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STAT2
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Second Edition©2019 Ann Cannon; George W. Cobb; Bradley A. Hartlaub; Julie M. Legler; Robin H. Lock; Thomas L. Moore; Allan J. Rossman; Jeffrey A. Witmer
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In your introductory statistics course, you saw many facets of statistics but you probably did little if any work with the formal concept of a statistical model. To us, modeling is a very important part of statistics. In this book, we develop statistical models, building on ideas you encountered in your introductory course. We start by reviewing some topics from Stat 101 but adding the lens of modeling as a way to view ideas. Then we expand our view as we develop more complicated models.You will find a thread running through the book:
- Choose a type of model.
- Fit the model to data.
- Assess the fit and make any needed changes.
- Use the fitted model to understand the data and the population from which they came.
We hope that the Choose, Fit, Assess, Use quartet helps you develop a systematic approach to analyzing data.
Modern statistical modeling involves quite a bit of computing. Fortunately, good software exists that enables flexible model fitting and easy comparisons of competing models. We hope that by the end of your Stat2 course, you will be comfortable using software to fit models that allow for deep understanding of complex problems.
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Learn MoreTable of Contents
Chapter 0 What Is a Statistical Model?
0.1 Model Basics
0.2 A Four-Step Process
Unit A: Linear Regression
Chapter 1 Simple Linear Regression
1.1 The Simple Linear Regression Model
1.2 Conditions for a Simple Linear Model
1.3 Assessing Conditions
1.4 Transformations/Reexpressions
1.5 Outliers and Influential Points
Chapter 2 Inference for Simple Linear Regression
2.1 Inference for Regression Slope
2.2 Partitioning Variability—ANOVA
2.3 Regression and Correlation
2.4 Intervals for Predictions
2.5 Case Study: Butterfly Wings
Chapter 3 Multiple Regression
3.1 Multiple Linear Regression Model
3.2 Assessing a Multiple Regression Model
3.3 Comparing Two Regression Lines
3.4 New Predictors from Old
3.5 Correlated Predictors
3.6 Testing Subsets of Predictors
3.7 Case Study: Predicting in Retail Clothing
Chapter 4 Additional Topics in Regression
4.1 Topic: Added Variable Plots
4.2 Topic: Techniques for Choosing Predictors
4.3 Cross-validation
4.4 Topic: Identifying Unusual Points in Regression
4.5 Topic: Coding Categorical Predictors
4.6 Topic: Randomization Test for a Relationship
4.7 Topic: Bootstrap for Regression
Unit B: Analysis of Variance
Chapter 5 One-way ANOVA and Randomized Experiments
5.1 Overview of ANOVA
5.2 The One-way Randomized Experiment and Its Observational Sibling
5.3 Fitting the Model
5.4 Formal Inference: Assessing and Using the Model
5.5 How Big Is the Effect?: Confidence Intervals and Effect Sizes
5.6 Using Plots to Help Choose a Scale for the Response
5.7 Multiple Comparisons and Fisher’s Least Significant Difference
5.8 Case Study: Words with Friends
Chapter 6 Blocking and Two-way ANOVA
6.1 Choose: RCB Design and Its Observational Relatives
6.2 Exploring Data from Block Designs
6.3 Fitting the Model for a Block Design
6.4 Assessing the Model for a Block Design
6.5 Using the Model for a Block Design
Chapter 7 ANOVA with Interaction and Factorial Designs
7.1 Interaction
7.2 Design: The Two-way Factorial Experiment
7.3 Exploring Two-way Data
7.4 Fitting a Two-way Balanced ANOVA Model
7.5 Assessing Fit: Do We Need a Transformation?
7.6 USING a Two-way ANOVA Model
Chapter 8 Additional Topics in Analysis of Variance
8.1 Topic: Levene’s Test for Homogeneity of Variances
8.2 Topic: Multiple Tests
8.3 Topic: Comparisons and Contrasts
8.4 Topic: Nonparametric Statistics
8.5 Topic: Randomization F-Test
8.6 Topic: Repeated Measures Designs and Data Sets
8.7 Topic: ANOVA and Regression with Indicators
8.8 Topic: Analysis of Covariance
Unit C: Logistic Regression
Chapter 9 Logistic Regression
9.1 Choosing a Logistic Regression Model
9.2 Logistic Regression and Odds Ratios
9.3 Assessing the Logistic Regression Model
9.4 Formal Inference: Tests and Intervals
Chapter 10 Multiple Logistic Regression
10.1 Overview
10.2 Choosing, Fitting, and Interpreting Models
10.3 Checking Conditions
10.4 Formal Inference: Tests and Intervals
10.5 Case study: Attractiveness and Fidelity
Chapter 11 Additional Topics in Logistic Regression
11.1 Topic: Fitting the Logistic Regression Model
11.2 Topic: Assessing Logistic Regression Models
11.3 Randomization Tests for Logistic Regression
11.4 Analyzing Two-Way Tables with Logistic Regression
11.5 Simpson’s Paradox
Chapter 12 Time Series Analysis
12.1 Functions of Time
12.2 Measuring Dependence on Past Values: Autocorrelation
