70 statistics for social understanding with stata and SPSS rowman littlefield publishers (2019)

STATISTICS
for
SOCIAL
UNDERSTANDING
With Stata and SPSS

NANCY WHITTIER

Smith College
TINA WILDHAGEN

Smith College
HOWARD J. GOLD

Smith College

Lanham • Boulder • New York • London


Executive Editor: Nancy Roberts
Assistant Editor: Megan Manzano
Senior Marketing Manager: Amy Whitaker
Interior Designer: Integra Software Services Pvt. Ltd.
Credits and acknowledgments for material borrowed from other sources, and
reproduced with permission, appear on the appropriate page within the text.
Published by Rowman & Littlefield
An imprint of The Rowman & Littlefield Publishing Group, Inc.
4501 Forbes Boulevard, Suite 200, Lanham, Maryland 20706
www.rowman.com
6 Tinworth Street, London SE11 5AL, United Kingdom

Copyright © 2020 by The Rowman & Littlefield Publishing Group, Inc.
All rights reserved. No part of this book may be reproduced in any form or by
any electronic or mechanical means, including information storage and retrieval
systems, without written ­permission from the publisher, except by a reviewer
who may quote passages in a review.
British Library Cataloguing in Publication Information Available
Library of Congress Cataloging-in-Publication Data
Names: Whittier, Nancy, 1966– author. | Wildhagen, Tina, 1980– author. |
Gold, Howard J., 1958– author.
Title: Statistics for social understanding: with Stata and SPSS / Nancy ­Whitter
(Smith College), Tina Wildhagen (Smith College), Howard J. Gold
(Smith ­College).
Description: Lanham : Rowman & Littlefield, [2020] | Includes bibliographical
references and index.
Identifiers: LCCN 2018043885 (print) | LCCN 2018049835 (ebook) |
ISBN 9781538109847 (electronic) | ISBN 9781538109823 (cloth : alk. paper) |
ISBN 9781538109830 (pbk. : alk. paper)
Subjects: LCSH: Statistics. | Social sciences—Statistical methods. | Stata.
Classification: LCC QA276.12 (ebook) | LCC QA276.12 .W5375 2020 (print) |
DDC 519.5—dc23
LC record available at />∞ ™ The paper used in this publication meets the minimum requirements of

American National Standard for Information Sciences—Permanence of Paper
for Printed Library Materials, ANSI/NISO Z39.48-1992.
Printed in the United States of America


Brief Contents

Preface viii

About the Authors  xvi
CHAPTER 1

Introduction 1

CHAPTER 2

Getting to Know Your Data  54

CHAPTER 3

Examining Relationships between Two Variables  121

CHAPTER 4

Typical Values in a Group  161

CHAPTER 5

The Diversity of Values in a Group  203

CHAPTER 6

Probability and the Normal Distribution  241

CHAPTER 7

From Sample to Population  280

CHAPTER 8

Estimating Population Parameters  314

CHAPTER 9

Differences between Samples and Populations  356

CHAPTER 10 Comparing Groups  399
CHAPTER 11 Testing Mean Differences among Multiple Groups  435
CHAPTER 12 T
 esting the Statistical Significance of Relationships in
Cross-Tabulations 463
CHAPTER 13 R
 uling Out Competing Explanations for Relationships
between Variables  501
CHAPTER 14 Describing Linear Relationships between Variables  542
SOLUTIONS TO ODD-NUMBERED PRACTICE PROBLEMS 599
GLOSSARY 649
APPENDIX A Normal Table  656
APPENDIX B Table of t-Values  658
APPENDIX C F-Table, for Alpha = .05  660
APPENDIX D Chi-Square Table  662
APPENDIX E Selected List of Formulas  664
APPENDIX F Choosing Tests for Bivariate Relationships  666
INDEX 667

iii


Contents

Preface viii
About the Authors  xvi

CHAPTER 1  Introduction 1
Why Study Statistics?  1
Research Questions and the Research
Process 3
Pinning Things Down: Variables and
Measurement 4
Units of Analysis  6
Measurement Error: Validity and Reliability  6
Levels of Measurement  9
Causation: Independent and Dependent
Variables 11
Getting the Data: Sampling and
Generalizing 12
Sampling Methods  13

Sources of Secondary Data: Existing Data
Sets, Reports, and “Big Data”  15
Big Data  17

Growth Mindset and Math Anxiety  18
Using This Book  20
Statistical Software  21
Chapter Summary  23
Using Stata  25
Using SPSS  33
Practice Problems  45

Notes 52

CHAPTER 2  Getting to Know Your
Data 54
Frequency Distributions  55
Percentages and Proportions  57
Cumulative Percentage and Percentile  60

iv

Percent Change  62
Rates and Ratios  63
Rates 63
Ratios 65

Working with Frequency Distribution
Tables 65
Missing Values  65
Simplifying Tables by Collapsing
Categories 67

Graphical Displays of a Single Variable:
Bar Graphs, Pie Charts, Histograms,
Stem-and-Leaf Plots, and Frequency
Polygons 69
Bar Graphs and Pie Charts  69
Histograms 72
Stem-and-Leaf-Plots 73
Frequency Polygons  75

Time Series Charts  76
Comparing Two Groups on the Same
Variable Using Tables, Graphs, and
Charts 77
Chapter Summary  84
Using Stata  85
Using SPSS  95
Practice Problems  109
Notes 120

CHAPTER 3  Examining Relationships
between Two Variables  121
Cross-Tabulations and Relationships
between Variables  122
Independent and Dependent Variables  123
Column, Row, and Total Percentages  127

Interpreting the Strength of
Relationships 134


Contents

Interpreting the Direction of
Relationships 136
Graphical Representations of Bivariate
Relationships 140
Chapter Summary  142
Using Stata  143
Using SPSS  147

