Statistics for Data Science and Analytics

Peter C. Bruce is Founder of the Institute for Statistics Education at Statistics.com, now part of Elder Research, Inc. He is the developer of Resampling Stats software, and the author or co-author of a number of peer-reviewed articles and several books. Dr. Peter Gedeck, PhD, is a scientist in the research informatics team at Collaborative Drug Discovery, specializing in the development of machine learning algorithms to predict biological and physicochemical properties of drug candidates. Janet Dobbins is the Chair of the Board of Directors for Data Community DC, a non-profit 501(c)(3) corporation committed to promoting data science by fostering education, opportunity, and professional development through high-quality community-driven events. She previously served as the Vice President of Business Development and Strategic Partnership at The Institute for Statistics Education at Statistics.com. Bruce and Gedeck are part of the author teams for the best-selling books Machine Learning for Business Analytics (Wiley) and Practical Statistics for Data Scientists(O’Reilly).

• About the Authors xviiAcknowledgments xixAbout the Companion Website xxiIntroduction xxiii1 Statistics and Data Science 11.1 Big Data: Predicting Pregnancy 21.2 Phantom Protection from Vitamin E 21.3 Statistician, Heal Thyself 31.4 Identifying Terrorists in Airports 41.5 Looking Ahead 51.6 Big Data and Statisticians 52 Designing and Carrying Out a Statistical Study 92.1 Statistical Science 92.2 Big Data 102.3 Data Science 102.4 Example: Hospital Errors 112.5 Experiment 122.6 Designing an Experiment 132.7 The Data 192.8 Variables and Their Flavors 212.9 Python: Data Structures and Operations 252.10 Are We Sure We Made a Difference? 342.11 Is Chance Responsible? The Foundation of Hypothesis Testing 342.12 Probability 362.13 Significance or Alpha Level 382.14 Other Kinds of Studies 402.15 When to Use Hypothesis Tests 422.16 Experiments Falling Short of the Gold Standard 422.17 Summary 432.18 Python: Iterations and Conditional Execution 442.19 Python: Numpy, scipy, and pandas—The Workhorses of Data Science 50Exercises 563 Exploring and Displaying the Data 613.1 Exploratory Data Analysis 613.2 What to Measure—Central Location 623.3 What to Measure—Variability 653.4 What to Measure—Distance (Nearness) 693.5 Test Statistic 713.6 Examining and Displaying the Data 723.7 Python: Exploratory Data Analysis/Data Visualization 80Exercises 884 Accounting for Chance—Statistical Inference 914.1 Avoid Being Fooled by Chance 914.2 The Null Hypothesis 924.3 Repeating the Experiment 934.4 Statistical Significance 994.5 Power 1034.6 The Normal Distribution 1034.7 Summary 1054.8 Python: Random Numbers 105Exercises 1155 Probability 1215.1 What Is Probability 1215.2 Simple Probability 1225.3 Probability Distributions 1265.4 From Binomial to Normal Distribution 1295.5 Appendix: Binomial Formula and Normal Approximation 1335.6 Python: Probability 134Exercises 1416 Categorical Variables 1436.1 Two-way Tables 1436.2 Conditional Probability 1446.3 Bayesian Estimates 1476.4 Independence 1506.5 Multiplication Rule 1546.6 Simpson’s Paradox 1566.7 Python: Counting and Contingency Tables 157Exercises 1637 Surveys and Sampling 1677.1 Literary Digest—Sampling Trumps “All Data” 1677.2 Simple Random Samples 1707.3 Margin of Error: Sampling Distribution for a Proportion 1727.4 Sampling Distribution for a Mean 1747.5 The Bootstrap 1767.6 Rationale for the Bootstrap 1777.7 Standard Error 1887.8 Other Sampling Methods 1887.9 Absolute vs. Relative Sample Size 1927.10 Python: Random Sampling Strategies 192Exercises 2028 More than Two Samples or Categories 2078.1 Count Data—R × C Tables 2078.2 The Role of Experiments (Many Are Costly) 2088.3 Chi-Square Test 2108.4 Single Sample—Goodness-of-Fit 2158.5 Numeric Data: ANOVA 2178.6 Components of Variance 2228.7 Factorial Design 2248.8 The Problem of Multiple Inference 2268.9 Continuous Testing 2288.10 Bandit Algorithms 2298.11 Appendix: ANOVA, the Factor Diagram, and the F-Statistic 2308.12 More than One Factor or Variable—From ANOVA to Statistical Models 2378.13 Python: Contingency Tables and Chi-square Test 2378.14 Python: ANOVA 241Exercises 2469 Correlation 2499.1 Example: Delta Wire 2499.2 Example: Cotton Dust and Lung Disease 2519.3 The Vector Product Sum Test 2529.4 Correlation Coefficient 2569.5 Correlation is not Causation 2609.6 Other Forms of Association 2619.7 Python: Correlation 262Exercises 26910 Regression 27110.1 Finding the Regression Line by Eye 27210.2 Finding the Regression Line by Minimizing Residuals 27410.3 Linear Relationships 27610.4 Prediction vs. Explanation 28010.5 Python: Linear Regression 284Exercises 29311 Multiple Linear Regression 29511.1 Terminology 29511.2 Example—Housing Prices 29611.3 Interaction 30111.4 Regression Assumptions 30411.5 Assessing Explanatory Regression Models 30611.6 Assessing Regression for Prediction 31411.7 Python: Multiple Linear Regression 324Exercises 33212 Predicting Binary Outcomes 33712.1 K-Nearest-Neighbors 33712.2 Python: Classification 343Exercises 346Index 349