Active Statistics

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Information

Web page for the book Active Statistics by Andrew Gelman and Aki Vehtari.

Published by Cambridge University Press in 2024 (March).
© Copyright by Andrew Gelman and Aki Vehtari 2024.

This book provides statistics instructors and students with complete classroom material for a one- or two-semester course on applied regression and causal inference. It is built around 52 stories, 52 class-participation activities, 52 hands-on computer demonstrations, and 52 discussion problems that allow instructors and students to explore in a fun way the real-world complexity of the subject. The book fosters an engaging ‘flipped classroom’ environment with a focus on visualization and understanding. The book provides instructors with frameworks for self-study or for structuring the course, along with tips for maintaining student engagement at all levels, and practice exam questions to help guide learning. Designed to accompany the authors’ previous textbook Regression and Other Stories, its modular nature and wealth of material allow this book to be adapted to different courses and texts or be used by learners as a hands-on workbook.

• Buy Active Statistics from Cambridge University Press.

• Active Statistics online PDF. This PDF is free to view and download for personal use only. Not for re-distribution, re-sale or use in derivative works.
  With permission from Cambridge University Press. The linked version has corrections up to the date mentioned on the front page. It is best to link to and download from this site https://avehtari.github.io/ActiveStatistics/, so that you and others will get the latest corrections and see the extra online material.

• Podcast: a special episode of Learning Bayesian Statistics with Andrew Gelman talking about the Active Statistics book

• Regression and Other Stories book webpage.

• If you notice an error submit an issue or send an email.

Contents

• Part 1: Organizing a plan of study
  1. Active learning
     1.1. Flipped classroom and collaborative learning
     1.2. What happens during the semester?
     1.3. Active learning in class
     1.4. Scheduling
     1.5. Assessment and feedback
     1.6. Some general issues in teaching and communication
     
  2. Setting up a course of study
     2.1 What to learn and how to learn it
     2.2 Computing
     2.3 Course material
     2.4 Real data and simulated data
     2.5 Two kinds of computer demonstrations
     2.6 Challenges in learning particular topics
     2.7 Adapting to your goals and learning style
     2.8 Using these materials in introductory or more advanced courses
     2.9 Balance between challenges and solutions
     
• Part 2: Stories, activities, problems, and demonstrations
  3. Week by week: the first semester
     3.1 Introduction to quantitative social science
     3.2 Prediction as a unifying theme in statistics and causal inference
     3.3 Data collection and visualization
     3.4 Review of mathematics and probability
     3.5 Statistical inference
     3.6 Simulation
     3.7 Background on regression modeling
     3.8 Linear regression with a single predictor
     3.9 Least squares and fitting regression models
     3.10 Prediction and Bayesian inference
     3.11 Linear regression with multiple predictors
     3.12 Assumptions, diagnostics, and model evaluation
     3.13 Regression with linear and log transformations
  4. Week by week: the second semester
     4.14 Review of basic statistics and regression modeling
     4.15 Logistic regression163
     4.16 Working with logistic regression
     4.17 Other generalized linear models
     4.18 Design and sample size decisions
     4.19 Poststratification and missing-data imputation
     4.20 How can flipping a coin help you estimate causal effects?
     4.21 Causal inference using regression on the treatment variable
     4.22 Causal inference as prediction
     4.23 Imbalance and lack of complete overlap
     4.24 Additional topics in causal inference
     4.25 Advanced regression and multilevel models
     4.26 Review of the course
• Appendices
  1. Pre-test questions
     A.1 First semester
     A.2 Second semester
  2. Final exam questions
     B.1 Multiple-choice questions for the first semester
     B.2 Multiple-choice questions for the second semester
     B.3 Take-home exam
  3. Outlines of classroom activities
     C.1 First semester
     C.2 Second semester