Practice Problems  152
Notes 160

CHAPTER 4  Typical Values in a
Group 161
What Does It Mean to Describe What Is
Typical? 162
Mean 163
Median 167
Mode 171
Finding the Mode, Median, and Mean in
Frequency Distributions  173
Choosing the Appropriate Measure of
Central Tendency  175
Median Versus Mean Income  179
Chapter Summary  181
Using Stata  182
Using SPSS  187
Practice Problems  193
Notes 202

CHAPTER 5  The Diversity of Values
in a Group  203
Range 205
Interquartile Range  205
Standard Deviation  210
Using the Standard Deviation to Compare
Distributions 212
Comparing Apples and Oranges  214
Skewed Versus Symmetric Distributions  218

Chapter Summary  220
Using Stata  221
Using SPSS  225
Practice Problems  231
Notes 240

CHAPTER 6  Probability and the Normal
Distribution 241
The Rules of Probability  242
The Addition Rule  245
The Complement Rule  246
The Multiplication Rule with
Independence 248
The Multiplication Rule without
Independence 249
Applying the Multiplication Rule with
Independence to the “Linda” and
“Birth-Order” Probability
Problems 251

Probability Distributions  253
The Normal Distribution  254

Standardizing Variables and Calculating
z-Scores 258
Chapter Summary  266
Using Stata  267
Using SPSS  270
Practice Problems  272
Notes 279

CHAPTER 7  From Sample to
Population 280
Repeated Sampling, Sample Statistics, and
the Population Parameter  281
Sampling Distributions  284
Finding the Probability of Obtaining a Specific
Sample Statistic  287
Estimating the Standard Error from a
Known Population Standard
Deviation 288
Finding and Interpreting the z-Score for
Sample Means  289
Finding and Interpreting the z-Score for
Sample Proportions  292

The Impact of Sample Size on the Standard
Error 293
Chapter Summary  295
Using Stata  295
Using SPSS  300
Practice Problems  306
Notes 313

v


vi

Contents

CHAPTER 8  Estimating Population
Parameters 314
Inferential Statistics and the Estimation of
Population Parameters  315
Confidence Intervals Manage Uncertainty
through Margins of Error  317
Certainty and Precision of Confidence
Intervals 317
Confidence Intervals for Proportions  318
Constructing a Confidence Interval for
Proportions: Examples  322

Confidence Intervals for Means  326
The t-Distribution  326
Calculating Confidence Intervals for Means:
Examples 329

The Relationship between Sample Size and
Confidence Interval Range  333
The Relationship between Confidence
Level and Confidence Interval
Range 335
Interpreting Confidence Intervals  337
How Big a Sample?  338
Assumptions for Confidence Intervals  341
Chapter Summary  342
Using Stata  344
Using SPSS  346
Practice Problems  349

Notes 354

CHAPTER 9  Differences between
Samples and Populations  356
The Logic of Hypothesis Testing  357
Null Hypotheses (H0) and Alternative
Hypotheses (Ha) 358
One-Tailed and Two-Tailed Tests  359

Hypothesis Tests for Proportions  359
The Steps of the Hypothesis Test  364

One-Tailed and Two-Tailed Tests  365
Hypothesis Tests for Means  367
Example: Testing a Claim about a Population
Mean 373

Error and Limitations: How Do We Know We
Are Correct?  375
Type I and Type II Errors  376

What Does Statistical Significance Really
Tell Us? Statistical and Practical
Significance 379
Chapter Summary  381
Using Stata  382
Using SPSS  386
Practice Problems  392
Notes 398

CHAPTER 10  Comparing Groups  399
Two-Sample Hypothesis Tests  401
The Logic of the Null and Alternative
Hypotheses in Two-Sample Tests  401
Notation for Two-Sample Tests  402
The Sampling Distribution for Two-Sample
Tests 403

Hypothesis Tests for Differences
between Means  404
Confidence Intervals for Differences
between Means  411
Hypothesis Tests for Differences between
Proportions 412
Confidence Intervals for Differences between
Proportions 416
Statistical and Practical Significance
in Two-Sample Tests  418
Chapter Summary  419
Using Stata  420
Using SPSS  424
Practice Problems  429
Notes 434

CHAPTER 11  Testing Mean Differences
among Multiple Groups  435
Comparing Variation within and between
Groups 436
Hypothesis Testing Using ANOVA  438
Analysis of Variance Assumptions  439

The Steps of an ANOVA Test  440
Determining Which Means Are Different:
Post-Hoc Tests  446
ANOVA Compared to Repeated t-Tests  447
Chapter Summary  448
Using Stata  448


Contents

Using SPSS  450
Practice Problems  453
Notes 461

The “Best-Fitting” Line  552
Slope and Intercept  553
Calculating the Slope and Intercept  556

Goodness-of-Fit Measures  557

CHAPTER 12  Testing the Statistical
Significance of Relationships in
Cross-Tabulations 463
The Logic of Hypothesis Testing with
Chi-Square 466
The Steps of a Chi-Square Test  469
Size and Direction of Effects: Analysis of
Residuals 475
Example: Gender and Perceptions of
Health 477

Assumptions of Chi-Square  481
Statistical Significance and Sample Size  481
Chapter Summary  486
Using Stata  487
Using SPSS  489
Practice Problems  492
Notes 500

CHAPTER 13  Ruling Out Competing
Explanations for Relationships
between Variables  501
Criteria for Causal Relationships  506
Modeling Spurious Relationships  508
Modeling Non-Spurious Relationships  513
Chapter Summary  520
Using Stata  521
Using SPSS  526
Practice Problems  532
Notes 541

CHAPTER 14  Describing Linear
Relationships between
Variables 542
Correlation Coefficients  544
Calculating Correlation Coefficients  545

Scatterplots: Visualizing Correlations  546
Regression: Fitting a Line to a
Scatterplot 550

R-Squared (r2) 557
Standard Error of the Estimate  558

Dichotomous (“Dummy”) Independent
Variables 559
Multiple Regression  563
Statistical Inference for Regression  565
The F-Statistic  566
Standard Error of the Slope  568

