Applied univariate, bivariate, and multivariate statistics. (2021)

• Record Type: Book
• Further Information: Note: Daniel J. Denis.
• Authors: Denis, Daniel J, 1974-
• Contents: 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 Scheffé 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 C
• Edition: Second edition
• Publisher Details: Hoboken : John Wiley & Sons, Inc
• Publication Date: 2021
• Extent: 1 online resource
• Subjects: 519.53; Analysis of variance; Multivariate analysis
• Languages: English
• ISBNs: 9781119583011; 9781119583028
• Related ISBNs: 9781119583042
• Notes: Note: Includes bibliographical references and index.; 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).
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