List of classroom activities

First semester

Week	Stories	Activities	Computer demonstrations	Discussion problems
1. Introduction	Wikipedia Literary Digest poll of 1936	Design a study Design experiment to distinguish two hypotheses	Collect and analyze simulated data Predict elections from economy	Find the hidden assumption Find the hidden assumptions
2. Overview of applied regression (Chapter 1 of Regression and Other Stories)	United Nations peacekeeping Girls and sports	Bag of candies and sampling bias Gather and plot data from students	Graph of data and fitted line Tinker with an example	Height and earnings Graph hypothetical data
3. Data collection and visualization (Chapter 2 of ROS)	Political leanings of sports fans Use comparisons to redraw a graph	Measure handedness Scatterplot charades	Download and work with data Make plots clearer	Tell stories with graphs Plots of baby names
4. Basics of math and probability (Chapter 3 of ROS)	Death rate in the pandemic Galton’s giants	Amoebas and exponential growth Squares, cubes, and power-law growth	Matrix manipulations Compute weighted averages	College admissions Probability of a rare event
5. Statistical inference (Chapter 4 of ROS)	They got the wrong standard error Claims of implausibly large effects	Design a bogus study Think about effect sizes	Simulate fake data and confidence interval Proportions, means, and differences	Confidence intervals and true values Standard error for feeling thermometers
6. Simulation (Chapter 5 of ROS)	Proportion of identical twins Simulate a process of innovation	Real vs. fake coin flips Simulate a probability process	Break R functions Simulate 100 coin flips	Discrete / continuous distribution Simulate clustering of buses
7. Background on regression modeling (Chapter 6 of ROS)	Slope when predicting elections from the economy Clinton/Trump vote vs. polls, and predictions	Simulate fake data and fit a regression Memory quiz and regression to the mean	Play with a simulated regression Challenges in setting up a simulation	Examples of regression to the mean Uniform partisan swing
8. Linear regression with a single predictor (Chapter 7 of ROS)	\(5^2 + 12^2 = 13^2\) African countries in the U.N.	Simulate and recover regression lines Socioeconomic status and political views	Regression, transformations, and sample size Take average or regress on a constant term	Predict elections from incumbency How large was the sample size?
9. Fitting regression models (Chapter 8 of ROS)	Ronald Reagan and the evangelical vote Does having a girl make you more conservative/liberal?	Move a point and shift the regression line	Play with the regression estimate Compare lm and stan_glm	From inference to decision Sample size and statistical significance
10. Prediction and Bayesian inference (Chapter 9 of ROS)	Fairness of random exams Uncertainties in election forecasts	Coverage of prediction intervals Prior for a real-world parameter	Different forms of predictive uncertainty Bayes estimate of childhood intervention	Coverage of prediction intervals Prior for a real-world parameter
11. Linear regression with multiple predictors (Chapter 10 of ROS)	Incumbency advantage in elections Beauty and teaching evaluations	Memory quiz with pre-test and treatment Design a study with regression in mind	Regression with interactions Adding interactions to a model	Regression adjustment Why look at a pre-test?
12. Assumptions, diagnostics, evaluation (Chapter 11 of ROS)	Actual vs. guessed exam scores Model checking for baseball analytics	Sample size and statistical significance Assumptions of regression	Take difference or regress on an indicator Simulate and debug	Assumptions of regression Patterns of residuals
13. Transformations and regression (Chapter 12 of ROS)	Logarithm of world population Price elasticity of demand	Predictive uncertainties Combining predictors to create a score	Centered and standardized predictors Regressions with logged variables	When to use the log scale Straight line fit to non-linear data