Assumptions of Regression  571
Chapter Summary  573
Using Stata  575
Using SPSS  581
Practice Problems  588
Notes 598
SOLUTIONS TO ODD-NUMBERED
PRACTICE PROBLEMS  599
GLOSSARY  649
APPENDIX A  Normal Table  656
APPENDIX B  Table of t-Values  658
APPENDIX C  F-Table, for Alpha = .05  660
APPENDIX D  Chi-Square Table  662
APPENDIX E  Selected List of Formulas  664
APPENDIX F  Choosing Tests for Bivariate
Relationships 666
INDEX  667

vii

Preface

The idea for Statistics for Social Understanding: With Stata and SPSS began with our
desire to offer a different kind of book to
our statistics students. We wanted a book
that would introduce students to the way
statistics are actually used in the social
­sciences: as a tool for advancing understanding of the social world. We wanted
thorough coverage of statistical topics,
with a balanced approach to calculation
and the use of statistical software, and
we wanted the textbook to cover the use
of software as a way to explore data and
­answer exciting questions. We also wanted
a textbook that incorporated Stata, which
is widely used in graduate programs and
is increasingly used in undergraduate
classes, as well as SPSS, which remains
widespread. We wanted a book designed
for introductory students in the social sciences, including those with little quantitative background, but one that did not talk
down to students and that covered the
conceptual aspects of statistics in detail
even when the mathematical ­details were
minimized. We wanted a clearly written,
engaging book, with plenty of practice
problems of every type and easily available data sets for classroom use.
We are excited to introduce this book
to students and instructors. We are three
­experienced instructors of statistics, two

sociologists and a political scientist, with

viii

more than sixty combined years of teaching experience in this area. We drew on
our teaching experience and research on
the teaching and learning of statistics
to write what we think will be a more
effective textbook for fostering student
­
learning.
In addition, we are excited to share
our experiences teaching statistics to
­social ­science students by authoring the
book’s ancillary materials, which include
not only practice problems, test banks,
and data sets but also suggested class exercises, P
­ owerPoint slides, assignments,
lecture notes, and class exercises.
Statistics for Social Understanding is distinguished by several features: (1) It is the
only major introductory statistics book to
integrate Stata and SPSS, giving instructors a choice of which software package
to use. (2) It teaches statistics the way
they are used in the social sciences. This
includes beginning every chapter with
examples from real research and taking
students through research questions as
we cover statistical techniques or software
applications. It also includes extensive
discussion of relationships between variables, through the earlier placement of the

chapter on cross-tabulation, the addition
of a dedicated chapter on causality, and
comparative examples throughout every
chapter of the book. (3) It is informed by


Preface

research on the teaching and learning of
quantitative material and uses principles
of universal design to optimize its contents for a variety of learning styles.

Distinguishing
Features
1) Integrates Stata and SPSS
While most existing textbooks use only
SPSS or assume that students will purchase an additional, costly, supplemental text for Stata, this book can be used
with either Stata or SPSS. We include
parallel sections for both SPSS and Stata
at the end of every chapter. These sections are written to ensure that students
understand that software is a tool to be
used to improve their own statistical
reasoning, not a replacement for it.1 The
book walks students through how to use
Stata and SPSS to analyze interesting
and relevant research questions. We not
only provide students with the syntax
or menu selections that they will use to
carry out these commands but also carefully explain the statistical procedures
that the commands are telling Stata or

SPSS to perform. In this way, we encourage students to engage in statistical reasoning as they use software, not to think
of Stata or SPSS as doing the statistical
reasoning for them. For Stata, we teach
students the basic underlying structure
of Stata syntax. This approach facilitates
a more intuitive understanding of how
the program works, promoting greater
confidence and competence among students. For SPSS, we teach students to
navigate the menus fluently.

ix

2) Draws on teaching
and learning research
Our approach is informed by research on
teaching and learning in math and statistics and takes a universal design approach
to accommodate multiple learning styles.
We take the following research-based
approaches:
• Research on teaching math shows that

students learn better when teachers use
multiple examples and explanations
of topics.2 The book explains topics in
multiple ways, using both alternative
verbal explanations and visual representations. As e­ xperienced instructors,
we know the topics that students frequently stumble over and give special
attention to ­explaining these areas in
multiple ways. This ­approach also accommodates differences in learning
styles across students.

• Some chapter examples and practice

problems lead students through the
process of addressing a problem by
acknowledging commonly held mis­
conceptions before presenting the
proper solution. This approach is based
on research that shows that simply
presenting students with information
that corrects their statistical misconceptions is not enough to change these
“strong and resilient” misconceptions.3
Students need to be able to examine
the differences in the reasoning underlying incorrect and correct strategies
of statistical work.
• Each chapter provides numerous, care-

fully proofread, practice problems, with
additional practice problems on the
text’s website. Students learn best by


x

Preface

doing, and the book provides numerous opportunities for problem-solving.
• The book avoids the “busy” layout

used by some textbooks, which can
distract students’ attention from the

content, particularly those with learning differences. Drawing on the principles of universal design, our book
utilizes a clean, streamlined layout
that will allow all students to focus on
the content without unnecessary distractions.4 Boxes are clearly labeled
as either “In Depth,” which provide
more detailed discussion or coverage
of more complex topics, or “Application,” which provide additional examples. We avoid sidebars; terms defined
in the glossary are bolded and defined
in the text, not in a sidebar.
• In keeping with principles of universal

design, we use both text and images to
explain material (with more figures
and illustrations than in many books).

