Applied Univariate, Bivariate, and Multivariate Statistics Using Python - Denis, Daniel J

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Preface xii

1 A Brief Introduction and Overview of Applied Statistics 1

1.1 How Statistical Inference Works 4

1.2 Statistics and Decision-Making 7

1.3 Quantifying Error Rates in Decision-Making: Type I and Type II Errors 8

1.4 Estimation of Parameters 9

1.5 Essential Philosophical Principles for Applied Statistics 11

1.6 Continuous vs. Discrete Variables 13

1.6.1 Continuity Is Not Always Clear-Cut 15

1.7 Using Abstract Systems to Describe Physical Phenomena:

Understanding Numerical vs. Physical Differences 16

1.8 Data Analysis, Data Science, Machine Learning, Big Data 18

1.9 Training and Testing Models: What Statistical Learning Means in the Age of Machine Learning and Data Science 20

1.10 Where We Are Going From Here: How to Use This Book 22

Review Exercises 23

2 Introduction to Python and the Field of Computational Statistics 25

2.1 The Importance of Specializing in Statistics and Research, Not Python: Advice for Prioritizing Your Hierarchy 26

2.2 How to Obtain Python 28

2.3 Python Packages 29

2.4 Installing a New Package in Python 31

2.5 Computing z-Scores in Python 32

2.6 Building a Dataframe in Python: And Computing Some Statistical Functions 35

2.7 Importing a .txt or .csv File 38

2.8 Loading Data into Python 39

2.9 Creating Random Data in Python 40

2.10 Exploring Mathematics in Python 40

2.11 Linear and Matrix Algebra in Python: Mechanics of Statistical Analyses 41

2.11.1 Operations on Matrices 44

2.11.2 Eigenvalues and Eigenvectors 47

Review Exercises 48

3 Visualization in Python: Introduction to Graphs and Plots 50

3.1 Aim for Simplicity and Clarity in Tables and Graphs: Complexity is for Fools! 52

3.2 State Population Change Data 54

3.3 What Do the Numbers Tell Us? Clues to Substantive Theory 56

3.4 The Scatterplot 58

3.5 Correlograms 59

3.6 Histograms and Bar Graphs 61

3.7 Plotting Side-by-Side Histograms 62

3.8 Bubble Plots 63

3.9 Pie Plots 65

3.10 Heatmaps 66

3.11 Line Charts 68

3.12 Closing Thoughts 69

Review Exercises 70

4 Simple Statistical Techniques for Univariate and Bivariate Analyses 72

4.1 Pearson Product-Moment Correlation 73

4.2 A Pearson Correlation Does Not (Necessarily) Imply Zero Relationship 75

4.3 Spearman's Rho 76

4.4 More General Comments on Correlation: Don't Let a Correlation Impress You Too Much! 79

4.5 Computing Correlation in Python 80

4.6 T-Tests for Comparing Means 84

4.7 Paired-Samples t-Test in Python 88

4.8 Binomial Test 90

4.9 The Chi-Squared Distribution and Goodness-of-Fit Test 91

4.10 Contingency Tables 93

Review Exercises 94

5 Power, Effect Size, P-Values, and Estimating Required Sample Size Using Python 96

5.1 What Determines the Size of a P-Value? 96

5.2 How P-Values Are a Function of Sample Size 99

5.3 What is Effect Size? 100

5.4 Understanding Population Variability in the Context of Experimental Design 102

5.5 Where Does Power Fit into All of This? 103

5.6 Can You Have Too Much Power? Can a Sample Be Too Large? 104

5.7 Demonstrating Power Principles in Python: Estimating Power or Sample Size 106

5.8 Demonstrating the Influence of Effect Size 108

5.9 The Influence of Significance Levels on Statistical Power 108

5.10 What About Power and Hypothesis Testing in the Age of Big Data? 110

5.11 Concluding Comments on Power, Effect Size...