Second semester

Week	Stories	Activities	Computer demonstrations	Discussion problems
14. Review of statistics and regression (Chapters 1–12 of ROS)	Biased samples and coverage of intervals The problem of too much talent?	Self-selected treatment assignment Design a study to explore nonlinearity	Causal inference adjusting for pre-treatment Simulating patterns of bias	Sampling and adjustment Causal inference, adjustment
15. Logistic regression (Chapter 13 of ROS)	Item-response analysis of final exams Survey nonresponse	“Two truths and a lie” game Predict the views of others	Displaying a logistic curve Logistic regression probabilities	Real-world logistic regression Where logistic regression makes no sense
16. Working with logistic regression (Chapter 14 of ROS)	“Keys to the White House” Opiate of the masses	Job training and predictive comparisons Logistic regression with interactions	Predictions from logistic regression Linear or logistic regression	Experimental design Design with pre-test
17. Other generalized linear models (Chapter 15 of ROS)	Patterns of gun ownership Structure in social networks	How similar are you to your friends? Alternative models for discrete data	Simulating overdispersed data Generalized linear model with offset	Identification in linear models Functional forms for non-linear models
18. Design and sample size decisions (Chapter 16 of ROS)	The multiverse and the feedback loop Lucky golf balls and implausible effect sizes	Design an experiment from scratch Hypothetical study of left-handedness	Design analysis by simulation Design for estimating interactions	Designing a survey Designing future studies
19. Poststratification and missing-data imputation (Chapter 17 of ROS)	Estimating state-level opinion Environmental Sustainability Index	Generalizing from class to population Experimental design and effect sizes	Regression and post-stratification Random imputation	Network sampling Problems with missing data
20. Causal inference and randomized experiments (Chapter 18 of ROS)	Varying treatment effects Ballot-order effects	Potential outcomes for basketball Potential outcomes for ballot order	Data analysis for basketball activity Sample and population averages	Randomization and ethics Assumptions in randomized experiments
21. Causal inference using regression on treatment (Chapter 19 of ROS)	Pest control experiment Social penumbras	Adjustments in causal inference Average treatment effects	Benefits of pre-treatment data Combining pre-treatment predictors	Causal logistic regression Holding all else equal?
22. Causal inference (Chapters 18–19 of ROS)	No effect of heart stents? The freshman fallacy	Components of an observational study Study makers vs. study breakers	Playing with least squares Don’t adjust for intermediate outcomes	Individual and average effects Nudge meta-analysis
23. Observational studies with measured confounders (Chapter 20 of ROS)	Retrospective evaluation of a policy Postal service modeling	Imbalance and lack of overlap Victimization and views on crime policy	Poststratification for causal inference Measurement error models	Effects of campaign contributions Effects and variation
24. Additional topics in causal inference (Chapter 21 of ROS)	Deterrent effect of death penalty Regression discontinuity mishaps	Two measures of the same quantity “Why” questions and causal inference	Instrumental variables Adjustment in regression discontinuity	Effects of masks Admissions test coaching
25. Advanced regression and multilevel models (Chapter 22 of ROS)	Nonlinearity in leafout dates Governors’ elections and lifespans	Nonlinear treatment effect When do students stop coming to class?	Modeling golf putting in Stan Opinions on same-sex marriage	Noisy time series 20 data points and 16 predictors
26. Review of the course (Chapters 1–22 of ROS)	Randomized trials in international development Is North Carolina less democratic than North Korea?	Designing a paper helicopter Review in groups	Quadratic regression Bias and unmodeled uncertainty	Design using simulation Electoral integrity index

Reviews

• ‘This book is an extraordinarily rich and generous resource for teaching statistics. Full of stories about challenging statistical problems, the examples reflect all the messiness of real life, and encourage class discussion of what went wrong and how to do things better. The extensive collection of lesson plans and exercises provides a fine inspiration to adopt a different, more active, style of teaching.’ - David Spiegelhalter - University of Cambridge
• ‘This is a wonderful read for any statistics teacher. The focus on real-world applications and statistical thinking ensures that everyone will gain new insights and perspectives no matter how long you have been teaching.’ - Beth Chance - California Polytechnic State University
• ‘I have to say reading this book came as a pleasant surprise for me. I thought I was going to be reviewing another statistics book and instead, it was an insightful read on how to think about teaching statistics. I found it engaging and helpful in rethinking how I approach teaching statistics.’ - Pamela Davis-Kean - University of Michigan