Table of Contents

1: Introduction to Data

1.1 What Are Data?

1.2 Classifying and Storing Data

1.3 Investigating Data

1.4 Organizing Categorical Data

1.5 Collecting Data to Understand Causality

2: Picturing Variation with Graphs

2.1 Visualizing Variation in Numerical Data

2.2 Summarizing Important Features of a Numerical Distribution

2.3 Visualizing Variation in Categorical Variables

2.4 Summarizing Categorical Distributions

2.5 Interpreting Graphs

3: Numerical Summaries of Center and Variation

3.1 Summaries for Symmetric Distributions

3.2 What's Unusual? The Empirical Rule and z-Scores

3.3 Summaries for Skewed Distributions

3.4 Comparing Measures of Center

3.5 Using Boxplots for Displaying Summaries

4: Regression Analysis: Exploring Associations between Variables

4.1 Visualizing Variability with a Scatterplot

4.2 Measuring Strength of Association with Correlation

4.3 Modeling Linear Trends

4.4 Evaluating the Linear Model

5: Modeling Variation with Probability

5.1 What Is Randomness?

5.2 Finding Theoretical Probabilities

5.3 Associations in Categorical Variables

5.4 Finding Empirical Probabilities

6: Modeling Rando Events: The Normal and Binomial Models

6.1 Probability Distributions Are Models of Random Experiments

6.2 The Normal Model

6.3 The Binomial Model (Optional)

7: Survey Sampling and Inference

7.1 Learning about the World through Surveys

7.2 Measuring the Quality of a Survey

7.3 The Central Limit Theorem for Sample Proportions

7.4 Estimating the Population Proportion with Confidence Intervals

7.5 Comparing Two Population Proportions with Confidence

8: Hypothesis Testing for Population Proportions

8.1 The Essential Ingredients of Hypothesis Testing

8.2 Hypothesis Testing in Four Steps

8.3 Hypothesis Tests in Detail

8.4 Comparing Proportions from Two Populations

9: Inferring Population Means

9.1 Sample Means of Rando Samples

9.2 The Central Limit Theorem for Sample Means

9.3 Answering Questions about the Mean of a Population

9.4 Hypothesis Testing for Means

9.5 Comparing Two Population Means

9.6 Overview of Analyzing Means

10: Associations between Categorical Variables

10.1 The Basic Ingredients for Testing with Categorical Variables

10.2 The Chi-Square Test for Goodness of Fit

10.3 Chi-Square Tests for Associations between Categorical Variables

10.4 Hypothesis Tests When Sample Sizes Are Small

11: Multiple Comparisons and Analysis of Variance

11.1 Multiple Comparisons

11.2 The Analysis of Variance

11.3 The ANOVA Test

11.4 Post-Hoc Procedures

12: Experimental Design: Controlling Variation

12.1 Variation Out of Control

12.2 Controlling Variation in Surveys

12.3 Reading Research Papers

13: Inference without Normality

13.1 Transforming Data

13.2 The Sign Test for Paired Data

13.3 Mann-Whitney Test for Two Independent Groups

13.4 Randomization Tests

14: Inference for Regression

14.1 The Linear Regression Model

14.2 Using the Linear Model

14.3 Predicting Values and Estimating Means