Introduction to the Practice

of Statistics

NINTH EDITION

David S. Moore

George P. McCabe

Bruce A. Craig

Purdue University

Vice President, STEM: Ben Roberts

Publisher: Terri Ward

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Printing and Binding: LSC Communications

Cover Illustration: Drawing Water: Spring 2011 detail

(Midwest) by David Wicks

“Look Back” Arrow: NewCorner/Shutterstock

Library of Congress Control Number: 2016946039

Student Edition Hardcover:

ISBN-13: 978-1-319-01338-7

ISBN-10: 1-319-01338-4

Student Edition Loose-leaf:

ISBN-13: 978-1-319-01362-2

ISBN-10: 1-319-01362-7

Instructor Complimentary Copy:

ISBN-13: 978-1-319-01428-5

ISBN-10: 1-319-01428-3

© 2017, 2014, 2012, 2009 by W. H. Freeman and Company

All rights reserved

Printed in the United States of America

First printing

W. H. Freeman and Company

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Brief Contents

To Teachers: About This Book

To Students: What Is Statistics?

About the Authors

Data Table Index

Beyond the Basics Index

PART I Looking at Data

CHAPTER 1 Looking at Data—Distributions

CHAPTER 2 Looking at Data—Relationships

CHAPTER 3 Producing Data

PART II Probability and Inference

CHAPTER 4 Probability: The Study of Randomness

CHAPTER 5 Sampling Distributions

CHAPTER 6 Introduction to Inference

CHAPTER 7 Inference for Means

CHAPTER 8 Inference for Proportions

PART III Topics in Inference

CHAPTER 9 Inference for Categorical Data

CHAPTER 10 Inference for Regression

CHAPTER 11 Multiple Regression

CHAPTER 12 One-Way Analysis of Variance

CHAPTER 13 Two-Way Analysis of Variance

Tables

Answers to Odd-Numbered Exercises

Notes and Data Sources

Index

Contents

To Teachers: About This Book

To Students: What Is Statistics?

