Social statistics for a diverse society 7th edition pdf

Social Statistics for a Diverse Society

Eighth Edition

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Social Statistics for a Diverse Society

Eighth Edition

Chava Frankfort-Nachmias University of Wisconsin Anna Leon-Guerrero

Pacific Lutheran University

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Printed in the United States of America

Library of Congress Cataloging-in-Publication Data

Names: Frankfort-Nachmias, Chava, author. | Leon-Guerrero, Anna, author.

Title: Social statistics for a diverse society / Chava Frankfort-Nachmias, University of Wisconsin, Anna Leon-Guerrero, Pacific Lutheran University.

Description: Eighth edition. | Los Angeles : SAGE, [2016] | Includes bibliographical references and index.

Identifiers: LCCN 2016039109 | ISBN 978-1-5063-4720-2 (pbk. : alk. paper)

Subjects: LCSH: Social sciences—Statistical methods. | Statistics.

Classification: LCC HA29 .N25 2016 | DDC 519.5—dc23 LC record available at https://lccn.loc.gov/2016039109

This book is printed on acid-free paper.

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https://lccn.loc.gov/2016039109
Brief Contents

Preface About the Authors CHAPTER 1 • The What and the Why of Statistics CHAPTER 2 • The Organization and Graphic Presentation of Data CHAPTER 3 • Measures of Central Tendency CHAPTER 4 • Measures of Variability CHAPTER 5 • The Normal Distribution CHAPTER 6 • Sampling and Sampling Distributions CHAPTER 7 • Estimation CHAPTER 8 • Testing Hypotheses CHAPTER 9 • Bivariate Tables CHAPTER 10 • The Chi-Square Test and Measures of Association CHAPTER 11 • Analysis of Variance CHAPTER 12 • Regression and Correlation Appendix A. Table of Random Numbers Appendix B. The Standard Normal Table Appendix C. Distribution of t Appendix D. Distribution of Chi-Square Appendix E. Distribution of F Appendix F. A Basic Math Review Learning Check Solutions Answers to Odd-Numbered Exercises Glossary Notes Index

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Detailed Contents

Preface About the Authors CHAPTER 1 • The What and the Why of Statistics

The Research Process Asking Research Questions The Role of Theory Formulating the Hypotheses

Independent and Dependent Variables: Causality Independent and Dependent Variables: Guidelines

Collecting Data Levels of Measurement

Nominal Level of Measurement Ordinal Level of Measurement Interval-Ratio Level of Measurement Cumulative Property of Levels of Measurement Levels of Measurement of Dichotomous Variables

Discrete and Continuous Variables A Closer Look 1.1: A Cautionary Note: Measurement Error

Analyzing Data and Evaluating the Hypotheses Descriptive and Inferential Statistics Evaluating the Hypotheses

Examining a Diverse Society A Closer Look 1.2: A Tale of Simple Arithmetic: How Culture May Influence How We Count

Learning Statistics Data at Work

CHAPTER 2 • The Organization and Graphic Presentation of Data Frequency Distributions Proportions and Percentages Percentage Distributions The Construction of Frequency Distributions

Frequency Distributions for Nominal Variables Frequency Distributions for Ordinal Variables Frequency Distributions for Interval-Ratio Variables

Cumulative Distributions A Closer Look 2.1: Real Limits, Stated Limits, and Midpoints of Class Intervals

Rates Reading the Research Literature: Access to Public Benefits

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Graphic Presentation of Data The Pie Chart The Bar Graph The Histogram The Statistical Map The Line Graph The Time-Series Chart Statistics in Practice: Foreign-Born Population 65 Years and Over

A Closer Look 2.2: A Cautionary Note: Distortions in Graphs Data at Work: Kurt Taylor Gaubatz: Graduate Program in International Studies

CHAPTER 3 • Measures of Central Tendency The Mode The Median

Finding the Median in Sorted Data An Odd Number of Cases An Even Number of Cases

Finding the Median in Frequency Distributions Locating Percentiles in a Frequency Distribution

The Mean A Closer Look 3.1: Finding the Mean in a Frequency Distribution Understanding Some Important Properties of the Arithmetic Mean

Interval-Ratio Level of Measurement Center of Gravity Sensitivity to Extremes

Reading the Research Literature: The Case of Reporting Income Statistics in Practice: The Shape of the Distribution