12.3 ARIMA models
12.4 Case Study: Residual Oil
Answers to Selected Exercises
General Index
Dataset Index
0.1 Model Basics
0.2 A Four-Step Process
Unit A: Linear Regression
Chapter 1 Simple Linear Regression
1.1 The Simple Linear Regression Model
1.2 Conditions for a Simple Linear Model
1.3 Assessing Conditions
1.4 Transformations/Reexpressions
1.5 Outliers and Influential Points
Chapter 2 Inference for Simple Linear Regression
2.1 Inference for Regression Slope
2.2 Partitioning Variability—ANOVA
2.3 Regression and Correlation
2.4 Intervals for Predictions
2.5 Case Study: Butterfly Wings
Chapter 3 Multiple Regression
3.1 Multiple Linear Regression Model
3.2 Assessing a Multiple Regression Model
3.3 Comparing Two Regression Lines
3.4 New Predictors from Old
3.5 Correlated Predictors
3.6 Testing Subsets of Predictors
3.7 Case Study: Predicting in Retail Clothing
Chapter 4 Additional Topics in Regression
4.1 Topic: Added Variable Plots
4.2 Topic: Techniques for Choosing Predictors
4.3 Cross-validation
4.4 Topic: Identifying Unusual Points in Regression
4.5 Topic: Coding Categorical Predictors
4.6 Topic: Randomization Test for a Relationship
4.7 Topic: Bootstrap for Regression
Unit B: Analysis of Variance
Chapter 5 One-way ANOVA and Randomized Experiments
5.1 Overview of ANOVA
5.2 The One-way Randomized Experiment and Its Observational Sibling
5.3 Fitting the Model
5.4 Formal Inference: Assessing and Using the Model
5.5 How Big Is the Effect?: Confidence Intervals and Effect Sizes
5.6 Using Plots to Help Choose a Scale for the Response
5.7 Multiple Comparisons and Fisher’s Least Significant Difference
5.8 Case Study: Words with Friends
Chapter 6 Blocking and Two-way ANOVA
6.1 Choose: RCB Design and Its Observational Relatives
6.2 Exploring Data from Block Designs
6.3 Fitting the Model for a Block Design
6.4 Assessing the Model for a Block Design
6.5 Using the Model for a Block Design
Chapter 7 ANOVA with Interaction and Factorial Designs
7.1 Interaction
7.2 Design: The Two-way Factorial Experiment
7.3 Exploring Two-way Data
7.4 Fitting a Two-way Balanced ANOVA Model
7.5 Assessing Fit: Do We Need a Transformation?
7.6 USING a Two-way ANOVA Model
Chapter 8 Additional Topics in Analysis of Variance
8.1 Topic: Levene’s Test for Homogeneity of Variances
8.2 Topic: Multiple Tests
8.3 Topic: Comparisons and Contrasts
8.4 Topic: Nonparametric Statistics
8.5 Topic: Randomization F-Test
8.6 Topic: Repeated Measures Designs and Data Sets
8.7 Topic: ANOVA and Regression with Indicators
8.8 Topic: Analysis of Covariance
Unit C: Logistic Regression
Chapter 9 Logistic Regression
9.1 Choosing a Logistic Regression Model
9.2 Logistic Regression and Odds Ratios
9.3 Assessing the Logistic Regression Model
9.4 Formal Inference: Tests and Intervals
Chapter 10 Multiple Logistic Regression
10.1 Overview
10.2 Choosing, Fitting, and Interpreting Models
10.3 Checking Conditions
10.4 Formal Inference: Tests and Intervals
10.5 Case study: Attractiveness and Fidelity
Chapter 11 Additional Topics in Logistic Regression
11.1 Topic: Fitting the Logistic Regression Model
11.2 Topic: Assessing Logistic Regression Models
11.3 Randomization Tests for Logistic Regression
11.4 Analyzing Two-Way Tables with Logistic Regression
11.5 Simpson’s Paradox
Chapter 12 Time Series Analysis
12.1 Functions of Time
12.2 Measuring Dependence on Past Values: Autocorrelation
12.3 ARIMA models
12.4 Case Study: Residual Oil
Answers to Selected Exercises
General Index
Dataset Index
Ann Cannon
Ann Cannon is the Watson M. Davis Professor of Mathematics and Statistics at Cornell College in Mount Vernon, Iowa, where she has taught statistics for 30 years. She earned her MA and PhD in statistics from Iowa State University, and her BA in mathematics from Grinnell College. Ann is a Fellow of the American Statistical Association (ASA) and won the Mu Sigma Rho (national statistics honor society) William D. Warde Statistics Education Award. Ann has been very involved with the Statistics and Data Science Education Section of the ASA, serving on the executive committee as member-at-large, secretary/treasurer, and chair. She has also served on the ASA/MAA Joint Committee on Undergraduate Statistics, and as the Secretary/Treasurer and Chair of the Iowa Chapter of the ASA. Ann is currently associate editor for the Journal of Statistics and Data Science Education. Ann has been involved with the AP® Statistics Reading for 20 years, serving as Reader, Table Leader, Question Leader, and Assistant Chief Reader. Ann is coauthor of STAT2: Modeling with Regression and ANOVA (now in its second edition), a textbook designed for the college statistics course following the introductory statistics course. In her spare time, Ann enjoys playing the French horn (particularly in pit orchestras for musical theater), reading, and traveling.