About the Authors

Data Table Index

Beyond the Basics Index

PART I Looking at Data

CHAPTER 1 Looking at Data—Distributions

Introduction

1.1 Data

Key characteristics of a data set

Section 1.1 Summary

Section 1.1 Exercises

1.2 Displaying Distributions with Graphs

Categorical variables: Bar graphs and pie charts

Quantitative variables: Stemplots and histograms

Histograms

Data analysis in action: Don’t hang up on me

Examining distributions

Dealing with outliers

Time plots

Section 1.2 Summary

Section 1.2 Exercises

1.3 Describing Distributions with Numbers

Measuring center: The mean

Measuring center: The median

Mean versus median

Measuring spread: The quartiles

The five-number summary and boxplots

The 1.5 × IQR rule for suspected outliers

Measuring spread: The standard deviation

Properties of the standard deviation

Choosing measures of center and spread

Changing the unit of measurement

Section 1.3 Summary

Section 1.3 Exercises

1.4 Density Curves and Normal Distributions

Density curves

Measuring center and spread for density curves

Normal distributions

The 68–95–99.7 rule

Standardizing observations

Normal distribution calculations

Using the standard Normal table

Inverse Normal calculations

Normal quantile plots

Beyond the Basics: Density estimation

Section 1.4 Summary

Section 1.4 Exercises

Chapter 1 Exercises

CHAPTER 2 Looking at Data—Relationships

Introduction

2.1 Relationships

Examining relationships

Section 2.1 Summary

Section 2.1 Exercises

2.2 Scatterplots

Interpreting scatterplots

The log transformation

Adding categorical variables to scatterplots

Scatterplot smoothers

Categorical explanatory variables

Section 2.2 Summary

Section 2.2 Exercises

2.3 Correlation

The correlation r

Properties of correlation

Section 2.3 Summary

Section 2.3 Exercises

2.4 Least-Squares Regression

Fitting a line to data

Prediction

Least-squares regression

Interpreting the regression line

Facts about least-squares regression

Correlation and regression

Another view of r2

Section 2.4 Summary

Section 2.4 Exercises

2.5 Cautions about Correlation and Regression

Residuals

Outliers and influential observations

Beware of the lurking variable

Beware of correlations based on averaged data

Beware of restricted ranges

Beyond the Basics: Data mining

Section 2.5 Summary

Section 2.5 Exercises

2.6 Data Analysis for Two-Way Tables

The two-way table

Joint distribution

Marginal distributions

Describing relations in two-way tables

Conditional distributions

Simpson’s paradox

Section 2.6 Summary

Section 2.6 Exercises

2.7 The Question of Causation

Explaining association

Establishing causation

Section 2.7 Summary

Section 2.7 Exercises

Chapter 2 Exercises

CHAPTER 3 Producing Data

Introduction

3.1 Sources of Data

Anecdotal data

Available data

Sample surveys and experiments

Section 3.1 Summary

Section 3.1 Exercises

3.2 Design of Experiments

Comparative experiments

Randomization

Randomized comparative experiments

How to randomize

Randomization using software

Randomization using random digits

Cautions about experimentation

Matched pairs designs

Block designs

Section 3.2 Summary

Section 3.2 Exercises

3.3 Sampling Design

Simple random samples

How to select a simple random sample

Stratified random samples

Multistage random samples

Cautions about sample surveys

Beyond the Basics: Capture-recapture sampling

Section 3.3 Summary

Section 3.3 Exercises

3.4 Ethics

Institutional review boards

Informed consent

Confidentiality

Clinical trials

Behavioral and social science experiments

Section 3.4 Summary

Section 3.4 Exercises

Chapter 3 Exercises

PART II Probability and Inference

CHAPTER 4 Probability: The Study of Randomness

Introduction

4.1 Randomness

The language of probability

Thinking about randomness

The uses of probability

Section 4.1 Summary

Section 4.1 Exercises

4.2 Probability Models

Sample spaces

Probability rules

Assigning probabilities: Finite number of outcomes

Assigning probabilities: Equally likely outcomes

Independence and the multiplication rule

Applying the probability rules

Section 4.2 Summary

Section 4.2 Exercises

4.3 Random Variables

Discrete random variables

Continuous random variables

Normal distributions as probability distributions

Section 4.3 Summary

Section 4.3 Exercises

4.4 Means and Variances of Random Variables

The mean of a random variable

Statistical estimation and the law of large numbers

Thinking about the law of large numbers

Beyond the Basics: More laws of large numbers

Rules for means

The variance of a random variable

Rules for variances and standard deviations

Section 4.4 Summary

Section 4.4 Exercises

4.5 General Probability Rules

General addition rules

Conditional probability

General multiplication rules

Tree diagrams

Bayes’s rule

Independence again

Section 4.5 Summary

Section 4.5 Exercises

Chapter 4 Exercises

CHAPTER 5 Sampling Distributions

Introduction

5.1 Toward Statistical Inference

Sampling variability

Sampling distributions

Bias and variability

Sampling from large populations

Why randomize?