3) Incorporates real-world
research and a real-world
approach to the use of
statistics
Each chapter begins with an engaging
real-world social science question and
examples from research. Chapters integrate examples and applications throughout. Chapters raise real-world questions
that can be addressed using a given technique, explain the technique, provide an
example using the same question, and
show how related questions can also be
addressed using Stata or SPSS. We use
data sets that are widely used in the social
sciences, including the General Social Survey, American National Election Study,

World Values Survey, and School Survey

on Crime and Safety. Applied questions
draw from sociology, political science,
criminology, and related fields. Several
data sets, including all of those used in
the software sections, are available to students and instructors (in both Stata and
SPSS formats) through the textbook’s
website. By using and making available
major social science data sets, we engage
students in a problem-focused effort to
make sense of real and engaging data
and enable them to ask and answer their
own questions. Robust ancillary materials, such as sample class exercises and
assignments, make it easy for instructors
to structure students’ engagement with
these data. The SPSS and Stata sections at
the end of each chapter allow students to
follow along.
Throughout the book, we discuss
­issues and questions that working ­social
scientists routinely confront, such as how
to use missing data, recode variables
­(including conceptual and statistical considerations), combine variables into new
measures, think about outliers or atypical cases, choose appropriate measures,
weigh considerations of causation, and
interpret results.
The focus in every chapter on relationships between variables or comparisons
across groups also reflects our commitment to showing students the power of
statistics to answer important real-world
questions.

4) Uses accessible, noncondescending approach
and tone
We have written a text that is student-friendly
but not condescending. We have found that,


Preface

in an effort to assuage students’ anxiety
about statistics, some texts strike a tone that
communicates the expectation that students
lack confidence in their abilities. We are
conscious of the possibility that addressing
students with the assumption that they hate
or are intimidated by statistics could activate stereotype threat—the well-established
fact that, when students feel that they are
expected to perform poorly, their anxiety
over disproving that stereotype makes their
performance worse than it otherwise would
be. In selecting examples, we have remained
alert to the risk of stereotype threat, choosing examples that do not activate (or even
challenge) gender or racial stereotypes
about academic performance.

5) Balances calculation
and concepts
This book is aimed at courses that teach
statistics from the perspective of social
science. Thus, the book frames the point
of learning statistics as the analysis of

important social science questions. While
we include some formulas and hand calculation, we do so in order to help students understand where the numbers
come from. We believe students need to
be able to reason statistically, not simply
use software to produce results, but we
recognize that most working researchers rely on statistical software, and we
strike a balance among these skills. At the
same time, we spend more time on conceptual understanding, including more
in-depth consideration of topics relating
to causality, and we include topics often
omitted from other texts such as the use
of confidence intervals as a follow-up to
a hypothesis test. A lighter focus on hand
calculation opens up time in the semester

xi

for topics that are most important to
understanding statistical social sciences.
Our aim is to give students the tools
they might use as working ­
researchers
in a variety of professions (from jobs in
small organizations where they might be
reading and writing up external data or
doing program evaluation, to research
or data analysis jobs) and prepare them
for ­higher-level statistics classes if they
choose to take them.

For Instructors
Organization of the Text
The textbook begins with descriptive statistics in chapters 2 through 5. One key difference from many introductory statistics
texts is that we introduce cross-tabulations
early, after frequency distributions and
before central tendency and variability.
In our experience as instructors, we have
noticed that students often begin thinking about relationships between variables
at the very beginning of the class, asking
questions about how groups differ in their
frequency distributions of some variable,
for example. Cross-tabulations follow naturally at this point in the class and allow
students to engage in real-world data analysis and investigate questions of causality
relatively early in the course. Chapters
6 and 7 lay the foundation for inferential
statistics, covering probability, the normal distribution, and sampling distributions. We cover elementary probability
in the context of the normal distribution,
with a focus on the logic of probability
and probabilistic reasoning in order to lay
the groundwork for an understanding of
inferential statistics. Chapters 8 through


xii

Preface

12 cover the basics of inferential statistics,
including confidence intervals, hypothesis
testing, z- and t-tests, analysis of v

­ ariance,
and chi-square. C
­hapter 13, unusual
among introductory statistics texts, focuses
on the logic of causality and control variables. Most existing texts address this topic
more briefly (or not at all), but, in our experience, it is an important topic that we all
supplement in lecture. Finally, chapter 14
covers correlation and regression. While
that chapter is pitched to an introductory
level, we pay more attention to multiple
regression than do many texts, because it
is so widely used, and we have a box on
logistic regression to introduce students
to the range of models that working social
scientists employ.
Instructors who wish to cover chapters in a different order—for example,
delaying cross-tabulations until later in
the s­emester—can readily do so. Some
courses may not cover probability or
analysis of variance, and those chapters
can be omitted. For instructors who want
to follow the order of this book in their
class, the ancillary materials make it easy
to do so.

For Students
In a course evaluation, one of our students
offered advice to future students:
Use the textbook! it is incredibly specific
and helpful.

We agree, and not just because we wrote
it! We suggest reading the assigned section of the chapter before class and working the example problems, pencil in hand,
as you read. Make a note of anything you

don’t understand and ask questions or
attend especially to that material in class.
After class, look back at the “Chapter
Summary” and work the practice problems to consolidate your understanding.
If you found a chapter especially difficult
on your first pass through, try to reread
it after you have covered the material in
class. This may seem time-consuming, but
you not only will improve your understanding (and your grade) but will save
time when it comes to studying for midterm and final exams or completing class
projects. As another student explained:
The textbook format let me go through
the material from class at a slower
pace and I could turn to it for step-bystep help in doing the assignments.

Similarly, you should look through the
software sections before you conduct
these exercises in class or lab. You do not
need to try to memorize the SPSS or Stata
commands, but familiarize yourself with
the procedures and the reasons for them.
As with the rest of the chapter, hands-on
practice is key here, too.
Remember, you are taking this class
because you want to understand the social

world. As another of our students wrote:
If you are not too familiar with working with numbers, that is just fine!
This course is designed as an analytical course which means that you will
be focusing more so on the meaning
behind numbers and statistics rather
than just focusing on finding “correct”
answers.

The companion website contains more
study materials and gives you access to


Preface

xiii

the data sets used for the software sections
in the textbook. You can use these data sets
and your newfound skill in SPSS or Stata
to investigate questions you are interested
in, beyond those we cover.
Chapter 1 contains more tips on studying and learning as well as overcoming
math anxiety.