The Symmetrical Distribution The Positively Skewed Distribution The Negatively Skewed Distribution Guidelines for Identifying the Shape of a Distribution A Closer Look 3.2: A Cautionary Note: Representing Income

Considerations for Choosing a Measure of Central Tendency Level of Measurement Skewed Distribution Data at Work: Ben Anderstone: Political Consultant Symmetrical Distribution

CHAPTER 4 • Measures of Variability The Importance of Measuring Variability The Index of Qualitative Variation

Steps for Calculating the IQV Expressing the IQV as a Percentage

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Statistics in Practice: Diversity in U.S. Society The Range The Interquartile Range The Box Plot The Variance and the Standard Deviation

Calculating the Deviation From the Mean Calculating the Variance and the Standard Deviation

Considerations for Choosing a Measure of Variation A Closer Look 4.1: More on Interpreting the Standard Deviation

Reading the Research Literature: Community College Mentoring Data at Work: Sruthi Chandrasekaran: Senior Research Associate

CHAPTER 5 • The Normal Distribution Properties of the Normal Distribution

Empirical Distributions Approximating the Normal Distribution Areas Under the Normal Curve Interpreting the Standard Deviation

An Application of the Normal Curve Transforming a Raw Score Into a Z Score

The Standard Normal Distribution The Standard Normal Table

1. Finding the Area Between the Mean and a Positive or Negative Z Score 2. Finding the Area Above a Positive Z Score or Below a Negative Z Score 3. Transforming Proportions and Percentages Into Z Scores

Finding a Z Score Which Bounds an Area Above It Finding a Z Score Which Bounds an Area Below It

4. Working With Percentiles in a Normal Distribution Finding the Percentile Rank of a Score Higher Than the Mean Finding the Percentile Rank of a Score Lower Than the Mean Finding the Raw Score Associated With a Percentile Higher Than 50 Finding the Raw Score Associated With a Percentile Lower Than 50

Reading the Research Literature: Child Health and Academic Achievement A Closer Look 5.1: Percentages, Proportions, and Probabilities Data at Work: Claire Wulf Winiarek: Director of Collaborative Policy Engagement

CHAPTER 6 • Sampling and Sampling Distributions Aims of Sampling Basic Probability Principles Probability Sampling

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The Simple Random Sample The Systematic Random Sample The Stratified Random Sample

The Concept of the Sampling Distribution The Population A Closer Look 6.1: Disproportionate Stratified Samples and Diversity The Sample The Dilemma The Sampling Distribution

The Sampling Distribution of the Mean An Illustration Review The Mean of the Sampling Distribution The Standard Error of the Mean

The Central Limit Theorem The Size of the Sample The Significance of the Sampling Distribution and the Central Limit Theorem

Statistics in Practice: A Sampling Lesson Data at Work: Emily Treichler: Postdoctoral Fellow

CHAPTER 7 • Estimation Point and Interval Estimation Confidence Intervals for Means

A Closer Look 7.1: Estimation as a Type of Inference Determining the Confidence Interval

Calculating the Standard Error of the Mean Deciding on the Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results

Reducing Risk Estimating Sigma

Calculating the Estimated Standard Error of the Mean Deciding on the Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results

Sample Size and Confidence Intervals Statistics in Practice: Hispanic Migration and Earnings

A Closer Look 7.2: What Affects Confidence Interval Width? Summary Confidence Intervals for Proportions

Determining the Confidence Interval

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Calculating the Estimated Standard Error of the Proportion Deciding on the Desired Level of Confidence and Finding the Corresponding Z Value Calculating the Confidence Interval Interpreting the Results

Reading the Research Literature: Women Victims of Intimate Violence Data at Work: Laurel Person Mecca: Research Specialist

CHAPTER 8 • Testing Hypotheses Assumptions of Statistical Hypothesis Testing Stating the Research and Null Hypotheses

The Research Hypothesis (H1) The Null Hypothesis (H0)

Probability Values and Alpha A Closer Look 8.1: More About Significance

The Five Steps in Hypothesis Testing: A Summary Errors in Hypothesis Testing

The t Statistic and Estimating the Standard Error The t Distribution and Degrees of Freedom Comparing the t and Z Statistics

Hypothesis Testing With One Sample and Population Variance Unknown Hypothesis Testing With Two Sample Means

The Assumption of Independent Samples Stating the Research and Null Hypotheses

The Sampling Distribution of the Difference Between Means Estimating the Standard Error Calculating the Estimated Standard Error The t Statistic Calculating the Degrees of Freedom for a Difference Between Means Test