Section 5.1 Summary

Section 5.1 Exercises

5.2 The Sampling Distribution of a Sample Mean

The mean and standard deviation of x̅

The central limit theorem

A few more facts

Beyond the Basics: Weibull distributions

Section 5.2 Summary

Section 5.2 Exercises

5.3 Sampling Distributions for Counts and Proportions

The binomial distributions for sample counts

Binomial distributions in statistical sampling

Finding binomial probabilities

Binomial mean and standard deviation

Sample proportions

Normal approximation for counts and proportions

The continuity correction

Binomial formula

The Poisson distributions

Section 5.3 Summary

Section 5.3 Exercises

Chapter 5 Exercises

CHAPTER 6 Introduction to Inference

Introduction

Overview of inference

6.1 Estimating with Confidence

Statistical confidence

Confidence intervals

Confidence interval for a population mean

How confidence intervals behave

Choosing the sample size

Some cautions

Section 6.1 Summary

Section 6.1 Exercises

6.2 Tests of Significance

The reasoning of significance tests

Stating hypotheses

Test statistics

P-values

Statistical significance

Tests for a population mean

Two-sided significance tests and confidence intervals

The P-value versus a statement of significance

Section 6.2 Summary

Section 6.2 Exercises

6.3 Use and Abuse of Tests

Choosing a level of significance

What statistical significance does not mean

Don’t ignore lack of significance

Statistical inference is not valid for all sets of data

Beware of searching for significance

Section 6.3 Summary

Section 6.3 Exercises

6.4 Power and Inference as a Decision

Power

Increasing the power

Inference as decision

Two types of error

Error probabilities

The common practice of testing hypotheses

Section 6.4 Summary

Section 6.4 Exercises

Chapter 6 Exercises

CHAPTER 7 Inference for Means

Introduction

7.1 Inference for the Mean of a Population

The t distributions

The one-sample t confidence interval

The one-sample t test

Matched pairs t procedures

Robustness of the t procedures

Beyond the Basics: The bootstrap

Section 7.1 Summary

Section 7.1 Exercises

7.2 Comparing Two Means

The two-sample z statistic

The two-sample t procedures

The two-sample t confidence interval

The two-sample t significance test

Robustness of the two-sample procedures

Inference for small samples

Software approximation for the degrees of freedom

The pooled two-sample t procedures

Section 7.2 Summary

Section 7.2 Exercises

7.3 Additional Topics on Inference

Choosing the sample size

Inference for non-Normal populations

Section 7.3 Summary

Section 7.3 Exercises

Chapter 7 Exercises

CHAPTER 8 Inference for Proportions

Introduction

8.1 Inference for a Single Proportion

Large-sample confidence interval for a single proportion

Beyond the Basics: The plus four confidence interval for a single proportion

Significance test for a single proportion

Choosing a sample size for a confidence interval

Choosing a sample size for a significance test

Section 8.1 Summary

Section 8.1 Exercises

8.2 Comparing Two Proportions

Large-sample confidence interval for a difference in proportions

Beyond the Basics: The plus four confidence interval for a difference in proportions

Significance test for a difference in proportions

Choosing a sample size for two sample proportions

Beyond the Basics: Relative risk

Section 8.2 Summary

Section 8.2 Exercises

Chapter 8 Exercises

PART III Topics in Inference

CHAPTER 9 Inference for Categorical Data

Introduction

9.1 Inference for Two-Way Tables

The hypothesis: No association

Expected cell counts

The chi-square test

Computations

Computing conditional distributions

The chi-square test and the z test

Beyond the Basics: Meta-analysis

Section 9.1 Summary

Section 9.1 Exercises

9.2 Goodness of Fit

Section 9.2 Summary

Section 9.2 Exercises

Chapter 9 Exercises

CHAPTER 10 Inference for Regression

Introduction

10.1 Simple Linear Regression

Statistical model for linear regression

Preliminary data analysis and inference considerations

Estimating the regression parameters

Checking model assumptions

Confidence intervals and significance tests

Confidence intervals for mean response

Prediction intervals

Transforming variables

Beyond the Basics: Nonlinear regression

Section 10.1 Summary

Section 10.1 Exercises

10.2 More Detail about Simple Linear Regression

Analysis of variance for regression

The ANOVA F test

Calculations for regression inference

Inference for correlation

Section 10.2 Summary

Section 10.2 Exercises

Chapter 10 Exercises

CHAPTER 11 Multiple Regression

Introduction

11.1 Inference for Multiple Regression

Population multiple regression equation

Data for multiple regression

Multiple linear regression model

Estimation of the multiple regression parameters

Confidence intervals and significance tests for regression coefficients

ANOVA table for multiple regression

Squared multiple correlation R2

Section 11.1 Summary

Section 11.1 Exercises

11.2 A Case Study

Preliminary analysis

Relationships between pairs of variables

Regression on high school grades

Interpretation of results

Examining the residuals

Refining the model

Regression on SAT scores

Regression using all variables

Test for a collection of regression coefficients

Beyond the Basics: Multiple logistic regression

Section 11.2 Summary

Section 11.2 Exercises

Chapter 11 Exercises

CHAPTER 12 One-Way Analysis of Variance

Introduction

12.1 Inference for One-Way Analysis of Variance

Data for one-way ANOVA

Comparing means

The two-sample t statistic

An overview of ANOVA

The ANOVA model

Estimates of population parameters

Testing hypotheses in one-way ANOVA

The ANOVA table

The F test

Software

Beyond the Basics: Testing the equality of spread

Section 12.1 Summary

Section 12.1 Exercises

12.2 Comparing the Means

Contrasts

Multiple comparisons

Power

Section 12.2 Summary

Section 12.2 Exercises

Chapter 12 Exercises

CHAPTER 13 Two-Way Analysis of Variance

Introduction

13.1 The Two-Way ANOVA Model

Advantages of two-way ANOVA

The two-way ANOVA model

Main effects and interactions

13.2 Inference for Two-Way ANOVA

The ANOVA table for two-way ANOVA

Chapter 13 Summary

Chapter 13 Exercises

Tables

Answers to Odd-Numbered Exercises

Notes and Data Sources

Index

To Teachers: About This Book

Statistics is the science of data. Introduction to the Practice of Statistics (IPS) is an introductory text based on this

