STAT2

Modeling with Regression and ANOVA

Second Edition

Publication Date: December 16, 2019

Hardcover ISBN: 9781319054076

Pages: 624

The unifying theme of this text is the use of models in statistical data analysis.

Now available with Macmillan’s online learning platform Achieve Essentials, STAT2 introduces students to statistical modeling beyond what they have learned in a Stat 101 college course or an AP Statistics course. Building on basic concepts and methods learned in that course, STAT2 empowers students to analyze richer datasets that include more variables and address a broader range of research questions.

Other than a working understanding of exponential and logarithmic functions, there are no prerequisites beyond successful completion of their first statistics course. To help all students make a smooth transition to this course, Chapter 0 reminds students of basic statistical terminology and also uses the familiar two-sample t-test as a way to illustrate the approach of specifying, estimating, and testing a statistical model.

Using STAT2, students will:

Go beyond their Stat 101 experience by learning to develop and apply models with both quantitative and categorical response variables, and with multiple explanatory variables. STAT2 Chapters are grouped into units that consider models based on the type of response and type of predictors.
Discover that the practice of statistical modeling involves applying an interactive process. STAT2 employs a four-step process in all statistical modeling: Choose a form for the model, fit the model to the data, assess how well the model describes the data, and use the model to address the question of interest.
Learn how to apply their developing judgment about statistical modeling. STAT2 introduces the idea of constructing statistical models at the very beginning, in a setting that students encountered in their Stat 101 course. This modeling focus continues throughout the course as students encounter new and increasingly more complicated scenarios.
Analyze and draw conclusions from real data, which is crucial for preparing students to use statistical modeling in their professional lives. STAT2 incorporates real and rich data throughout the text. Using real data to address genuine research questions helps motivate students to study statistics. The richness stems not only from interesting contexts in a variety of disciplines, but also from the multivariable nature of most datasets.

Achieve Essentials for Stat2 connects the problem-solving techniques and real world examples in the book to rich digital resources that foster further understanding and application of statistics. Assets in Achieve Essentials support learning before, during, and after class for students, while providing instructors with class performance analytics in an easy-to-use interface.

The unifying theme of this text is the use of models in statistical data analysis.

Using STAT2, students will:

Go beyond their Stat 101 experience by learning to develop and apply models with both quantitative and categorical response variables, and with multiple explanatory variables. STAT2 Chapters are grouped into units that consider models based on the type of response and type of predictors.
Discover that the practice of statistical modeling involves applying an interactive process. STAT2 employs a four-step process in all statistical modeling: Choose a form for the model, fit the model to the data, assess how well the model describes the data, and use the model to address the question of interest.
Learn how to apply their developing judgment about statistical modeling. STAT2 introduces the idea of constructing statistical models at the very beginning, in a setting that students encountered in their Stat 101 course. This modeling focus continues throughout the course as students encounter new and increasingly more complicated scenarios.
Analyze and draw conclusions from real data, which is crucial for preparing students to use statistical modeling in their professional lives. STAT2 incorporates real and rich data throughout the text. Using real data to address genuine research questions helps motivate students to study statistics. The richness stems not only from interesting contexts in a variety of disciplines, but also from the multivariable nature of most datasets.

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Data Set files needed to complete exercises and examples in the book can be downloaded from the open-access student companion website. Data Sets are available in Excel, CSV, Minitab, R, JMP, TI, SPSS, PC-Text, and Mac-Text formats.

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

Achieve Online Homework

Over 3,000 homework questions of varying difficulty, Bloom’s level, and question type. Every homework question includes a hint, answer-specific feedback, and a fully worked solution. Question types in Achieve include

Multiple choice
Ranking
Sorting
Numeric entry
Multi-part questions
Questions with algorithmically regenerating values

LearningCurve adaptive quizzing puts the concept of "testing to learn" into action, motivating students to engage with the texts content to identify areas of proficiency. Easy-to-use reporting tools help teachers pinpoint areas to focus on in class.
A mobile, interactive e-book, powered by VitalSource, allows students to highlight and take notes, print select pages, and have the text read aloud to them.
R Markdown files demonstrate how to solve selected data-driven exercises from the book using R.

Statistical software options

CrunchIt!, Macmillan’s proprietary online statistical software powered by R, handles every computation and graphing function an introductory statistics student needs. CrunchIt! is preloaded with data sets, and it allows editing and importing additional data.
Students also receive access to JMP Student Edition (developed by SAS). With the student edition of JMP, students handle large data, visualizations, and analysis for which the professional version is renowned. Additionally, text-specific data sets are included for download.
For other statistical software, Achieve includes data sets, including those for

Excel
Minitab
R & RCmdr
SPSS
TI Calculators
Mac-text & PC-text
CSV file export

In the text
Flexibility Within and Between Units

The units and chapters are arranged to promote flexibility regarding order and depth in which topics are covered. Within a unit, some instructors may choose to “splice” in an additional topic when related ideas are first introduced. For example, Section 5.7 in the first ANOVA chapter introduces techniques for conducting pairwise comparisons with one-way ANOVA using Fisher’s LSD method. Instructors who prefer a more thorough discussion of pairwise comparison issues at this point, including alternate techniques such as the Bonferroni adjustment or Tukey’s HSD method, can proceed to present those ideas from Topic 8.2. Other instructors might want to move immediately to two-way ANOVA in Chapter 6 and then study pairwise procedures later.
Instructors can also adjust the order of topics between the units. For example, some might prefer to consider logistic regression models (Unit C) before studying ANOVA models (Unit B). Others might choose to study all three types of models in the “simple setting” (Chapters 1–2, 5, 9), and then return to consider each type of model with multiple predictors. One could also move to the ANOVA material in Unit B directly after starting with a review of the two-sample t-test for means in Chapter 0 and simple linear regression in Chapters 1 and 2.

