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

Daniel J. Denis

This edition first published 2021

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ISBN 978-1-119-57814-7 (hardback)

ISBN 978-1-119-57817-8 (ePDF)

ISBN 978-1-119-57818-5 (ePub)

ISBN 978-1-119-57820-8 (oBook)

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To Kaiser

1 Cover

2 Title page Applied Univariate, Bivariate, and Multivariate Statistics Using Python A Beginner’s Guide to Advanced Data Analysis Daniel J. Denis

3 Copyright

4 Dedication

5 Preface

6 Chapter 1: A Brief Introduction and Overview of Applied Statistics 1.1 How Statistical Inference Works1.2 Statistics and Decision-Making1.3 Quantifying Error Rates in Decision-Making: Type I and Type II Errors1.4 Estimation of Parameters1.5 Essential Philosophical Principles for Applied Statistics1.6 Continuous vs. Discrete Variables1.6.1 Continuity Is Not Always Clear-Cut1.7 Using Abstract Systems to Describe Physical Phenomena: Understanding Numerical vs. Physical Differences1.8 Data Analysis, Data Science, Machine Learning, Big Data1.9 “Training” and “Testing” Models: What “Statistical Learning” Means in the Age of Machine Learning and Data Science1.10 Where We Are Going From Here: How to Use This BookReview Exercises

7 Chapter 2: Introduction to Python and the Field of Computational Statistics 2.1 The Importance of Specializing in Statistics and Research, Not Python: Advice for Prioritizing Your Hierarchy2.2 How to Obtain Python2.3 Python Packages2.4 Installing a New Package in Python2.5 Computing z-Scores in Python2.6 Building a Dataframe in Python: And Computing Some Statistical Functions2.7 Importing a .txt or .csv File2.8 Loading Data into Python2.9 Creating Random Data in Python2.10 Exploring Mathematics in Python2.11 Linear and Matrix Algebra in Python: Mechanics of Statistical Analyses2.11.1 Operations on Matrices2.11.2 Eigenvalues and EigenvectorsReview Exercises

8 Chapter 3: Visualization in Python: Introduction to Graphs and Plots 3.1 Aim for Simplicity and Clarity in Tables and Graphs: Complexity is for Fools!3.2 State Population Change Data3.3 What Do the Numbers Tell Us? Clues to Substantive Theory3.4 The Scatterplot3.5 Correlograms3.6 Histograms and Bar Graphs3.7 Plotting Side-by-Side Histograms3.8 Bubble Plots3.9 Pie Plots3.10 Heatmaps3.11 Line Charts3.12 Closing ThoughtsReview Exercises

9 Chapter 4: Simple Statistical Techniques for Univariate and Bivariate Analyses 4.1 Pearson Product-Moment Correlation4.2 A Pearson Correlation Does Not (Necessarily) Imply Zero Relationship4.3 Spearman’s Rho4.4 More General Comments on Correlation: Don’t Let a Correlation Impress You Too Much!4.5 Computing Correlation in Python4.6 T-Tests for Comparing Means4.7 Paired-Samples t-Test in Python4.8 Binomial Test4.9 The Chi-Squared Distribution and Goodness-of-Fit Test4.10 Contingency TablesReview Exercises

10 Chapter 5: Power, Effect Size, P-Values, and Estimating Required Sample Size Using Python 5.1 What Determines the Size of a P-Value?5.2 How P-Values Are a Function of Sample Size5.3 What is Effect Size?5.4 Understanding Population Variability in the Context of Experimental Design5.5 Where Does Power Fit into All of This?5.6 Can You Have Too Much Power? Can a Sample Be Too Large?5.7 Demonstrating Power Principles in Python: Estimating Power or Sample Size5.8 Demonstrating the Influence of Effect Size5.9 The Influence of Significance Levels on Statistical Power5.10 What About Power and Hypothesis Testing in the Age of “Big Data”?5.11 Concluding Comments on Power, Effect Size, and Significance TestingReview Exercises

11 Chapter 6: Analysis of Variance 6.1 T-Tests for Means as a “Special Case” of ANOVA6.2 Why Not Do Several t-Tests?6.3 Understanding ANOVA Through an Example6.4 Evaluating Assumptions in ANOVA6.5 ANOVA in Python6.6 Effect Size for Teacher6.7 Post-Hoc Tests Following the ANOVA F-Test6.8 A Myriad of Post-Hoc Tests6.9 Factorial ANOVA6.10 Statistical Interactions6.11 Interactions in the Sample Are a Virtual Guarantee: Interactions in the Population Are Not6.12 Modeling the Interaction Term6.13 Plotting Residuals6.14 Randomized Block Designs and Repeated Measures6.15 Nonparametric Alternatives6.15.1 Revisiting What “Satisfying Assumptions” Means: A Brief Discussion and Suggestion of How to Approach the Decision Regarding Nonparametrics6.15.2 Your Experience in the Area Counts6.15.3 What If Assumptions Are Truly Violated?6.15.4 Mann-Whitney U Test6.15.5 Kruskal-Wallis Test as a Nonparametric Alternative to ANOVAReview Exercises