principle. We present methods of basic statistics in a way that emphasizes working with data and mastering statistical

reasoning. IPS is elementary in mathematical level but conceptually rich in statistical ideas. After completing a course

based on our text, we would like students to be able to think objectively about conclusions drawn from data and use

statistical methods in their own work.

In IPS, we combine attention to basic statistical concepts with a comprehensive presentation of the elementary

statistical methods that students will find useful in their work. IPS has been successful for several reasons:

1. IPS examines the nature of modern statistical practice at a level suitable for beginners. We focus on the

production and analysis of data as well as the traditional topics of probability and inference.

2. IPS has a logical overall progression, so data production and data analysis are a major focus, while inference is

treated as a tool that helps us draw conclusions from data in an appropriate way.

3. IPS presents data analysis as more than a collection of techniques for exploring data. We emphasize systematic

ways of thinking about data. Simple principles guide the analysis: always plot your data; look for overall patterns

and deviations from them; when looking at the overall pattern of a distribution for one variable, consider shape,

center, and spread; for relations between two variables, consider form, direction, and strength; always ask

whether a relationship between variables is influenced by other variables lurking in the background. We warn

students about pitfalls in clear cautionary discussions.

4. IPS uses real examples to drive the exposition. Students learn the technique of least-squares regression and how

to interpret the regression slope. But they also learn the conceptual ties between regression and correlation and

the importance of looking for influential observations.

5. IPS is aware of current developments both in statistical science and in teaching statistics. Brief, optional Beyond

the Basics sections give quick overviews of topics such as density estimation, scatterplot smoothers, data mining,

nonlinear regression, and meta-analysis. Chapter 16 gives an elementary introduction to the bootstrap and other

computer-intensive statistical methods.

The title of the book expresses our intent to introduce readers to statistics as it is used in practice. Statistics in

practice is concerned with drawing conclusions from data. We focus on problem solving rather than on methods that

may be useful in specific settings.

GAISE The College Report of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) Project

(www.amstat.org/education/gaise/) was funded by the American Statistical Association to make recommendations for

how introductory statistics courses should be taught. This report and its update contain many interesting teaching

suggestions, and we strongly recommend that you read it. The philosophy and approach of IPS closely reflect the

GAISE recommendations. Let’s examine each of the latest recommendations in the context of IPS.

1. Teach statistical thinking. Through our experiences as applied statisticians, we are very familiar with the

components that are needed for the appropriate use of statistical methods. We focus on formulating questions,

collecting and finding data, evaluating the quality of data, exploring the relationships among variables,

performing statistical analyses, and drawing conclusions. In examples and exercises throughout the text, we

emphasize putting the analysis in the proper context and translating numerical and graphical summaries into

conclusions.

2. Focus on conceptual understanding. With the software available today, it is very easy for almost anyone to apply

a wide variety of statistical procedures, both simple and complex, to a set of data. Without a firm grasp of the

concepts, such applications are frequently meaningless. By using the methods that we present on real sets of data,

we believe that students will gain an excellent understanding of these concepts. Our emphasis is on the input

(questions of interest, collecting or finding data, examining data) and the output (conclusions) for a statistical

analysis. Formulas are given only where they will provide some insight into concepts.

3. Integrate real data with a context and a purpose. Many of the examples and exercises in IPS include data that we

have obtained from collaborators or consulting clients. Other data sets have come from research related to these

activities. We have also used the Internet as a data source, particularly for data related to social media and other

topics of interest to undergraduates. Our emphasis on real data, rather than artificial data chosen to illustrate a

http://www.amstat.org/education/gaise/

calculation, serves to motivate students and help them see the usefulness of statistics in everyday life. We also

frequently encounter interesting statistical issues that we explore. These include outliers and nonlinear

relationships. All data sets are available from the text website.

