Applied univariate, bivariate and multivariate statistics. (2015)

• Record Type: Book
• Further Information: Note: Daniel J. Denis.
• Authors: Denis, Daniel J, 1974-
• Contents: 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; ; 5.9.1 Varieties of Nesting: Nesting of Levels versus Subjects 257; ; 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; <br />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? 3
• Edition: 1st
• Publisher Details: Hoboken, New Jersey : John Wiley & Sons
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 519.53; Statistics; Social sciences -- Statistical methods
• Languages: English
• ISBNs: 9781118632239
• Related ISBNs: 9781118632314
• Notes: Note: Description based on CIP data; resource not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.