Reasoning with Data

An Introduction to Traditional and Bayesian Statistics Using R

Jeffrey M. Stanton

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Engaging and accessible, this book teaches readers how to use inferential statistical thinking to check their assumptions, assess evidence about their beliefs, and avoid overinterpreting results that may look more promising than they really are. It provides step-by-step guidance for using both classical (frequentist) and Bayesian approaches to inference. Statistical techniques covered side by side from both frequentist and Bayesian approaches include hypothesis testing, replication, analysis of variance, calculation of effect sizes, regression, time series analysis, and more. Students also get a complete introduction to the open-source R programming language and its key packages. Throughout the text, simple commands in R demonstrate essential data analysis skills using real-data examples. The companion website provides annotated R code for the book's examples, in-class exercises, supplemental reading lists, and links to online videos, interactive materials, and other resources.

Pedagogical Features

“Written with students and scholars in mind, this text is informative, reader-friendly, and, yes, enjoyable….Stanton emphasizes concepts, not formulas, and promotes hands-on examples. His timely introduction and coverage of the open-source R programming language for statistical data analysis is another strength of this text….This volume will be an invaluable addition to both undergraduate and graduate collections. Highly recommended. Upper-division undergraduates through faculty and professionals.”

Choice Reviews


Reasoning with Data takes a careful and principled approach to guiding readers gracefully from the traditional moorings of frequentist statistics into Bayesian analyses and the functionality and frontiers of the R platform. Stanton provides a range of clear explanations, examples, and practice exercises, fueled by his unbounded enthusiasm and rock-solid expertise. This book is an indispensable resource for undergraduate and graduate students across disciplines—as well as researchers—who want to extend their thinking and their research into where the future is headed.”

—Frederick L. Oswald, PhD, Department of Psychology, Rice University


“Offering an up-to-date and refreshing approach, this is a highly useful guide to the statistics our students will be using today, including Bayesian reasoning. Rather than providing an array of equations to memorize, the emphasis is on building conceptual knowledge. The equations that are provided are essential for understanding how to reason with statistics. I plan to use this book as as the text for the first in the series of statistical courses required for our doctoral students in education. It also would be appropriate for advanced undergraduates or anyone who wants to begin to use R. The book has a good focus on Bayesian inference, which is not covered consistently in stats courses, but is critical for the kinds of complex data we use in education and psychology.”

—Carol McDonald Connor, PhD, Chancellor's Professor, School of Education, University of California, Irvine


“What do R and traditional and Bayesian statistics have in common? They allow us to answer questions that are important for science and practice. Stanton has produced a wonderful book that will be useful for students as well as established scholars.”

—Herman Aguinis, PhD, Avram Tucker Distinguished Scholar and Professor of Management, George Washington University School of Business


“This may be an uncommon thing to say about a book on statistics, but Reasoning with Data is enjoyable and entertaining—really! Stanton takes the reader on an experiential hands-on tour of random sampling, statistical inference, and drawing conclusions from numerical results. The concreteness of the presentation and examples will make it easy for the reader to intuitively grasp the fundamental concepts. The book is very timely because both Bayesian inference and R are becoming 'must-have' tools for social and behavioral scientists. At the same time, Stanton provides a solid grounding in the historical approach of null hypothesis significance testing, including both its strengths and weaknesses. This text should have a very wide audience, and would be appropriate as an upper-level undergraduate or entry-level graduate statistics text in any of the social sciences.”

—Emily A. Butler, PhD, Family Studies and Human Development, University of Arizona

Table of Contents

Introduction

Getting Started

1. Statistical Vocabulary

Descriptive Statistics

Measures of Central Tendency

Measures of Dispersion

Distributions and Their Shapes

Conclusion

Exercises

2. Reasoning with Probability

Outcome Tables

Contingency Tables

Conclusion

Exercises

3. Probabilities in the Long Run

Sampling

Repetitious Sampling with R

Using Sampling Distributions and Quantiles to Think about Probabilities

Conclusion

Exercises

4. Introducing the Logic of Inference Using Confidence Intervals

Exploring the Variability of Sample Means with Repetitious Sampling

Our First Inferential Test: The Confidence Interval

Conclusion

Exercises

5. Bayesian and Traditional Hypothesis Testing

The Null Hypothesis Significance Test

Replication and the NHST

Conclusion

Exercises

6. Comparing Groups and Analyzing Experiments

Frequentist Approach to ANOVA

Bayesian Approach to ANOVA

Finding an Effect

Conclusion

Exercises

7. Associations between Variables

Inferential Reasoning about Correlation

Null Hypothesis Testing on the Correlation

Bayesian Tests on the Correlation Coefficient

Categorical Associations

Exploring the Chi-Square Distribution with a Simulation

The Chi-Square Test with Real Data

Bayesian Approach to Chi-Square Test

Conclusion

Exercises

8. Linear Multiple Regression

Bayesian Approach to Linear Regression

A Linear Regression Model with Real Data

Conclusion

Exercises

9. Interactions in ANOVA and Regression

Interactions in ANOVA

Interactions in Multiple Regression

Bayesian Analysis of Regression Interactions

Conclusion

Exercises

10. Logistic Regression

A Logistic Regression Model with Real Data

Bayesian Estimation of Logistic Regression

Conclusion

Exercises

11. Analyzing Change over Time

Repeated Measures Analysis

Time-Series Analysis

Exploring a Time Series with Real Data

Finding Change Points in Time Series

Probabilities in Change-Point Analysis

Conclusion

Exercises

12. Dealing with Too Many Variables

Internal Consistency Reliability

Rotation

Conclusion

Exercises

13. All Together Now

The Big Picture

Appendix A. Getting Started with R

Running R and Typing Commands

Installing Packages

Quitting, Saving, and Restoring

Conclusion

Appendix B. Working with Data Sets in R

Data Frames in R

Reading Data Frames from External Files

Appendix C. Using dplyr with Data Frames

References

Index


About the Author

Jeffrey M. Stanton, PhD, is Associate Provost for Academic Affairs and Professor in the School of Information Studies at Syracuse University. Dr. Stanton's interests center on research methods, psychometrics, and statistics, with a particular focus on self-report techniques, such as surveys. He has conducted research on a variety of substantive topics in organizational psychology, including the interactions of people and technology in institutional contexts. He is the author of numerous scholarly articles and several books, including Information Nation: Education and Careers in the Emerging Information Professions and The Visible Employee: Using Workplace Monitoring and Surveillance to Protect Information Assets—Without Compromising Employee Privacy or Trust. Dr. Stanton’s background also includes more than a decade of experience in business, both in established firms and startup companies.

Audience

Students and instructors in psychology, human development, education, sociology, public health, communication, and management; applied researchers who want to refresh their skills.

Course Use

Serves as a text in advanced undergraduate- or beginning graduate-level courses in inferential or applied statistics.