# Statistics: The Art and Science of Learning from Data, 5th edition

Published by Pearson (October 14, 2020) © 2021

**Alan Agresti**University of Florida**Christine A. Franklin**University of Georgia**Bernhard Klingenberg**Williams College

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For courses in introductory statistics.

### The art and science of learning from data

**Statistics, 5th Edition** helps students understand what statistics is all about and learn the right questions to ask when analyzing data, rather than just memorize procedures. It conveys the ideas that have turned statistics into an essential science of modern life, without compromising rigor. Students will stay engaged with the real-world data in the examples and exercises. Based on the authors' belief that it's important for students to learn and analyze both quantitative and categorial data, this text pays greater attention to the analysis of proportions than many other introductory statistics texts.

### Hallmark features of this title

- The authors give
**greater attention to the analysis of proportions than many other introductory statistics texts.**Concepts are introduced first with categorical data, and then with quantitative data. **The****importance of the statistical investigative process**is emphasized in Chapter 1.**Featured examples and exercises**throughout use the most recent data available.- The approach emphasizes
**using interval estimation for inference**with**less reliance on significance testing**, and incorporates the 2016 American Statistical Association's statement on P-values.

### New and updated features of this title

**Integrates the online apps from****ArtofStat.com**into every chapter through multiple screenshots and activities, inviting the user to replicate results using data from the authors' many examples. These apps can be used live in lectures (and together with students) to visualize concepts or carry out analysis, or can be recorded for asynchronous online instructions. Students can download or screenshot results for homework assignments or projects. At the end of each chapter, a**new section on statistical software**describes the functionality of each app used in the chapter.**Streamlined Chapter 1**continues to emphasize the importance of the statistical investigative process and adds an introduction on the opportunities and challenges with Big Data and Data Science, including a discussion of ethical considerations.**A new section on linear transformations**in Chapter 2.**Emphasis on the two descriptive statistics**most likely encountered by students in their daily lives (differences and ratios of proportions) in Section 3.1.**Expanded discussion on multivariate thinking**in Section 3.3.**Significantly expanded coverage of resampling methods,**with a thorough discussion of the bootstrap for one and two-sample problems and for the correlation coefficient, in new Sections 7.3, 8.3, and 10.3.

- Preface

### I: GATHERING AND EXPLORING DATA

- Statistics: The Art and Science of Learning From Data
- 1.1 Using Data to Answer Statistical Questions
- 1.2 Sample Versus Population
- 1.3 Organizing Data, Statistical Software, and the New Field of Data Science

- Chapter Summary
- Chapter Exercises

- Exploring Data With Graphs and Numerical Summaries
- 2.1 Different Types of Data
- 2.2 Graphical Summaries of Data
- 2.3 Measuring the Center of Quantitative Data
- 2.4 Measuring the Variability of Quantitative Data
- 2.5 Using Measures of Position to Describe Variability
- 2.6 Linear Transformations and Standardizing
- 2.7 Recognizing and Avoiding Misuses of Graphical Summaries

- Chapter Summary
- Chapter Exercises

- Exploring Relationships Between Two Variables
- 3.1 The Association Between Two Categorical Variables
- 3.2 The Relationship Between Two Quantitative Variables
- 3.3 Linear Regression: Predicting the Outcome of a Variable
- 3.4 Cautions in Analyzing Associations

- Chapter Summary
- Chapter Exercises

- Gathering Data
- 4.1 Experimental and Observational Studies
- 4.2 Good and Poor Ways to Sample
- 4.3 Good and Poor Ways to Experiment
- 4.4 Other Ways to Conduct Experimental and Nonexperimental Studies

- Chapter Summary
- Chapter Exercises

### II: PROBABILITY, PROBABILITY DISTRIBUTIONS, AND SAMPLING DISTRIBUTIONS

- Probability in Our Daily Lives
- 5.1 How Probability Quantifies Randomness
- 5.2 Finding Probabilities
- 5.3 Conditional Probability
- 5.4 Applying the Probability Rules

- Chapter Summary
- Chapter Exercises

- Random Variables and Probability Distributions
- 6.1 Summarizing Possible Outcomes and Their Probabilities
- 6.2 Probabilities for Bell-Shaped Distributions
- 6.3 Probabilities When Each Observation Has Two Possible Outcomes

- Chapter Summary
- Chapter Exercises

- Sampling Distributions
- 7.1 How Sample Proportions Vary Around the Population Proportion
- 7.2 How Sample Means Vary Around the Population Mean
- 7.3 Using the Bootstrap to Find Sampling Distributions

- Chapter Summary
- Chapter Exercises

### III: INFERENTIAL STATISTICS

- Statistical Inference: Confidence Intervals
- 8.1 Point and Interval Estimates of Population Parameters
- 8.2 Confidence Interval for a Population Proportion
- 8.3 Confidence Interval for a Population Mean
- 8.4 Bootstrap Confidence Intervals