4. Foster active learning in the classroom. As we mentioned earlier, we believe that statistics is exciting as

something to do rather than something to talk about. Throughout the text, we provide exercises in Use Your

Knowledge sections that ask the students to perform some relatively simple tasks that reinforce the material just

presented. Other exercises are particularly suited to being worked on and discussed within a classroom setting.

5. Use technology for developing concepts and analyzing data. Technology has altered statistical practice in a

fundamental way. In the past, some of the calculations that we performed were particularly difficult and tedious.

In other words, they were not fun. Today, freed from the burden of computation by software, we can concentrate

our efforts on the big picture: what questions are we trying to address with a study and what can we conclude

from our analysis?

6. Use assessments to improve and evaluate student learning. Our goal for students who complete a course based

on IPS is that they are able to design and carry out a statistical study for a project in their capstone course or

other setting. Our exercises are oriented toward this goal. Many ask about the design of a statistical study and the

collection of data. Others ask for a paragraph summarizing the results of an analysis. This recommendation

includes the use of projects, oral presentations, article critiques, and written reports. We believe that students

using this text will be well prepared to undertake these kinds of activities. Furthermore, we view these activities

not only as assessments but also as valuable tools for learning statistics.

Teaching Recommendations We have used IPS in courses taught to a variety of student audiences. For general

undergraduates from mixed disciplines, we recommend covering Chapters 1 through 8 and Chapters 9, 10, or 12. For a

quantitatively strong audience—sophomores planning to major in actuarial science or statistics—we recommend

moving more quickly. Add Chapters 10 and 11 to the core material in Chapters 1 through 8. In general, we recommend

deemphasizing the material on probability because these students will take a probability course later in their program.

For beginning graduate students in such fields as education, family studies, and retailing, we recommend that the

students read the entire text (Chapters 11 and 13 lightly), again with reduced emphasis on Chapter 4 and some parts of

Chapter 5. In all cases, beginning with data analysis and data production (Part I) helps students overcome their fear of

statistics and builds a sound base for studying inference. We believe that IPS can easily be adapted to a wide variety of

audiences.

The Ninth Edition: What’s New?

Chapter 1 now begins with a short section giving an overview of data.

“Toward Statistical Inference” (previously Section 3.3), which introduces the concepts of statistical inference and

sampling distributions, has been moved to Section 5.1 to better assist with the transition from a single data set to

sampling distributions.

Coverage of mosaic plots as a visual tool for relationships between two categorical variables has been added to

Chapters 2 and 9.

Chapter 3 now begins with a short section giving a basic overview of data sources.

Coverage of equivalence testing has been added to Chapter 7.

There is a greater emphasis on sample size determination using software in Chapters 7 and 8.

Resampling and bootstrapping are now introduced in Chapter 7 rather than Chapter 6.

“Inference for Categorical Data” is the new title for Chapter 9, which includes goodness of fit as well as

inference for two-way tables.

There are more JMP screenshots and updated screenshots of Minitab, Excel, and SPSS outputs.

Design A new design incorporates colorful, revised figures throughout to aid the students’ understanding of text

material. Photographs related to chapter examples and exercises make connections to real-life applications and

provide a visual context for topics. More figures with software output have been included.

Exercises and Examples More than 30% of the exercises are new or revised, and there are more than 1700

exercises total. Exercise sets have been added at the end of sections in Chapters 9 through 12. To maintain the

attractiveness of the examples to students, we have replaced or updated a large number of them. More than 30%

of the 430 examples are new or revised. A list of exercises and examples categorized by application area is

provided on the inside of the front cover.

In addition to the new ninth edition enhancements, IPS has retained the successful pedagogical features from previous

editions:

Look Back At key points in the text, Look Back margin notes direct the reader to the first explanation of a topic,

providing page numbers for easy reference.

Caution Warnings in the text, signaled by a caution icon, help students avoid common errors and

misconceptions.

Challenge Exercises More challenging exercises are signaled with an icon. Challenge exercises are varied: some

are mathematical, some require open-ended investigation, and others require deeper thought about the basic

concepts.

Applets Applet icons are used throughout the text to signal where related interactive statistical applets can be

found on the IPS website and in LaunchPad.

Use Your Knowledge Exercises We have found these exercises to be a very useful learning tool. They appear

throughout each section and are listed, with page numbers, before the section-ending exercises.