George W. Cobb
George Cobb is Robert l. Rooke Professor emeritus at Mount Holyoke College, where he taught from 1974 to 2009 after earning his PhD in statistics from Harvard University.  He is a Fellow of the American Statistical Association, served a term as ASA vice-president, and received the ASA Founder’s award.  He is also recipient of the of the Lifetime Achievement award of the US Conference on Teaching Statistics.  He is author or co-author of several books, including Introduction to Design and Analysis of Experiments and Statistics in Action.  His interests include Markov chain Monte Carlo, applications of statistics to the law, and bluegrass banjo.
Bradley A. Hartlaub
Brad Hartlaub is a Professor in the Department of Mathematics and Statistics at Kenyon College. He is a nonparametric statistician who has served as the Chief Reader of the AP Statistics Program and is an active member of the American Statistical Associations Section on Statistical Education. Brad was selected as a Fellow of the American Statistical Association in 2006. He has served the College as a department chair, a division chair, a supervisor of undergraduate research, and an associate provost. He has received research grants to support his work with undergraduate students from the Andrew W. Mellon Foundation, the Council on Undergraduate Research, and the National Science Foundation. Brad received the Trustee Award for Distinguished Teaching in 1996, and the Distinction in Mentoring Award in 2014.
Julie M. Legler
Julie Legler earned a BA and MS in Statistics from the University of Minnesota and later a doctorate in biostatistics from Harvard.  She has taught statistics at the undergraduate level for nearly 20 years. In addition, she spent 7 years at the National Institutes of Health,  first as a postdoc and then as a mathematical statistician at the National Cancer Institute.  She has published in the areas of latent variable modeling, surveillance modeling, and undergraduate research.  Currently she is professor of statistics and director of the Statistics Program at St. Olaf College.  Recently she was named the Director of Collaborative Undergraduate Research and Inquiry  at St. Olaf.
Robin H. Lock
Robin H. Lock is the Jack and Sylvia Burry Professor of Statistics at St. Lawrence University where he has taught since 1983 after receiving his PhD from the University of Massachusetts- Amherst. He is a Fellow of the American Statistical Association, past Chair of the Joint MAA-ASA Committee on Teaching Statistics, a member of the committee that developed GAISE (Guidelines for Assessment and Instruction in Statistics Education), and on the editorial board of CAUSE (the Consortium for the Advancement of Undergraduate Statistics Education). He has won the national Mu Sigma Rho Statistics Education award and numerous awards for presentations on statistics education at national conferences.
Thomas L. Moore
Thomas Moore earned a B.A. from Carleton College, an M.S. from the University of Iowa, and a Ph.D. from Dartmouth.  He has been on the faculty at Grinnell College since 1980 and has concentrated his scholarship on statistics education.  He chaired the Statistics Education Section of ASA in 1995 and the MAAs SIGMAA for Statistics Education in 2004.  He is a Fellow of American Statistical Association and was the2008 Mu Sigma Rho Statistical Education Award winner.
Allan J. Rossman
Allan J. Rossman is Professor and Chair of the Statistics Department at Cal Poly – San Luis Obispo. He served as Chief Reader of the Advanced Placement program in Statistics from 2009-2014. He was Program Chair for the 2007 Joint Statistical Meetings and for the U.S. Conference in Teaching Statistics since 2013. He is a Fellow of the American Statistical Association and has received the Mathematical Association of America’s Haimo Award for Distinguished College or University Teaching of Mathematics and the ASA’s Waller Distinguished Teaching Career Award.
Jeffrey A. Witmer
Jeff Witmer is Professor of Mathematics at Oberlin College.  He earned a doctorate in statistics from the University of Minnesota in 1983. His scholarly work has been primarily in the areas of Bayesian decision theory and statistics education.  He is a Fellow of the American Statistical Association and served as editor of STATS magazine.  Among the books he has written or co-authored are Activity Based Statistics and Statistics for the Life Sciences.
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