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

ISBN-13: 9781119578147 / Angielski / Twarda / 2021 / 304 str.

Daniel J. Denis

Spis treści

Preface xii1 A Brief Introduction and Overview of Applied Statistics 11.1 How Statistical Inference Works 41.2 Statistics and Decision-Making 71.3 Quantifying Error Rates in Decision-Making: Type I and Type II Errors 81.4 Estimation of Parameters 91.5 Essential Philosophical Principles for Applied Statistics 111.6 Continuous vs. Discrete Variables 131.6.1 Continuity Is Not Always Clear-Cut 151.7 Using Abstract Systems to Describe Physical Phenomena:Understanding Numerical vs. Physical Differences 161.8 Data Analysis, Data Science, Machine Learning, Big Data 181.9 "Training" and "Testing" Models: What "Statistical Learning" Means in the Age of Machine Learning and Data Science 201.10 Where We Are Going From Here: How to Use This Book 22Review Exercises 232 Introduction to Python and the Field of Computational Statistics 252.1 The Importance of Specializing in Statistics and Research, Not Python: Advice for Prioritizing Your Hierarchy 262.2 How to Obtain Python 282.3 Python Packages 292.4 Installing a New Package in Python 312.5 Computing z-Scores in Python 322.6 Building a Dataframe in Python: And Computing Some Statistical Functions 352.7 Importing a .txt or .csv File 382.8 Loading Data into Python 392.9 Creating Random Data in Python 402.10 Exploring Mathematics in Python 402.11 Linear and Matrix Algebra in Python: Mechanics of Statistical Analyses 412.11.1 Operations on Matrices 442.11.2 Eigenvalues and Eigenvectors 47Review Exercises 483 Visualization in Python: Introduction to Graphs and Plots 503.1 Aim for Simplicity and Clarity in Tables and Graphs: Complexity is for Fools! 523.2 State Population Change Data 543.3 What Do the Numbers Tell Us? Clues to Substantive Theory 563.4 The Scatterplot 583.5 Correlograms 593.6 Histograms and Bar Graphs 613.7 Plotting Side-by-Side Histograms 623.8 Bubble Plots 633.9 Pie Plots 653.10 Heatmaps 663.11 Line Charts 683.12 Closing Thoughts 69Review Exercises 704 Simple Statistical Techniques for Univariate and Bivariate Analyses 724.1 Pearson Product-Moment Correlation 734.2 A Pearson Correlation Does Not (Necessarily) Imply Zero Relationship 754.3 Spearman's Rho 764.4 More General Comments on Correlation: Don't Let a Correlation Impress You Too Much! 794.5 Computing Correlation in Python 804.6 T-Tests for Comparing Means 844.7 Paired-Samples t-Test in Python 884.8 Binomial Test 904.9 The Chi-Squared Distribution and Goodness-of-Fit Test 914.10 Contingency Tables 93Review Exercises 945 Power, Effect Size, P-Values, and Estimating Required Sample Size Using Python 965.1 What Determines the Size of a P-Value? 965.2 How P-Values Are a Function of Sample Size 995.3 What is Effect Size? 1005.4 Understanding Population Variability in the Context of Experimental Design 1025.5 Where Does Power Fit into All of This? 1035.6 Can You Have Too Much Power? Can a Sample Be Too Large? 1045.7 Demonstrating Power Principles in Python: Estimating Power or Sample Size 1065.8 Demonstrating the Influence of Effect Size 1085.9 The Influence of Significance Levels on Statistical Power 1085.10 What About Power and Hypothesis Testing in the Age of "Big Data"? 1105.11 Concluding Comments on Power, Effect Size, and Significance Testing 111Review Exercises 1126 Analysis of Variance 1136.1 T-Tests for Means as a "Special Case" of ANOVA 1146.2 Why Not Do Several t-Tests? 1166.3 Understanding ANOVA Through an Example 1176.4 Evaluating Assumptions in ANOVA 1216.5 ANOVA in Python 1246.6 Effect Size for Teacher 1256.7 Post-Hoc Tests Following the ANOVA F-Test 1256.8 A Myriad of Post-Hoc Tests 1276.9 Factorial ANOVA 1296.10 Statistical Interactions 1316.11 Interactions in the Sample Are a Virtual Guarantee: Interactions in the Population Are Not 1336.12 Modeling the Interaction Term 1336.13 Plotting Residuals 1346.14 Randomized Block Designs and Repeated Measures 1356.15 Nonparametric Alternatives 1386.15.1 Revisiting What "Satisfying Assumptions" Means: A Brief Discussion and Suggestion of How to Approach the Decision Regarding Nonparametrics 1406.15.2 Your Experience in the Area Counts 1406.15.3 What If Assumptions Are Truly Violated? 