Kosuke Imai is Professor of Government and of Statistics at Harvard University. Nora Webb Williams is Assistant Professor of Political Science at the University of Illinois, Urbana-Champaign.

• List of TablesList of FiguresPrefacePreface to the Original Book1 Introduction1.1 Overview of the Book1.2 How to Use This Book1.3 Introduction to R and the tidyverse1.3.1 Arithmetic Operations: R as a Calculator1.3.2 R Scripts1.3.3 Loading Packages1.3.4 Objects1.3.5 Vectors1.3.6 Functions1.3.7 Data Files: Loading and Subsetting1.3.8 Adding Variables1.3.9 Data Frames: Summarizing1.3.10 Saving Objects1.3.11 Loading Data in Other Formats1.3.12 Programming and Learning Tips1.4 Summary1.5 Exercises1.5.1 Bias in Self-Reported Turnout1.5.2 Understanding World Population Dynamics2 Causality2.1 Racial Discrimination in the Labor Market2.2 Subsetting Data in R2.2.1 Logical Values and Operators2.2.2 Relational Operators2.2.3 Subsetting2.2.4 Simple Conditional Statements2.2.5 Factor Variables2.3 Causal Effects and the Counterfactual2.4 Randomized Controlled Trials2.4.1 The Role of Randomization2.4.2 Social Pressure and Voter Turnout2.5 Observational Studies2.5.1 Minimum Wage and Unemployment2.5.2 Confounding Bias2.5.3 Before-and-After and Difference-in-Differences Designs2.6 Descriptive Statistics for a Single Variable2.6.1 Quantiles2.6.2 Standard Deviation2.7 Summary2.8 Exercises2.8.1 Efficacy of Small Class Size in Early Education2.8.2 Changing Minds on Gay Marriage2.8.3 Success of Leader Assassination as a Natural Experiment3 Measurement3.1 Measuring Civilian Victimization during Wartime3.2 Handling Missing Data in R3.3 Visualizing the Univariate Distribution3.3.1 Bar Plot3.3.2 Histogram3.3.3 Box Plot3.3.4 Printing and Saving Graphs3.4 Survey Sampling3.4.1 The Role of Randomization3.4.2 Nonresponse and Other Sources of Bias3.5 Measuring Political Polarization3.6 Summarizing Bivariate Relationships3.6.1 Scatter Plot3.6.2 Correlation3.7 Quantile–Quantile Plot3.8 Clustering3.8.1 Matrix in R3.8.2 List in R3.8.3 The k-Means Algorithm3.9 Summary3.10 Exercises3.10.1 Changing Minds on Gay Marriage: Revisited3.10.2 Political Efficacy in China and Mexico3.10.3 Voting in the United Nations General Assembly4 Prediction4.1 Predicting Election Outcomes4.1.1 Loops in R4.1.2 General Conditional Statements in R4.1.3 Poll Predictions4.2 Linear Regression4.2.1 Facial Appearance and Election Outcomes4.2.2 Correlation and Scatter Plots4.2.3 Least Squares4.2.4 Regression towards the Mean4.2.5 Merging Data Sets in R4.2.6 Model Fit4.3 Regression and Causation4.4 Randomized Experiments4.4.1 Regression with Multiple Predictors4.4.2 Heterogeneous Treatment Effects4.4.3 Regression Discontinuity Design4.5 Summary4.6 Exercises4.6.1 Prediction Based on Betting Markets4.6.2 Election and Conditional Cash Transfer Program in Mexico4.6.3 Government Transfer and Poverty Reduction in Brazil5 Discovery5.1 Textual Data5.1.1 The Disputed Authorship of The Federalist Papers5.1.2 Document-Term Matrix5.1.3 Topic Discovery5.1.4 Authorship Prediction5.1.5 Cross-Validation5.2 Network Data5.2.1 Marriage Network in Renaissance Florence5.2.2 Undirected Graph and Centrality Measures5.2.3 Twitter-Following Network5.2.4 Directed Graph and Centrality5.3 Spatial Data5.3.1 The 1854 Cholera Outbreak in London5.3.2 Spatial Data in R5.3.3 US Presidential Elections5.3.4 Expansion of Walmart5.3.5 Animation in R5.4 Summary5.5 Exercises5.5.1 Analyzing the Preambles of Constitutions5.5.2 International Trade Network5.5.3 Mapping US Presidential Election Results over Time6 Probability6.1 Probability6.1.1 Frequentist versus Bayesian6.1.2 Definition and Axioms6.1.3 Permutations6.1.4 Sampling with and without Replacement6.1.5 Combinations6.2 Conditional Probability6.2.1 Conditional, Marginal, and Joint Probabilities6.2.2 Independence6.2.3 Bayes’ Rule6.2.4 Predicting Race Using Surname and Residence Location6.3 Random Variables and Probability Distributions6.3.1 Random Variables6.3.2 Bernoulli and Uniform Distributions6.3.3 Binomial Distribution6.3.4 Normal Distribution6.3.5 Expectation and Variance6.3.6 Predicting Election Outcomes with Uncertainty6.4 Large Sample Theorems6.4.1 The Law of Large Numbers6.4.2 The Central Limit Theorem6.5 Summary6.6 Exercises6.6.1 The Mathematics of Enigma6.6.2 A Probability Model for Betting Market Election Prediction6.6.3 Election Fraud in Russia7 Uncertainty7.1 Estimation7.1.1 Unbiasedness and Consistency7.1.2 Standard Error7.1.3 Confidence Interval7.1.4 Margin of Error and Sample Size Calculation in Polls7.1.5 Analysis of Randomized Controlled Trials7.1.6 Analysis Based on Student’s t-Distribution7.2 Hypothesis Testing7.2.1 Tea-Tasting Experiment7.2.2 The General Framework7.2.3 One-Sample Tests7.2.4 Two-Sample Tests7.2.5 Pitfalls of Hypothesis Testing7.2.6 Power Analysis7.3 Linear Regression Model with Uncertainty7.3.1 Linear Regression as a Generative Model7.3.2 Unbiasedness of Estimated Coefficients7.3.3 Standard Errors of Estimated Coefficients7.3.4 Inference about Coefficients7.3.5 Inference about Predictions7.4 Summary7.5 Exercises7.5.1 Sex Ratio and the Price of Agricultural Crops in China7.5.2 Filedrawer and Publication Bias in Academic Research7.5.3 Analysis of the 1933 German Election during the Weimar Republic8 NextGeneral IndexR Index