PowerPoint® Slides. The PowerPoint
presentation provides lecture slides for
every chapter. In addition, multiple choice
review slides for classroom use are available for each chapter. The presentation is
available to adopters for download on the
text’s catalog page at https://rowman.

com/ISBN/9781538109830.

Ancillaries

For Students

This book is accompanied by a learning
package, written by the authors, that is
designed to enhance the experience of
­
both instructors and students.

For Instructors
Instructor’s Manual with Solutions.
This valuable resource includes a sample course syllabus and links to the publicly available data sets used in the Stata
and SPSS sections of the text. For each
chapter, it includes lecture notes, suggested classroom activities, discussion
questions, and the solutions to the practice problems. The Instructor’s Manual
with Solutions is available to adopters for download on the text’s catalog
page at />9781538109830.
Test Bank. The Test Bank includes both
short answer and multiple choice items
and is available in either Word or Respondus format. In either format, the Test Bank
can be fully edited and customized to best
meet your needs. The Test Bank is available to adopters for download on the text’s
catalog page at />ISBN/9781538109830.

Companion Website. Accompanying the
text is an open-access Companion Website
designed to reinforce key topics and concepts. For each chapter, students will have

access to:
Publicly available data sets used in the
Stata and SPSS sections
Flashcards of key concepts
Discussion questions
Students can access the Companion
Website from their computers or mobile
devices at man.
com/whittier.

Acknowledgements
We are grateful to many manuscript
­reviewers, both those who are identified
here and those who chose to remain anonymous, for their in-depth and thoughtful
comments as we developed this text. We
are fortunate to have benefited from their
knowledgeable and helpful input. We
thank the following reviewers:
Jacqueline Bergdahl, Department of
Sociology and Anthropology, Wright
State University


xiv

Preface

Christopher F. Biga, Department of Sociol­
ogy, University of Alabama at Birmingham
Andrea R. Burch, Department of Sociology, Alfred University

Sarah Croco, Department of Government,
University of Maryland—College Park
Michael Danza, Department of Sociology,
Copper Mountain College
William Douglas, Department of Communication, University of Houston
Ginny Garcia-Alexander, Department of
Sociology, Portland State University
Donald Gooch, Department of Government, Stephen F. Austin State University
J. Patrick Henry, Department of Sociology,
Eckerd College
Dadao Hou, Department of Sociology,
Texas A&M University
Kyungkook Kang, Department of Political
Science, University of Central Florida
Omar Keshk, Department of International
Relations, Ohio State University
Pamela Leong, Department of Sociology,
Salem State University
Kyle C. Longest, Department of Sociology,
Furman University
Jie Lu, Department of Government, American University—Kogod School of
Business
Catherine Moran, Department of Sociology, University of New Hampshire
Dawne Mouzon, Department of Public Policy, Rutgers University—New
Brunswick—Livingston
Dennis Patterson, Department of Political
Science, Texas Tech University
Michael Restivo, Department of Sociology,
SUNY Geneseo
Jeffrey Stone, Department of Sociology,

California State University—Los Angeles

Jeffrey Timberlake, Department of Sociology, University of Cincinnati
We also thank our research assistants at
Smith College. Sarah Feldman helped
with generating clear figures and
­practice problems and gave feedback on
the text early on, Elaona Lemoto assisted
with the final stages, and Sydney Pine
helped with the ancillary materials.
Dan B
­ennet, from the Smith College
­Information Technology Media Production department, helped us figure out
how to generate high-quality screenshots for the SPSS and Stata sections.
Leslie King offered helpful feedback
on early drafts of some chapters, and
Bobby Innes-Gold read and c­ ommented
on some chapters.
At Rowman & Littlefield, we are grateful to Nancy Roberts and Megan Manzano
for their help as we developed and wrote
the book and Alden Perkins for her coordination of the production process. Aswin
Venkateshwaran, Ramanan Sundararajan,
and Deepika Velumani at Integra expertly
shepherded the copy-editing and production process. We are grateful to Bill ­Rising
of Stata's author support program for his
detailed comments on the accuracy of the
text and the Stata code. We also thank
Sarah Perkins for mathematical proofreading. Amy Whitaker coordinated and
executed the sales and marketing efforts.
Finally, our greatest thanks go to

our students. Their questions, points of
confusion, and enthusiasm for learning
helped us craft this text and inspire us in
our teaching. This book is dedicated to
them.


Preface

xv

Notes
1

2

S. Friel. 2007. “The Research Frontier: Where Technology Interacts with the Teaching and Learning of
Data Analysis.” In M. K. Heid and G. W. Blume (eds.),
­Research on Technology and the Teaching and Learning of ­Mathematics: Syntheses and Perspectives,
Volume 2 (pp. 279–331). Greenwich: Information Age
Publishing, Inc.
J. R. Star. 2016. “Small Steps Forward: Improving Mathematics Instruction Incrementally.” Phi Delta Kappan 97:
58–62.

3

J. Garfield and D. Ben-Zvi. 2007. “How Students Learn
Statistics Revisited: A Current Review of Research on
Teaching and Learning Statistics.” International Statistical Review 75: 372–396.

4

S. E. Burgstahler. 2015. Universal Design in Higher
­Education: From Principles to Practice. Cambridge, MA:
Harvard Education Press.

