Applied Univariate, Bivariate, and Multivariate Statistics: Understanding Statistics for Social and Natural Scientists, With Applications in SPSS and R

Description

AN UPDATED GUIDE TO STATISTICAL MODELING TECHNIQUES USED IN THE SOCIAL AND BEHAVIORAL SCIENCES The revised and updated second edition of Applied Univariate, Bivariate, and Multivariate Statistics: Understanding Statistics for Social and Natural Scientists, with Applications in SPSS and R contains an accessible introduction to statistical modeling techniques commonly used in the social and behavioral sciences. The text offers a blend of statistical theory and methodology and reviews both the technical and theoretical aspects of good data analysis. Featuring applied resources at various levels, the book includes statistical techniques using software packages such as R and SPSS®. 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. The thoroughly updated edition includes new chapters on nonparametric statistics and multidimensional scaling, and expanded coverage of time series models. The second edition has been designed to be more approachable by minimizing theoretical or technical jargon and maximizing conceptual understanding with easy-to-apply software examples. This important text: Offers demonstrations of statistical techniques using software packages such as R and SPSS® Contains examples of hypothetical and real data with statistical analyses Provides historical and philosophical insights into many of the techniques used in modern social science Includes a companion website that includes further instructional details, additional data sets, solutions to selected exercises, and multiple programming options Written for students of social and applied sciences, Applied Univariate, Bivariate, and Multivariate Statistics, Second Edition offers a text to statistical modeling techniques used in social and behavioral sciences. COVER TITLE PAGE COPYRIGHT PAGE CONTENTS PREFACE ABOUT THE COMPANION WEBSITE CHAPTER 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 2 INTRODUCTORY STATISTICS 2.1 DENSITIES AND DISTRIBUTIONS 2.1.1 Plotting Normal 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, 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 2.6.1 Sample and Population Mean Vectors 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 2.20.3 Two-Sample t-Tests in R 2.21 STATISTICAL POWER 2.21.1 Visualizing Power 2.22 POWER ESTIMATION USING R AND G*POWER 2.22.1 Estimating Sample Size and Power for Independent Samples t-Test 2.23 PAIRED-SAMPLES t-TEST: STATISTICAL TEST FOR MATCHED-PAIRS (ELEMENTARY BLOCKING) DESIGNS 2.24 BLOCKING WITH SEVERAL CONDITIONS 2.25 COMPOSITE VARIABLES: LINEAR COMBINATIONS 2.26 MODELS IN MATRIX FORM 2.27 GRAPHICAL APPROACHES 2.27.1 Box-and-Whisker Plots 2.28 WHAT MAKES A p-VALUE SMALL? A CRITICAL OVERVIEW AND PRACTICAL DEMONSTRATION OF NULL HYPOTHESIS SIGNIFICANCE TESTING 2.28.1 Null Hypothesis Significance Testing (NHST): A Legacy of Criticism 2.28.2 The Make-Up of a p-Value: A Brief Recap and Summary 2.28.3 The Issue of Standardized Testing: Are Students in Your School Achieving More Than the National Average? 2.28.4 Other Test Statistics 2.28.5 The Solution 2.28.6 Statistical Distance: Cohen's d 2.28.7 What Does Cohen's d Actually Tell Us? 2.28.8 Why and Where the Significance Test Still Makes Sense 2.29 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES FURTHER DISCUSSION AND ACTIVITIES CHAPTER 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 3.1.2 Is Achievement 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 .2 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 Scheffé Test 3.14.4 Other Post-Hoc Tests 3.14.5 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 3.15.2 Computing f 3.16 FIXED EFFECTS ONE-WAY ANALYSIS OF VARIANCE IN R: MATHEMATICS ACHIEVEMENT AS A FUNCTION OF TEACHER 3.16.1 Evaluating Assumptions 3.16.2 Post-Hoc Tests on 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 4 FACTORIAL ANALYSIS OF VARIANCE 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 Cell Effects Versus Interaction Effects 4.2.5 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 4.4.4 Recap of Expected Mean Squares 4.5 INTERPRETING MAIN EFFECTS IN THE PRESENCE OF INTERACTIONS 4.6 EFFECT SIZE