Technology output screenshots Most statistical analyses rely heavily on statistical software. In this book, we

discuss the use of Excel 2013, JMP 12, Minitab 17, SPSS 23, CrunchIt, R, and a TI-83/-84 calculator for

conducting statistical analysis. As specialized statistical packages, JMP, Minitab, and SPSS are the most popular

software choices both in industry and in colleges and schools of business. R is an extremely powerful statistical

environment that is free to anyone; it relies heavily on members of the academic and general statistical

communities for support. As an all-purpose spreadsheet program, Excel provides a limited set of statistical

analysis options in comparison. However, given its pervasiveness and wide acceptance in industry and the

computer world at large, we believe it is important to give Excel proper attention. It should be noted that for

users who want more statistical capabilities but want to work in an Excel environment, there are a number of

commercially available add-on packages (if you have JMP, for instance, it can be invoked from within Excel).

Finally, instructions are provided for the TI-83/-84 calculators.

Even though basic guidance is provided in the book, it should be emphasized that IPS is not bound to any of these

programs. Computer output from statistical packages is very similar, so you can feel quite comfortable using any one

these packages.

Acknowledgments

We are pleased that the first eight editions of Introduction to the Practice of Statistics have helped to move the teaching

of introductory statistics in a direction supported by most statisticians. We are grateful to the many colleagues and

students who have provided helpful comments, and we hope that they will find this new edition another step forward.

In particular, we would like to thank the following colleagues who offered specific comments on the new edition:

Ali Arab, Georgetown University

Tessema Astatkie, Dalhousie University

Fouzia Baki, McMaster University

Lynda Ballou, New Mexico Institute of Mining and Technology

Sanjib Basu, Northern Illinois University

David Bosworth, Hutchinson Community College

Max Buot, Xavier University

Nadjib Bouzar, University of Indianapolis

Matt Carlton, California Polytechnic State University–San Luis Obispo

Gustavo Cepparo, Austin Community College

Pinyuen Chen, Syracuse University

Dennis L. Clason, University of Cincinnati–Blue Ash College

Tadd Colver, Purdue University

Chris Edwards, University of Wisconsin–Oshkosh

Irina Gaynanova, Texas A&M University

Brian T. Gill, Seattle Pacific University

Mary Gray, American University

Gary E. Haefner, University of Cincinnati

Susan Herring, Sonoma State University

Lifang Hsu, Le Moyne College

Tiffany Kolba, Valparaiso University

Lia Liu, University of Illinois at Chicago

Xuewen Lu, University of Calgary

Antoinette Marquard, Cleveland State University

Frederick G. Schmitt, College of Marin

James D. Stamey, Baylor University

Engin Sungur, University of Minnesota–Morris

Anatoliy Swishchuk, University of Calgary

Richard Tardanico, Florida International University

Melanee Thomas, University of Calgary

Terri Torres, Oregon Institute of Technology

Mahbobeh Vezvaei, Kent State University

Yishi Wang, University of North Carolina–Wilmington

John Ward, Jefferson Community and Technical College

Debra Wiens, Rocky Mountain College

Victor Williams, Paine College

Christopher Wilson, Butler University

Anne Yust, Birmingham-Southern College

Biao Zhang, The University of Toledo

Michael L. Zwilling, University of Mount Union

The professionals at Macmillan, in particular, Terri Ward, Karen Carson, Jorge Amaral, Emily Tenenbaum, Ed

Dionne, Blake Logan, and Susan Wein, have contributed greatly to the success of IPS. In addition, we would like to

thank Tadd Colver at Purdue University for his valuable contributions to the ninth edition, including authoring the

back-of-book answers, solutions, and Instructor’s Guide. We’d also like to thank Monica Jackson at American

University for accuracy reviewing the back-of-book answers and solutions and for authoring the test bank. Thanks also

to Michael Zwilling at University of Mount Union for accuracy reviewing the test bank, Christopher Edwards at

University of Wisconsin Oshkosh for authoring the lecture slides, and James Stamey at Baylor University for authoring

the Clicker slides.

Most of all, we are grateful to the many friends and collaborators whose data and research questions have enabled

us to gain a deeper understanding of the science of data. Finally, we would like to acknowledge the contributions of

John W. Tukey, whose contributions to data analysis have had such a great influence on us as well as a whole

generation of applied statisticians.

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