5

S. J. Spencer, C. Logel, and P. G. Davies. 2016.
­“Stereotype Threat.” Annual Review of Psychology 67:
415–437.


About the Authors

Nancy Whittier is Sophia Smith Professor of
Sociology at Smith College. She has taught
statistics and research methods for twentyfive years and also teaches classes on
gender, sexuality, and social movements.
She is the author of  Frenemies: Feminists,
Conservatives, and Sexual Violence; The Politics of Child Sexual Abuse: Emotions, Social
Movements, and the State;  Feminist Generations and numerous articles on social
movements, gender, and sexual violence.
She is co-editor (with David S. Meyer and
Belinda Robnett) of Social Movements: Identities, Culture, and the State and (with Verta
Taylor and Leila Rupp) Feminist Frontiers.
Tina Wildhagen is Associate Professor
of Sociology and Dean of the Sophomore
Class at Smith College. She has taught statistics and quantitative research methods
for more than a decade and also teaches

courses on privilege and power in American education and inequality in higher
education. Her research and teaching

xvi

interests focus on social inequality in
the American education system and on
first-generation college students. Her
work appears in various scholarly journals, including The Sociological Quarterly,
Sociological Perspectives, The Teachers College Record, The Journal of Negro Education
and Sociology Compass.
Howard J. Gold is Professor of Government at Smith College. He has taught statistics for thirty years and also teaches courses
on American elections, public opinion
and the media, and political behavior. His
research focuses on public opinion, par­
tisanship, and voting behavior. He is the
co-author (with Donald Baumer) of Parties, Polarization and Democracy in the United
States and author of Hollow M
­ andates: American Public Opinion and the Conservative Shift.
His work has also ­appeared in American
Politics Quarterly, P
­olitical Research Quarterly, Polity, Public Opinion Quarterly, and
the Social Science Journal.


Introduction

Chapter 1 Using Statistics to Study the

Social World

Why Study Statistics?
We all live in social situations. We observe our surroundings, are socialized into our
cultures, navigate social norms, make political judgments and decisions, and participate
in social institutions. Social sciences assume that what we can see as individuals is not
the whole story of our social world. Political and social institutions and processes exist
on a large scale that is difficult to see without systematic research. For most students
in a social science statistics class, this basic insight is part of what drove your interest
in this field. Maybe you want to understand political processes more thoroughly,
understand how inequalities are produced, or understand the operation of the criminal
justice system.
Many students reading this book are taking a statistics class because it is required
for their major. Some readers are passionate about statistics, but most of you are
­probably mainly interested in sociology, political science, criminology, anthropology, education, or whatever your specific major is. Whatever your specific interest,
statistics can deepen your understanding and build your toolkit for communicating
social science insights to diverse audiences. You may think of statistics as a form
of math, but, in fact, statistics are more about thinking with numbers than they are
about ­computation. Although we do cover some simple computation in this book, our
emphasis is on understanding the logic and application of statistics and interpreting
their meaning for concrete topics in the social sciences. There is a good reason that
statistics are required for many social science majors: Statistical methods can tell us
a lot about the most interesting and important questions that social scientists study.
Statistics also can tell you a lot about the questions that motivated your own interest
in social sciences.

1


2

CHAPTER 1  Introduction

Statistics and quantitative data are important tools for understanding large-scale
social and political processes and institutions as well as how these structures shape
individual lives. They help us to comprehend trends and patterns that are too large for
us to see in other ways. Statistics do this in three main ways. First, they help us simply
to describe large-scale patterns. For example, what is the average income of residents in
a given state? Second, statistics help us determine the factors that shape these patterns.
This includes simple comparisons, such as how income varies by gender or by age.
It also includes more complicated mathematical models that can show how multiple
forces shape a given outcome. How do gender, age, race, and education interact to
shape income, for example? Third, statistics help us understand how and whether we
can generalize from data gathered from only some members of a group to draw conclusions about all members of that group. This aspect of statistics, called inferential statistics, uses ideas about probability to determine what kinds of generalizations we can
make. It is what allows researchers to draw meaningful conclusions from data about
relatively small numbers of people.
In this book, we emphasize what we can do with statistics, focusing on real social
science research and analyzing real data. Readers of this book will develop a strong
sense of how quantitative social scientists conduct their research and will get plenty
of practice in analyzing social science data. Not all of this book’s readers will pursue
careers as researchers, but many of you will have careers that include analyzing and
presenting information. And, all of you face the task of making sense of mountains
of information, including social science research findings, communicated by various
­media. This book provides essential tools for doing so.
Recently, some commentators have noted that we have entered a “post-fact,” or
“post-truth,” era. People mean different things by this, but one meaning is that the
sheer volume of people and agencies producing facts has multiplied to the point that
an expert can be found to attest to the accuracy of just about any claim.1 Just think of
the amount of information that you are exposed to on a weekly basis from various
social media platforms, websites, television, and other forms of media. How do you
make sense of it? How do you, for example, decide whether a claim you read online is

true or false? Statistics can powerfully influence opinion because they use numerical
data, which American culture assumes are objective and legitimate. But not all claims
are equally factual, even those that appear to be backed up by statistics. This book will
equip you with an understanding of how statistics work so that you can evaluate the
meaning and credibility of statistical data for yourself.
When quantitative research is carefully conceived and conducted, the results
of statistical analyses can yield valuable information not only about how the social
world works but also about how to effectively address social problems. For example,
in her 2007 book Marked, sociologist Devah Pager examined how having a criminal
record affects men’s employment prospects in blue collar jobs.2 She conducted a study
in which she hired paid research assistants, called testers, to submit fake résumés in
person to potential employers. The résumés were the same, with the only difference


Research Questions and the Research Process

3

being that some of them listed a parole officer as a reference, indicating that the applicant had spent time in prison, while the others did not have a parole officer as a reference. Did résumés without the parole officer reference fare better in the job search
process? Yes, they did. On average former offenders were 46% less likely to receive
a callback about the job, and the results of the analysis suggested that this difference
could be generalized to the overall population of men applying for blue collar jobs,
not just the testers in her study.3 Pager also varied the race of the testers applying
for jobs—half were white, and half were black. She found that having the mark of a
criminal record reduced the chances of a callback by 64% for black testers and 50%
for white testers, indicating that the damage of a criminal record is particularly acute
for black men.
By varying only whether the applicant had a criminal record, Pager controlled for
alternative explanations of the negative effect of a criminal record on the likelihood of
receiving a callback for a job. In other words, employers were reacting to the criminal

record itself, not factors that might be associated with a criminal record, such as erratic
work histories.
Pager’s study contains many of the key elements of statistical analysis that we discuss in this book: assessment of the relationship between two variables (criminal record
and employer callbacks); a careful investigation of whether one of the variables (criminal record) has a causal impact on the other (employer callback) and, if so, whether that
causal impact varies by another factor (race); and examination of the generalizability of
the results.

