Applied Univariate, Bivariate, and Multivariate Statistics

A clear and efficient balance between theory and application of statistical modeling techniques in the social and behavioral sciences

Written as a general and accessible introduction, Applied Univariate, Bivariate, and Multivariate Statistics provides an overview of statistical modeling techniques used in fields in the social and behavioral sciences. Blending statistical theory and methodology, the book surveys both the technical and theoretical aspects of good data analysis.

Featuring applied resources at various levels, the book includes statistical techniques such as t-tests and correlation as well as more advanced procedures such as MANOVA, factor analysis, and structural equation modeling. 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. Applied Univariate, Bivariate, and Multivariate Statistics also features

• Demonstrations of statistical techniques using software packages such as R and SPSS¯

• Examples of hypothetical and real data with subsequent statistical analyses

• Historical and philosophical insights into many of the techniques used in modern social science

• A companion website that includes further instructional details, additional data sets, solutions to selected exercises, and multiple programming options

An ideal textbook for courses in statistics and methodology at the upper- undergraduate and graduate-levels in psychology, political science, biology, sociology, education, economics, communications, law, and survey research, Applied Univariate, Bivariate, and Multivariate Statistics is also a useful reference for practitioners and researchers in their field of application.

DANIEL J. DENIS, PhD, is Associate Professor of Quantitative Psychology at the University of Montana where he teaches courses in univariate and multivariate statistics. He has published a number of articles in peer-reviewed journals and has served as consultant to researchers and practitioners in a variety of fields.

Autorentext

DANIEL J. DENIS, PhD, is Associate Professor of Quantitative Psychology at the University of Montana where he teaches courses in univariate and multivariate statistics. He has published a number of articles in peer-reviewed journals and has served as consultant to researchers and practitioners in a variety of fields.

Inhalt
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 GPower 218 4.16 Fixed Effects One-Way Analysis of Variance in ...