MEASURES 4.7 THREE-WAY, FOUR-WAY, AND HIGHER 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 Comparing Models Through AIC 4.10.2 Visualizing Main Effects and Interaction Effects Simultaneously 4.10.3 Simple Main Effects for Achievement Data: Breaking Down Interaction Effects 4.11 INTERACTION CONTRASTS 4.12 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES CHAPTER 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 H0 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 MAKE-UP 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 CHAPTER 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 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 CHAPTER 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 i 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 (OLS) 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 R2 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 7.23.3 Detecting Outliers 7.23.4 Normality of 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 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, HIERARCHICAL, FORWARD, STEPWISE 8.13.1 Simultaneous, Hierarchical, 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 9 INTERACTIONS IN MULTIPLE LINEAR REGRESSION 9.1 THE ADDITIVE REGRESSION MODEL WITH TWO PREDICTORS 9.2 WHY THE INTERACTION IS THE PRODUCT TERM xizi: 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 9.4.1 Is ANCOVA "Controlling" for Anything? 9.5 CONTINUOUS MODERATORS 9.6 SUMMING UP THE IDEA OF INTERACTIONS IN REGRESSION 9.7 DO MODERATORS REALLY "MODERATE" ANYTHING? 9.7.1 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 CHAPTER 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 10.6.1 A Generalized Linear Model for Binary Responses 10.6.2 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: LOGISTIC REGRESSION 10.9.1 The Logistic Regression Model 10.9.2 Interpreting the Logit: A Survey of Logistic Regression Output 10.10 LOGISTIC REGRESSION IN R 10.10.1 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 CHAPTER 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? 11.4.1 Control Over Type I Error Rate 11.4.2 Covariance Among Dependent Variables 11.4.3 Rao´s Paradox 11.5 MULTIVARIATE HYPOTHESES 11.6 ASSUMPTIONS OF MANOVA 11.7 HOTELLING´S T2: THE CASE OF GENERALIZING FROM UNIVARIATE TO MULTIVARIATE 11.8 THE COVARIANCE MATRIX S 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 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 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 12.2.2 Substituting the Maximizing Vector into Squared Standardized Difference 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 12.6.1 Statistical Lives 12.7 DISCRIMINANT ANALYSIS AND BEYOND 12.8 CANONICAL CORRELATION 12.9 MOTIVATING EXAMPLE FOR CANONICAL CORRELATION: HOTELLING´S 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 13 PRINCIPAL COMPONENTS ANALYSIS 13.1 HISTORY OF PRINCIPAL COMPONENTS ANALYSIS 13.2 HOTELLING 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 14 FACTOR ANALYSIS 14.1 HISTORY OF FACTOR ANALYSIS 14.2 FACTOR ANALYSIS AT A GLANCE 14.3 EXPLORATORY VERSUS 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 Sigma 14.9 AGAIN, WHY IS Sigma=..+. 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) 14.22 FACTOR ANALYSIS IN R: HOLZINGER AND SWINEFORD () 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 FURTHER DISCUSSION AND ACTIVITIES CHAPTER 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, ) 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 15.6.1 Path Model in AMOS 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 15.12 IDENTIFICATION 15.13 DISTURBANCE VARIABLES 15.14 MEASURES AND INDICATORS OF MODEL FIT 15.15 OVERALL MEASURES OF MODEL FIT 15.15.1 Root Mean Square Residual and Standardized Root Mean Square Residual 15.15.2 Root Mean Square Error of Approximation 15.16 MODEL COMPARISON MEASURES: INCREMENTAL FIT INDICES 15.17 WHICH INDICATOR OF MODEL FIT IS BEST? 15.18 STRUCTURAL EQUATION MODEL IN R 15.19 HOW ALL VARIABLES ARE LATENT: A SUGGESTION FOR RESOLVING THE MANIFEST-LATENT DISTINCTION 15.20 THE STRUCTURAL EQUATION MODEL AS A GENERAL MODEL: SOME CONCLUDING THOUGHTS ON STATISTICS AND SCIENCE 15.21 CHAPTER SUMMARY AND HIGHLIGHTS REVIEW EXERCISES FURTHER DISCUSSION AND ACTIVITIES REFERENCES INDEX EULA