Covariance Structures and General Modeling 15.11 The Discrepancy Function and Chi-Square 15.13 Identification 15.14 Disturbance Variables 15.15 Measures and Indicators of Model Fit 15.16 Overall Measures of Model Fit 15.16.1 Root Mean Square Residual and Standardized Root Mean Square Residual 15.16.2 Root Mean Square Error of Approximation 15.17 Model Comparison Measures: Incremental Fit Indices 15.18 Which Indicator of Model Fit Is Best? 15.19 Structural Equation Model in R 15.20 How All Variables Are Latent: A Suggestion for Resolving the Manifest-Latent Distinction 15.21 The Structural Equation Model as a General Model: Some Concluding Thoughts on Statistics and Science 15.22 Chapter Summary and Highlights Review Exercises References Index

Trade Policy 买家须知