Research Questions and the Research Process
Most research starts with a research question, which asks how two or more variables
are related. A variable is any characteristic that has more than one category or value.
In the social sciences, we must be able to answer our research questions using data.
In many cases, these questions may be fairly general. For example, sociologist Kristen
Luker writes about beginning a research project with a question about why women were
having abortions despite the availability of birth control.4 A criminologist may begin
by wanting to know what kinds of rehabilitation programs reduce recidivism. In other
cases, a question may expand on prior research. For example, research has shown that
Internet skills vary by class, race, and age.5 Do these factors affect the way Internet users
blog or contribute to Wikipedia? Or, if we know that children tend to generally share their
parents’ political viewpoints, does this hold true in votes for candidates in primaries?
Some research begins with a hypothesis, a specific prediction about how variables
are related. For example, a researcher studying political protest might hypothesize
that larger protests produce more news media coverage. Other research begins at a
more exploratory level. For example, the same researcher might collect data on several
possible variables about protests, such as the issue they focus on, the organizations


4

CHAPTER 1  Introduction

that sponsor them, whether they include violence, as well as their size, in order to
explore what shapes media coverage. Statistical methods can support both approaches
to research.
This book focuses on quantitative analysis—that is, analyses that use statistical
techniques to analyze numerical data. Many social scientists also use qualitative methods. Qualitative methods start with data that are not numerical, such as the text of
documents, interviews, or field observations. Qualitative data analysis often focuses on
meanings, processes, and interactions; like quantitative research, it may test hypotheses
or be more exploratory in nature. Qualitative research analysis often uses specialized
software programs. Increasingly, many researchers use mixed methods, which employ
both qualitative and quantitative data and analysis. While this book focuses on quantitative analysis, combining both methods can yield a richer and more accurate understanding of social phenomena than either approach alone.

Pinning Things Down: Variables and
Measurement
Answering any kind of social science research question entails gathering data.
Gathering useful data requires formulating the research question as precisely as
possible. Quantitative researchers first identify and define the question’s key concepts.
Concepts are the abstract factors or ideas, not always directly observable, that the
researcher wants to study. Many concepts have multiple dimensions. For example,
a researcher interested in how people’s social class affects their sense of well-being
must define what social class and well-being mean before examining whether they are
related. Using existing research and theory, the researcher might define a social class
as a segment of the population with similar levels of financial, social, and cultural
resources. She might decide that well-being is one’s sense of overall health, satisfaction,
and comfort in life. Stating clear definitions of concepts ensures that the researcher
and her audience understand what is meant by those concepts in the particular project
at hand.
Once researchers specify, or define, their concepts, they must decide how to measure these concepts. Deciding how to measure a concept is also referred to as operationalizing a concept, or operationalization. Operationalization, the process of
transforming concepts into variables, determines how the researcher will observe concepts using empirical data. Staying with the example of social class and well-being,
how would we place people into different class categories? Using the conceptual definition described above, the researcher might decide to use people’s income, wealth,
highest level of education, and occupation to measure their social class. All of these

are empirical indicators of financial, social, and cultural resources. To operationalize
well-being, the researcher might decide to measure an array of behaviors (e.g., number
of times per week that one exercises) and attitudes (e.g., overall sense of satisfaction
with one’s life).


5

Pinning Things Down: Variables and Measurement

TheoreƟcal

Concept

Well-being
DefiniƟon:
Sense of overall, health, saƟsfacƟon, and
comfort in life

Dimensions
Mental
Well-being

Physical
Well-being

Spiritual
Well-being

Variables

Number
of sick
days

RaƟng of
healthy
eaƟng habits

Stress
level

Frequency
of
depression

View of
self

Sense of
meaning
in life

Sense of
purpose
in life

Empirical

Frequency

of exercise

Figure 1.1  Conceptualization and Measurement of a Key Concept

This process of conceptualization and measurement, or operationalization, is how
concepts become variables in quantitative research. Figure 1.1 offers a visual representation of this process for the concept of well-being.
Figure 1.1 shows how researchers move from defining a key concept to specifying
how that concept will be empirically measured and transformed into variables. Starting from the top of the figure and moving down, we can see how the process works.
First, the concept of well-being is defined. Next, the dimensions of the concept (physical, mental, and spiritual) are specified. Finally, the researcher establishes empirical
measures for each dimension (e.g., frequency of exercise as an indicator of physical
well-being). These empirical measures are called variables. The arrow on the right side
of Figure 1.1 shows how moving from defining concepts to measuring them shifts from
the theoretical or abstract to the empirical realm, where variables can be measured.
Studying relationships among variables is the central focus of quantitative social science research.
A variable, remember, is any single factor that has more than one category or value.
For example, gender is a variable with multiple categories (e.g., man, woman, gender
non-binary, etc.). For some variables, such as body mass index, there is an established
standard for determining the value of the variable for different individuals (e.g., body
mass index is equal to weight divided by height squared). For variables that lack a clear
measurement standard, such as sense of purpose in life, researchers must establish their
categories and methods of measurement, usually guided by existing research.
In quantitative social science research, the survey item is among the most common tools used to operationalize concepts. Survey items have either closed- or openended response options. Closed-ended survey items provide survey respondents with


6

CHAPTER 1  Introduction

predefined response categories. The number of categories can range from as little as
two (e.g., yes or no) to very many (e.g., a feeling thermometer that asks respondents to

rate their feeling about something on a scale from 0 to 100 degrees). With closed-ended
survey items, the researcher decides on the measurement of the concept before administering the survey. Open-ended survey items do not provide response categories. For
example, an item might ask respondents to name the issue that is most important to
them in casting a vote for a candidate. Open-ended items give respondents more leeway in answering questions. Once the researcher has all responses to an open-ended
item, the researcher often devises response categories informed by the responses themselves and then assigns respondents to those categories based on their responses. For
example, with an open-ended question about which issues are important to voters, the
researcher might combine various responses having to do with jobs or the economy
into one category.

