Applied Univariate, Bivariate, and Multivariate Statistics Using Python: A Beginner's Guide to Advanced Data Analysis

Applied Univariate, Bivariate, and Multivariate Statistics Using Python
Contents
Preface
1. A Brief Introduction and Overview of Applied Statistics
	1.1 How Statistical Inference Works
	1.2 Statistics and Decision-Making
	1.3 Quantifying Error Rates in Decision-Making: Type I and Type II Errors
	1.4 Estimation of Parameters
	1.5 Essential Philosophical Principles for Applied Statistics
	1.6 Continuous vs. Discrete Variables
		1.6.1 Continuity Is Not Always Clear-Cut
	1.7 Using Abstract Systems to Describe Physical Phenomena:
Understanding Numerical vs. Physical Differences
	1.8 Data Analysis, Data Science, Machine Learning, Big Data
	1.9 “Training” and “Testing” Models: What “Statistical Learning”
Means in the Age of Machine Learning and Data Science
	1.10 Where We Are Going From Here: How to Use This Book
	Review Exercises
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 Hierarchy
	2.2 How to Obtain Python
	2.3 Python Packages
	2.4 Installing a New Package in Python
	2.5 Computing z-Scores in Python
	2.6 Building a Dataframe in Python: And Computing Some Statistical Functions
	2.7 Importing a .txt or .csv File
	2.8 Loading Data into Python
	2.9 Creating Random Data in Python
	2.10 Exploring Mathematics in Python
	2.11 Linear and Matrix Algebra in Python: Mechanics of Statistical Analyses
		2.11.1 Operations on Matrices
		2.11.2 Eigenvalues and Eigenvectors
	Review Exercises
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 Data
	3.3 What Do the Numbers Tell Us? Clues to Substantive Theory
	3.4 The Scatterplot
	3.5 Correlograms
	3.6 Histograms and Bar Graphs
	3.7 Plotting Side-by-Side Histograms
	3.8 Bubble Plots
	3.9 Pie Plots
	3.10 Heatmaps
	3.11 Line Charts
	3.12 Closing Thoughts
	Review Exercises
4. Simple Statistical Techniques for Univariate and Bivariate Analyses
	4.1 Pearson Product-Moment Correlation
	4.2 A Pearson Correlation Does Not (Necessarily) Imply Zero Relationship
	4.3 Spearman’s Rho
	4.4 More General Comments on Correlation:
Don’t Let a Correlation Impress You Too Much!
	4.5 Computing Correlation in Python
	4.6 T-Tests for Comparing Means
	4.7 Paired-Samples t-Test in Python
	4.8 Binomial Test
	4.9 The Chi-Squared Distribution and Goodness-of-Fit Test
	4.10 Contingency Tables
	Review Exercises
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 Size
	5.3 What is Effect Size?
	5.4 Understanding Population Variability in the Context of Experimental Design
	5.5 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 Size
	5.8 Demonstrating the Influence of Effect Size
	5.9 The Influence of Significance Levels on Statistical Power
	5.10 What About Power and Hypothesis Testing in the Age of “Big Data”?
	5.11 Concluding Comments on Power, Effect Size, and Significance Testing
	Review Exercises
6. Analysis of Variance
	6.1 T-Tests for Means as a “Special Case” of ANOVA
	6.2 Why Not Do Several t-Tests?
	6.3 Understanding ANOVA Through an Example
	6.4 Evaluating Assumptions in ANOVA
	6.5 ANOVA in Python
	6.6 Effect Size for Teacher
	6.7 Post-Hoc Tests Following the ANOVA F-Test
	6.8 A Myriad of Post-Hoc Tests
	6.9 Factorial ANOVA
	6.10 Statistical Interactions
	6.11 Interactions in the Sample Are a Virtual Guarantee: Interactions in the Population Are Not
	6.12 Modeling the Interaction Term
	6.13 Plotting Residuals
	6.14 Randomized Block Designs and Repeated Measures
	6.15 Nonparametric Alternatives
		6.15.1 Revisiting What “Satisfying Assumptions” Means:
A Brief Discussion and Suggestion of How to Approach the Decision Regarding Nonparametrics