1416.15.4 Mann-Whitney U Test 1446.15.5 Kruskal-Wallis Test as a Nonparametric Alternative to ANOVA 145Review Exercises 1477 Simple and Multiple Linear Regression 1487.1 Why Use Regression? 1507.2 The Least-Squares Principle 1527.3 Regression as a "New" Least-Squares Line 1537.4 The Population Least-Squares Regression Line 1547.5 How to Estimate Parameters in Regression 1557.6 How to Assess Goodness of Fit? 1577.7 R² - Coefficient of Determination 1587.8 Adjusted R² 1597.9 Regression in Python 1617.10 Multiple Linear Regression 1647.11 Defining the Multiple Regression Model 1647.12 Model Specification Error 1667.13 Multiple Regression in Python 1677.14 Model-Building Strategies: Forward, Backward, Stepwise 1687.15 Computer-Intensive "Algorithmic" Approaches 1717.16 Which Approach Should You Adopt? 1717.17 Concluding Remarks and Further Directions: Polynomial Regression 172Review Exercises 1748 Logistic Regression and the Generalized Linear Model 1768.1 How Are Variables Best Measured? Are There Ideal Scales on Which a Construct Should Be Targeted? 1788.2 The Generalized Linear Model 1808.3 Logistic Regression for Binary Responses: A Special Subclass of the Generalized Linear Model 1818.4 Logistic Regression in Python 1848.5 Multiple Logistic Regression 1888.5.1 A Model with Only Lag1 1918.6 Further Directions 192Review Exercises 1929 Multivariate Analysis of Variance (MANOVA) and Discriminant Analysis 1949.1 Why Technically Most Univariate Models are Actually Multivariate 1959.2 Should I Be Running a Multivariate Model? 1969.3 The Discriminant Function 1989.4 Multivariate Tests of Significance: Why They Are Different from the F-Ratio 1999.4.1 Wilks' Lambda 2009.4.2 Pillai's Trace 2019.4.3 Roy's Largest Root 2019.4.4 Lawley-Hotelling's Trace 2029.5 Which Multivariate Test to Use? 2029.6 Performing MANOVA in Python 2039.7 Effect Size for MANOVA 2059.8 Linear Discriminant Function Analysis 2059.9 How Many Discriminant Functions Does One Require? 2079.10 Discriminant Analysis in Python: Binary Response 2089.11 Another Example of Discriminant Analysis: Polytomous Classification 2119.12 Bird's Eye View of MANOVA, ANOVA, Discriminant Analysis, and Regression: A Partial Conceptual Unification 2129.13 Models "Subsumed" Under the Canonical Correlation Framework 214Review Exercises 21610 Principal Components Analysis 21810.1 What Is Principal Components Analysis? 21810.2 Principal Components as Eigen Decomposition 22110.3 PCA on Correlation Matrix 22310.4 Why Icebergs Are Not Good Analogies for PCA 22410.5 PCA in Python 22610.6 Loadings in PCA: Making Substantive Sense Out of an Abstract Mathematical Entity 22910.7 Naming Components Using Loadings: A Few Issues 23010.8 Principal Components Analysis on USA Arrests Data 23210.9 Plotting the Components 237Review Exercises 24011 Exploratory Factor Analysis 24111.1 The Common Factor Analysis Model 24211.2 Factor Analysis as a Reproduction of the Covariance Matrix 24311.3 Observed vs. Latent Variables: Philosophical Considerations 24411.4 So, Why is Factor Analysis Controversial? The Philosophical Pitfalls of Factor Analysis 24711.5 Exploratory Factor Analysis in Python 24811.6 Exploratory Factor Analysis on USA Arrests Data 250Review Exercises 25412 Cluster Analysis 25512.1 Cluster Analysis vs. ANOVA vs. Discriminant Analysis 25812.2 How Cluster Analysis Defines "Proximity" 25912.2.1 Euclidean Distance 26012.3 K-Means Clustering Algorithm 26112.4 To Standardize or Not? 26212.5 Cluster Analysis in Python 26312.6 Hierarchical Clustering 26612.7 Hierarchical Clustering in Python 268Review Exercises 272References 273Index 276

O autorze

Daniel J. Denis, PhD, is Professor of Quantitative Psychology at the University of Montana. He is author of Applied Univariate, Bivariate, and Multivariate Statistics and Applied Univariate, Bivariate, and Multivariate Statistics Using R