Units of Analysis
In the social sciences, researchers are interested in studying the characteristics of
individuals but also the characteristics of groups. Who or what is being studied is
the unit of analysis. A study of people’s voting patterns and political party affiliation
focuses on understanding individuals. But a study of counties that voted for a
Republican vs. Democratic candidate focuses on understanding characteristics of a
group, in this case counties. In the first case, researchers might seek to understand
what explains people’s votes; in the second case, researchers might seek to understand
what characteristics are associated with Republican vs. Democratic counties. When
the unit of measurement is the group, we sometimes also refer to it as aggregate level.
Aggregate-level units that researchers might be interested in include geographic
areas, organizations, religious congregations, families, sports teams, musical groups,
or businesses. One must be careful about making inferences across different levels
of measurement. A county may be Republican, but at the individual level, there are
both Democratic and Republican residents of that county. Drawing conclusions about
individuals based on the groups to which they belong is an error in logic known as the
ecological fallacy.

Measurement Error: Validity and Reliability
Most variables in the social sciences include some amount of error, which means that the
values recorded for a variable are to some degree inaccurate. Even many variables that

one might suspect would be simple to measure accurately, such as income, contain error.
How much money did you receive as income in the last calendar year? Some readers
may know the exact figure. But others would have to offer an estimate, maybe because
they cannot recall or because they worked multiple jobs and have trouble keeping


Measurement Error: Validity and Reliability

7

track of the income produced by each of them. Still others might purposefully report a
number that is higher or lower than their actual income. Researchers never know for
sure how much error their variables contain, but we can evaluate and minimize error in
measurement by assessing the validity and reliability of our variables.
Validity indicates the extent to which variables actually measure what they claim
to measure. When measures have a high degree of validity, this means that there is a
strong connection between the measurement of a concept and its conceptual definition.
In other words, valid measures are accurate indicators of the underlying concept. Imagine a researcher who claims that he has found that happiness declines as people exercise
more. How is that researcher measuring happiness? It turns out that he has operationalized happiness through responses to two survey questions: “How much energy do you
feel you have?” and “How much do you look forward to participating in family activities?” Do you think answers to these questions are good measures of happiness? They
may get at elements of happiness—happier people may have more energy or look forward to participating in activities more. But they are not direct measures of happiness,
and we could argue that they measure other things instead (such as how busy people
are or their health). What about a researcher who wants to measure the prevalence of
food insecurity, in which people do not have consistent access to sufficient food? This
could be operationalized in a survey question such as, “How often do you have insufficient food for yourself and your family” or “How often do you go hungry because
of inability to get sufficient food for yourself or your family?” It could also be operationalized by the number and size of food pantries per capita or food stamp usage.
Which way of operationalizing food insecurity is more accurate? The survey questions
have greater validity because both food pantries and food stamp usage are affected by
forces other than food insecurity (urban areas may have more food pantries per capita
than rural areas, not all people eligible for food stamps use them, and so forth). If the

researcher were interested instead in social services to reduce food insecurity, looking
at food pantries and food stamps would be a valid measure.
Even if a measure is valid, it may not yield consistent answers. This is the question of reliability. Reliable measures are those whose values are unaffected by the
measurement process or the measurement instrument itself (e.g., the survey). Imagine
asking the same group of college students to rate how often in a typical week they
spend time with friends, with the following response choices: “often,” “a few times,”
“occasionally,” and “rarely.” These response choices are likely to lead to problems with
reliability, because they are not precise. A student who gets together with friends about
five times a week might choose “often” or “a few times,” and if you asked her the
question again a week later she might choose the other option, even if her underlying
estimate of how often she spent time with friends was unchanged. In other words, the
same students may give quite different, or inconsistent, responses if asked the question repeatedly.
Measures also tend not to be reliable when they ask questions that respondents may
not have detailed understanding or information about. For example, a survey might ask
how many minutes a week people spend doing housework, or a survey of Americans


8

CHAPTER 1  Introduction

might ask their opinion of Britain’s foreign policy toward Chile. Because people do not
generally precisely track minutes spent doing housework, and Americans are unlikely
to know much about British foreign policy, their responses to such questions will be
inconsistent.
Reliability and validity do not necessarily coincide. For example, the time shown on
a clock may be reliable without being valid. Some households may deliberately set their
clocks to be a few minutes fast, ensuring that when the alarm goes off at what the clock
says is 6:45, the actual time is 6:30. In this case, the clock consistently—that is, reliably—
tells time, but that time is always wrong (or invalid).

Figure 1.2 uses a feeling thermometer, which asks people to rate their feeling about
something on a scale from 0 to 100 degrees, to illustrate how reliability and validity
can coincide or not. Imagine these are an individual’s responses to the same feeling
thermometer item asked five separate times. The true value of the person’s feeling is
42 degrees. In scenario A, the responses have a high degree of validity, or accuracy,
because they are all near 42 degrees, the accurate value. There is also a high degree of
reliability because the responses are consistent. Researchers strive to attain scenario A
by obtaining accurate and consistent measures. In scenario B, there is still a high degree
of consistency, and therefore reliability, in the measure. However, validity is low because
the responses are far from the true value of 42 degrees. Finally, scenario C reflects both
low reliability and low validity. The responses are inconsistent, or scattered across the

A. High Reliability, High Validity

B. High Reliability, Low Validity

100

100

50

50
True value: 42

0

Figure 1.2  Visualizing Reliability and Validity

C. Low Reliability, Low Validity

100

50

True value: 42

0

True value: 42

0