The Five Steps in Hypothesis Testing About Difference Between Means: A Summary

A Closer Look 8.2: Calculating the Estimated Standard Error and the Degrees of Freedom (df) When the Population Variances Are Assumed to Be Unequal

Statistics in Practice: Cigarette Use Among Teens Hypothesis Testing With Two Sample Proportions Reading the Research Literature: Reporting the Results of Hypothesis Testing

Data at Work: Stephanie Wood: Campus Visit Coordinator CHAPTER 9 • Bivariate Tables

How to Construct a Bivariate Table How to Compute Percentages in a Bivariate Table

Calculating Percentages Within Each Category of the Independent

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Variable Comparing the Percentages Across Different Categories of the Independent Variable

Reading the Research Literature: Hispanic and Non-Hispanic Homeless Populations

A Closer Look 9.1: How to Deal With Ambiguous Relationships Between Variables

The Properties of a Bivariate Relationship The Existence of the Relationship The Strength of the Relationship The Direction of the Relationship

Elaboration Testing for Nonspuriousness: Firefighters and Property Damage An Intervening Relationship: Religion and Attitude Toward Abortion Conditional Relationships: More on Abortion The Limitations of Elaboration

Reading the Research Literature: The Digital Divide Data at Work: Spencer Westby: Senior Editorial Analyst

CHAPTER 10 • The Chi-Square Test and Measures of Association The Concept of Chi-Square as a Statistical Test The Concept of Statistical Independence The Structure of Hypothesis Testing With Chi-Square

The Assumptions Stating the Research and the Null Hypotheses The Concept of Expected Frequencies Calculating the Expected Frequencies Calculating the Obtained Chi-Square The Sampling Distribution of Chi-Square Determining the Degrees of Freedom Making a Final Decision Review

Statistics in Practice: Respondent and Father Education A Closer Look 10.1: A Cautionary Note: Sample Size and Statistical Significance for Chi-Square

Proportional Reduction of Error A Closer Look 10.2: What Is Strong? What Is Weak? A Guide to Interpretation

Lambda: A Measure of Association for Nominal Variables Cramer’s V: A Chi-Square–Related Measure of Association for Nominal Variables Gamma and Kendall’s Tau-b: Symmetrical Measures of Association for Ordinal Variables

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Reading the Research Literature: India’s Internet-Using Population Data at Work: Patricio Cumsille: Professor

CHAPTER 11 • Analysis of Variance Understanding Analysis of Variance The Structure of Hypothesis Testing With ANOVA

The Assumptions Stating the Research and the Null Hypotheses and Setting Alpha The Concepts of Between and Within Total Variance The F Statistic A Closer Look 11.1: Decomposition of SST Making a Decision

The Five Steps in Hypothesis Testing: A Summary Statistics in Practice: The Ethical Consumer

A Closer Look 11.2: Assessing the Relationship Between Variables Reading the Research Literature: Emerging Adulthood

Data at Work: Kevin Hemminger: Sales Support Manager/Graduate Program in Research Methods and Statistics

CHAPTER 12 • Regression and Correlation The Scatter Diagram Linear Relationships and Prediction Rules

Finding the Best-Fitting Line A Closer Look 12.1: Other Regression Techniques

Defining Error The Residual Sum of Squares (∑e2) The Least Squares Line

Computing a and b A Closer Look 12.2: Understanding the Covariance Interpreting a and b

A negative relationship: Age and Internet Hours per Week Methods for Assessing the Accuracy of Predictions

Calculating Prediction Errors Calculating r2

Testing the Significance of r2 Using ANOVA Making a Decision Pearson’s Correlation Coefficient (r)

Characteristics of Pearson’s r Statistics in Practice: Multiple Regression

A Closer Look 12.3: Spurious Correlations and Confounding Effects ANOVA for Multiple Linear Regression Reading the Research Literature: Academic Intentions and Support

Data at Work: Shinichi Mizokami: Professor Appendix A. Table of Random Numbers

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Appendix B. The Standard Normal Table Appendix C. Distribution of t Appendix D. Distribution of Chi-Square Appendix E. Distribution of F Appendix F. A Basic Math Review Learning Check Solutions Answers to Odd-Numbered Exercises Glossary Notes Index

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Preface

You may be reading this introduction on your first day of class. We know you have some questions and concerns about what your course will be like. Math, formulas, and calculations? Yes, those will be part of your learning experience. But there is more.