		6.15.2 Your Experience in the Area Counts
		6.15.3 What If Assumptions Are Truly Violated?
		6.15.4 Mann-Whitney U Test
		6.15.5 Kruskal-Wallis Test as a Nonparametric Alternative to ANOVA
	Review Exercises
7. Simple and Multiple Linear Regression
	7.1 Why Use Regression?
	7.2 The Least-Squares Principle
	7.3 Regression as a “New” Least-Squares Line
	7.4 The Population Least-Squares Regression Line
	7.5 How to Estimate Parameters in Regression
	7.6 How to Assess Goodness of Fit?
	7.7 R2 – Coefficient of Determination
	7.8 Adjusted R2
	7.9 Regression in Python
	7.10 Multiple Linear Regression
	7.11 Defining the Multiple Regression Model
	7.12 Model Specification Error
	7.13 Multiple Regression in Python
	7.14 Model-Building Strategies: Forward, Backward, Stepwise
	7.15 Computer-Intensive “Algorithmic” Approaches
	7.16 Which Approach Should You Adopt?
	7.17 Concluding Remarks and Further Directions:
Polynomial Regression
	Review Exercises
8. Logistic Regression and the Generalized Linear Model
	8.1 How Are Variables Best Measured? Are There Ideal Scales on Which a Construct Should Be Targeted?
	8.2 The Generalized Linear Model
	8.3 Logistic Regression for Binary Responses: A Special Subclass of the Generalized Linear Model
	8.4 Logistic Regression in Python
	8.5 Multiple Logistic Regression
		8.5.1 A Model with Only Lag1
	8.6 Further Directions
	Review Exercises
9. Multivariate Analysis of Variance (MANOVA) and Discriminant Analysis
	9.1 Why Technically Most Univariate Models are Actually Multivariate
	9.2 Should I Be Running a Multivariate Model?
	9.3 The Discriminant Function
	9.4 Multivariate Tests of Significance: Why They Are
Different from the F-Ratio
		9.4.1 Wilks’ Lambda
		9.4.2 Pillai’s Trace
		9.4.3 Roy’s Largest Root
		9.4.4 Lawley-Hotelling’s Trace
	9.5 Which Multivariate Test to Use?
	9.6 Performing MANOVA in Python
	9.7 Effect Size for MANOVA
	9.8 Linear Discriminant Function Analysis
	9.9 How Many Discriminant Functions Does One Require?
	9.10 Discriminant Analysis in Python: Binary Response
	9.11 Another Example of Discriminant Analysis: Polytomous Classification
	9.12 Bird’s Eye View of MANOVA, ANOVA, Discriminant Analysis, and Regression: A Partial Conceptual Unification
	9.13 Models “Subsumed” Under the Canonical Correlation Framework
	Review Exercises
10. Principal Components Analysis
	10.1 What Is Principal Components Analysis?
	10.2 Principal Components as Eigen Decomposition
	10.3 PCA on Correlation Matrix
	10.4 Why Icebergs Are Not Good Analogies for PCA
	10.5 PCA in Python
	10.6 Loadings in PCA: Making Substantive Sense Out of an Abstract Mathematical Entity
	10.7 Naming Components Using Loadings: A Few Issues
	10.8 Principal Components Analysis on USA Arrests Data
	10.9 Plotting the Components
	Review Exercises
11. Exploratory Factor Analysis
	11.1 The Common Factor Analysis Model
	11.2 Factor Analysis as a Reproduction of the Covariance Matrix
	11.3 Observed vs. Latent Variables: Philosophical Considerations
	11.4 So, Why is Factor Analysis Controversial? The Philosophical Pitfalls of Factor Analysis
	11.5 Exploratory Factor Analysis in Python
	11.6 Exploratory Factor Analysis on USA Arrests Data
	Review Exercises
12. Cluster Analysis
	12.1 Cluster Analysis vs. ANOVA vs. Discriminant Analysis
	12.2 How Cluster Analysis Defines “Proximity”
		12.2.1 Euclidean Distance
	12.3 K-Means Clustering Algorithm
	12.4 To Standardize or Not?
	12.5 Cluster Analysis in Python
	12.6 Hierarchical Clustering
	12.7 Hierarchical Clustering in Python
	Review Exercises
References
Index
EULA