- Chapter Summary
- Chapter Exercises

- Statistical Inference: Significance Tests About Hypotheses
- 9.1 Steps for Performing a Significance Test
- 9.2 Significance Tests About Proportions
- 9.3 Significance Tests About a Mean
- 9.4 Decisions and Types of Errors in Significance Tests
- 9.5 Limitations of Significance Tests
- 9.6 The Likelihood of a Type II Error

- Chapter Summary
- Chapter Exercises

- Comparing Two Groups
- 10.1 Categorical Response: Comparing Two Proportions
- 10.2 Quantitative Response: Comparing Two Means
- 10.3 Comparing Two Groups with Bootstrap or Permutation Resampling
- 10.4 Analyzing Dependent Samples
- 10.5 Adjusting for the Effects of Other Variables

- Chapter Summary
- Chapter Exercises

### IV: ANALYZING ASSOCIATION AND EXTENDED STATISTICAL METHODS

- Analyzing the Association Between Categorical Variables
- 11.1 Independence and Dependence (Association)
- 11.2 Testing Categorical Variables for Independence
- 11.3 Determining the Strength of the Association
- 11.4 Using Residuals to Reveal the Pattern of Association
- 11.5 Fisher’s Exact and Permutation Tests

- Chapter Summary
- Chapter Exercises

- Analyzing the Association Between Quantitative Variables: Regression Analysis
- 12.1 Modeling How Two Variables Are Related
- 12.2 Inference About Model Parameters and the Association
- 12.3 Describing the Strength of Association
- 12.4 How the Data Vary Around the Regression Line
- 12.5 Exponential Regression: A Model for Nonlinearity

- Chapter Summary
- Chapter Exercises

- Multiple Regression
- 13.1 Using Several Variables to Predict a Response
- 13.2 Extending the Correlation and R2 for Multiple Regression
- 13.3 Using Multiple Regression to Make Inferences
- 13.4 Checking a Regression Model Using Residual Plots
- 13.5 Regression and Categorical Predictors
- 13.6 Modeling a Categorical Response

- Chapter Summary
- Chapter Exercises

- Comparing Groups: Analysis of Variance Methods
- 14.1 One-Way ANOVA: Comparing Several Means
- 14.2 Estimating Differences in Groups for a Single Factor
- 14.3 Two-Way ANOVA

- Chapter Summary
- Chapter Exercises

- Nonparametric Statistics
- 15.1 Compare Two Groups by Ranking
- 15.2 Nonparametric Methods for Several Groups and for Matched Pairs

- Chapter Summary
- Chapter Exercises

#### Appendix

#### Answers

#### Index

#### Index of Applications

#### Credits

### About our authors

**Alan Agresti **is Distinguished Professor Emeritus in the Department of Statistics at the University of Florida. He taught statistics there for 38 years, including the development of 3 courses in statistical methods for social science students and 3 courses in categorical data analysis. He is author of more than 100 refereed articles and 6 texts, including **Statistical Methods for the Social Sciences **(Pearson, 5th Edition, 2018) and **An Introduction to Categorical Data Analysis **(Wiley, 3rd Edition, 2019). He is a Fellow of the American Statistical Association and recipient of an Honorary Doctor of Science from De Montfort University in the UK. He has held visiting positions at Harvard University, Boston University, the London School of Economics, and Imperial College and has taught courses or short courses for universities and companies in about 30 countries worldwide. He has also received teaching awards from the University of Florida and an excellence in writing award from John Wiley & Sons.

**Christine Franklin **is the K-12 Statistics Ambassador for the American Statistical Association and elected ASA Fellow. She is retired from the University of Georgia as the Lothar Tresp Honoratus Honors Professor and Senior Lecturer Emerita in Statistics. She is the co-author of 2 textbooks and has published more than 60 journal articles and book chapters. Chris was the lead writer for American Statistical Association **Pre-K-12 Guidelines for the Assessment and Instruction in Statistics Education (GAISE) Framework** document, co-chair for the updated **Pre-K-12 GAISE II,** and chair of the ASA **Statistical Education of Teachers (SET**) report. She is a past Chief Reader for Advanced Placement Statistics, a Fulbright scholar to New Zealand (2015), recipient of the United States Conference on Teaching Statistics (USCOTS) Lifetime Achievement Award, the ASA Founder's award and an elected member of the International Statistical Institute (ISI). Chris loves being with her family, running, hiking, scoring baseball games and reading mysteries.

**Bernhard Klingenberg **is Professor of Statistics in the Department of Mathematics & Statistics at Williams College, where he has been teaching introductory and advanced statistics classes since 2004, and in the Graduate Data Science Program at New College of Florida, where he enjoys teaching statistical inference and modeling as well as data visualization. Bernhard is responsible for the development of the web apps, which he programs using the R package shiny. A native of Austria, Bernhard frequently returns there to hold visiting positions at universities and gives short courses on categorical data analysis in Europe and the United States. He has published several peer-reviewed articles in statistical journals and consults regularly with academia and industry. Bernhard enjoys photography (some of his pictures appear in this book), scuba diving, hiking state parks in Florida, and spending time with his wife and 4 children.

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