Exercises

Developing skills of statistical modeling requires considerable practice working with real data. Homework exercises are an important component of this book and appear at the end of each chapter. These exercises are grouped into four categories:

Conceptual exercises. These questions are brief and require minimal (if any) calculations. They give students practice with applying basic terminology and assess students’ understanding of concepts introduced in the chapter.
Guided exercises. These exercises ask students to perform various stages of a modeling analysis process by providing specific prompts for the individual steps.
Open-ended exercises. These exercises ask for more complete analyses and reporting of conclusions, without much or any step-by-step direction.
Supplemental exercises. Topics for these exercises go somewhat beyond the scope of the material covered in the chapter.

Exercises in the Additional Topics chapters (4, 8, and 11) are grouped to align with the independent topics in those chapters.

New statistical topics. Two topics that were requested most consistently from first edition users were repeated measures designs and time series. We have added new material (Topic 8.6) to give a brief introduction to repeated measures designs and for instructors who want more depth in this topic, we have included three more sections in the online material. We have also added Chapter 12, giving a brief introduction to working with time series data. In addition to these new sections and chapters, we have made numerous changes to include new ideas (e.g., effect sizes) and give more guidance to students (e.g., choosing a transformation).
New organization. We reorganized the material in Unit B to better integrate ideas of experimental design with the topics of ANOVA. Chapter 6 now focuses on block designs and the additive ANOVA model, with interaction coming in Chapter 7, and additional ANOVA topics in Chapter 8.
New exercises and examples. The second edition has 243 worked examples and 646 exercises for students, increases of 76% and 63% over the first edition. We have also updated and revised almost 100 examples and exercises that are carried over from the first edition.
New datasets. We have 64 new datasets dealing with real data, many from research studies. We have also updated datasets from the first edition to bring the total dataset count to 172. Datasets are available in various formats for different software packages and a data index after the general index lists all datasets and where they are used in the text.
New design. A new, full-color design incorporates all-new figures, charts, and graphs. In addition, important definitions and explanations are highlighted for emphasis. Our goal in creating this design was to make the reading and learning experience more approachable by instructors and students alike.

NEW PEDAGOGICAL FEATURES

Chapter opening section lists give an at-a-glance look at the content therein.
Learning objectives outline goals and expectations that help instructors create their syllabi and students understand where they’re headed.
Caution icons and text signal common misconceptions and important ideas to help the student avoid pitfalls and grasp key concepts.
Data icons highlight the data set in use for each example and exercise.
Key terms are highlighted in the margins to help students build a solid statistics vocabulary.

An approachable text with interesting and varied examples that demonstrates how statisticians approach data analysis. KB Boomer, Bucknell University

This book is consistent with the goals and recommendations of GAISE. It fits with my personal teaching philosophy, and it more than sufficiently covers all of the material needed in my course. It is well written, accessible to undergraduate non-majors, and contains up-to-date, engaging examples. Margaret Bryan, U Missouri - Columbia

This is THE BEST book as a second course for non-technical majors. I use it for undergraduates and graduates. The fact that it covers the main facets of applied statistics (regression, anova, and logistic) without a bunch of other topics that are not used much is a plus. Linda Clark, Central CT State

Very readable but not at too low a level. It is a wonderful approach to topics that we never have time for in a first statistics course. It allows the instructor to focus on a variety of topics, in different orders. Julie Clark, Hollins U

A wonderful text for courses that follow an introductory statistics course. There is a wealth of material that is accessible and is presented in a manner that is interesting and makes sense. Important ideas of model assumptions are stressed (never glossed over) and the data is all real-world. This text explains how a scientist in any field might actually use statistical ideas in his/her work. Julie Clark, Hollins U.

A gentle, well-written, introduction to regression (and ANOVA/design and categorical data analysis) with plenty of examples and loads of exercises with interesting data. Linda Brant Collins, U. Chicago

A very clear and thorough introduction to some traditionally tough concepts for students to grasp. I think a student could actually go out and conduct a statistical analysis after learning from this text. Leslie Hendrix, U. of South Carolina

It covers all the essential topics in regression without getting tangled up in the mathematics and focuses on the use and interpretation of data.
A wonderful text for courses that follow an introductory statistics course. There is a wealth of material that is accessible and is presented in a manner that is interesting and makes sense. Important ideas of model assumptions are stressed (never glossed over) and the data is all real-world. This text explains how a scientist in any field might actually use statistical ideas in his/her work. Elizabeth Johnson, George Mason U.

STAT2 simultaneously teaches students about the practice of analyzing data and the reasons the analysis works. Students using the text will come away with both practical skills and a solid understanding. I wouldnt want to teach out of any other book. Dominic Klyve, Central WA U.

STAT2: Why bother with any other book? Dominic Klyve, Central WA U.

This is an excellent book for students who are coming out of an AP Stat (or equivalent) course. It will solidify the foundation of students who are looking to take more than one or two statistics courses. Chris Lacke, Rowan U.

STAT2 is a very applied undergraduate statistics text that covers regression and ANOVA and offers a lot of flexibility in what topics you can cover and in the amount of detail you wish to present to your students. Wilmina Magret, John Carroll U.

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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