Table of Contents:
Table of Contents Preface Index of Applications I: EXPLORING AND UNDERSTANDING DATA Stats Starts Here 1.1 What Is Statistics? 1.2 Data 1.3 Variables 1.4 Models Displaying and Describing Data 2.1 Summarizing and Displaying a Categorical Variable 2.2 Displaying a Quantitative Variable 2.3 Shape 2.4 Center 2.5 Spread Relationships Between Categorical Variables–Contingency Tables 3.1 Contingency Tables 3.2 Conditional Distributions 3.3 Displaying Contingency Tables 3.4 Three Categorical Variables Understanding and Comparing Distributions 4.1 Displays for Comparing Groups 4.2 Outliers 4.3 Re-Expressing Data: A First Look The Standard Deviation as a Ruler and the Normal Model 5.1 Using the Standard Deviation to Standardize Values 5.2 Shifting and Scaling 5.3 Normal Models 5.4 Working with Normal Percentiles 5.5 Normal Probability Plots Review of Part I: Exploring and Understanding Data II. EXPLORING RELATIONSHIPS BETWEEN VARIABLES Scatterplots, Association, and Correlation 6.1 Scatterplots 6.2 Correlation 6.3 Warning: Correlation ≠ Causation *6.4 Straightening Scatterplots Linear Regression 7.1 Least Squares: The Line of “Best Fit” 7.2 The Linear Model 7.3 Finding the Least Squares Line 7.4 Regression to the Mean 7.5 Examining the Residuals 7.6 R2–The Variation Accounted for by the Model 7.7 Regression Assumptions and Conditions Regression Wisdom 8.1 Examining Residuals 8.2 Extrapolation: Reaching Beyond the Data 8.3 Outliers, Leverage, and Influence 8.4 Lurking Variables and Causation 8.5 Working with Summary Values *8.6 Straightening Scatterplots–The Three Goals *8.7 Finding a Good Re-Expression Multiple Regression 9.1 What Is Multiple Regression? 9.2 Interpreting Multiple Regression Coefficients 9.3 The Multiple Regression Model–Assumptions and Conditions 9.4 Partial Regression Plots *9.5 Indicator Variables Review of Part II: Exploring Relationships Between Variables III. GATHERING DATA Sample Surveys 10.1 The Three Big Ideas of Sampling 10.2 Populations and Parameters 10.3 Simple Random Samples 10.4 Other Sampling Designs 10.5 From the Population to the Sample: You Can’t Always Get What You Want 10.6 The Valid Survey 10.7 Common Sampling Mistakes, or How to Sample Badly Experiments and Observational Studies 11.1 Observational Studies 11.2 Randomized, Comparative Experiments 11.3 The Four Principles of Experimental Design 11.4 Control Groups 11.5 Blocking 11.6 Confounding Review of Part III: Gathering Data IV. RANDOMNESS AND PROBABILITY From Randomness to Probability 12.1 Random Phenomena 12.2 Modeling Probability 12.3 Formal Probability Probability Rules! 13.1 The General Addition Rule 13.2 Conditional Probability and the General Multiplication Rule 13.3 Independence 13.4 Picturing Probability: Tables, Venn Diagrams, and Trees 13.5 Reversing the Conditioning and Bayes' Rule Random Variables 14.1 Center: The Expected Value 14.2 Spread: The Standard Deviation 14.3 Shifting and Combining Random Variables 14.4 Continuous Random Variables Probability Models 15.1 Bernoulli Trials 15.2 The Geometric Model 15.3 The Binomial Model 15.4 Approximating the Binomial with a Normal Model 15.5 The Continuity Correction 15.6 The Poisson Model 15.7 Other Continuous Random Variables: The Uniform and the Exponential Review of Part IV: Randomness and Probability V. INFERENCE FOR ONE PARAMETER Sampling Distribution Models and Confidence Intervals for Proportions 16.1 The Sampling Distribution Model for a Proportion 16.2 When Does the Normal Model Work? Assumptions and Conditions 16.3 A Confidence Interval for a Proportion 16.4 Interpreting Confidence Intervals: What Does 95% Confidence Really Mean? 16.5 Margin of Error: Certainty vs. Precision *16.6 Choosing the Sample Size Confidence Intervals for Means 17.1 The Central Limit Theorem 17.2 A Confidence Interval for the Mean 17.3 Interpreting Confidence Intervals *17.4 Picking Our Interval up by Our Bootstraps 17.5 Thoughts About Confidence Intervals Testing Hypotheses 18.1 Hypotheses 18.2 P-Values 18.3 The Reasoning of Hypothesis Testing 18.4 A Hypothesis Test for the Mean 18.5 Intervals and Tests 18.6 P-Values and Decisions: What to Tell About a Hypothesis Test More About Tests and Intervals 19.1 Interpreting P-Values 19.2 Alpha Levels and Critical Values 19.3 Practical vs. Statistical Significance 19.4 Errors Review of Part V: Inference for One Parameter VI. INFERENCE FOR RELATIONSHIPS Comparing Groups 20.1 A Confidence Interval for the Difference Between Two Proportions 20.2 Assumptions and Conditions for Comparing Proportions 20.3 The Two-Sample z-Test: Testing for the Difference Between Proportions 20.4 A Confidence Interval for the Difference Between Two Means 20.5 The Two-Sample t-Test: Testing for the Difference Between Two Means *20.6 Randomization Tests and Confidence Intervals for Two Means *20.7 Pooling *20.8 The Standard Deviation of a Difference Paired Samples and Blocks 21.1 Paired Data 21.2 The Paired t-Test 21.3 Confidence Intervals for Matched Pairs 21.4 Blocking Comparing Counts 22.1 Goodness-of-Fit Tests 22.2 Chi-Square Test of Homogeneity 22.3 Examining the Residuals 22.4 Chi-Square Test of Independence Inferences for Regression 23.1 The Regression Model 23.2 Assumptions and Conditions 23.3 Regression Inference and Intuition 23.4 The Regression Table 23.5 Multiple Regression Inference 23.6 Confidence and Prediction Intervals *23.7 Logistic Regression *23.8 More About Regression Review of Part VI: Inference for Relationships VII. INFERENCE WHEN VARIABLES ARE RELATED Multiple Regression Wisdom 24.1 Multiple Regression Inference 24.2 Comparing Multiple Regression Model 24.3 Indicators 24.4 Diagnosing Regression Models: Looking at the Cases 24.5 Building Multiple Regression Models Analysis of Variance 25.1 Testing Whether the Means of Several Groups Are Equal 25.2 The ANOVA Table 25.3 Assumptions and Conditions 25.4 Comparing Means 25.5 ANOVA on Observational Data Multifactor Analysis of Variance 26.1 A Two Factor ANOVA Model 26.2 Assumptions and Conditions 26.3 Interactions Statistics and Data Science 27.1 Introduction to Data Mining Review of Part VII: Inference When Variables Are Related Parts I—V Cumulative Review Exercises Appendixes: Answers Credits Indexes Tables and Selected Formulas