Throughout our text we highlight the relevance of statistics in our daily and professional lives. Data are used to predict public opinion, consumer spending, and even a presidential election. How Americans feel about a variety of political and social topics—race relations, gun control, immigration, the economy, health care reform, or terrorism—are measured by surveys and polls and reported daily by the news media. Your recent Amazon purchase didn’t go unnoticed. The study of consumer trends, specifically focusing on young adults, helps determine commercial programming, product advertising and placement, and, ultimately, consumer spending. And as we prepare this text, just months before the 2016 Presidential election, weekly polls have begun predicting the historic election between Hillary Clinton and Donald Trump.

Statistics are not just a part of our lives in the form of news bits or information. And it isn’t just numbers either. As social scientists we rely on statistics to help us understand our social world. We use statistical methods and techniques to track demographic trends, to assess social differences, and to better inform social policy. We encourage you to move beyond just being a consumer of statistics and determine how you can use statistics to gain insight into important social issues that affect you and others.

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Teaching and Learning Goals

Three teaching and learning goals continue to be the guiding principles of our book, as they were in previous editions.

Our first goal is to introduce you to social statistics and demonstrate its value. Although most of you will not use statistics in your own student research, you will be expected to read and interpret statistical information presented by others in professional and scholarly publications, in the workplace, and in the popular media. This book will help you understand the concepts behind the statistics so that you will be able to assess the circumstances in which certain statistics should and should not be used.

A special characteristic of this book is its integration of statistical techniques with substantive issues of particular relevance in the social sciences. Our second goal is to demonstrate that substance and statistical techniques are truly related in social science research. Your learning will not be limited to statistical calculations and formulas. Rather, you will become proficient in statistical techniques while learning about social differences and inequality through numerous substantive examples and real-world data applications. Because the world we live in is characterized by a growing diversity—where personal and social realities are increasingly shaped by race, class, gender, and other categories of experience—this book teaches you basic statistics while incorporating social science research related to the dynamic interplay of our social worlds.

Our third goal is to enhance your learning by using straightforward prose to explain statistical concepts and by emphasizing intuition, logic, and common sense over rote memorization and derivation of formulas.

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Distinctive and Updated Features of Our Book

Our learning goals are accomplished through a variety of specific and distinctive features throughout this book.

A Close Link Between the Practice of Statistics, Important Social Issues, and Real-World Examples.

This book is distinct for its integration of statistical techniques with pressing social issues of particular concern to society and social science. We emphasize how the conduct of social science is the constant interplay between social concerns and methods of inquiry. In addition, the examples throughout the book—mostly taken from news stories, government reports, public opinion polls, scholarly research, and the National Opinion Research Center’s General Social Survey—are formulated to emphasize to students like you that we live in a world in which statistical arguments are common. Statistical concepts and procedures are illustrated with real data and research, providing a clear sense of how questions about important social issues can be studied with various statistical techniques.

A Focus on Diversity: The United States and International.

A strong emphasis on race, class, and gender as central substantive concepts is mindful of a trend in the social sciences toward integrating issues of diversity in the curriculum. This focus on the richness of social differences within our society and our global neighbors is manifested in the application of statistical tools to examine how race, class, gender, and other categories of experience shape our social world and explain social behavior.

Chapter Reorganization and Content.

Each revision presents many opportunities to polish and expand the content of our text. In this edition, we have made a number of changes in response to feedback from reviewers and fellow instructors. We merged frequency distributions and graphic presentation into one chapter. We expanded the discussion of probability in Chapters 6 and 7. We refined the discussion on the interpretation and application of descriptive statistics (variance and standard deviation) and inferential tests (t, Z, F ratio, and regression and correlation). End- of-chapter exercises have been organized into calculation and interpretation problems.

Reading the Research Literature, Statistics in Practice, A Closer Look, and Data at Work.

In your student career and in the workplace, you may be expected to read and interpret statistical information presented by others in professional and scholarly publications. These statistical analyses are a good deal more complex than most class and textbook

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presentations. To guide you in reading and interpreting research reports written by social scientists, most of our chapters include a Reading the Research Literature and a Statistics in Practice feature, presenting excerpts of published research reports or specific SPSS calculations using the statistical concepts under discussion. Being statistically literate involves more than just completing a calculation; it also includes learning how to apply and interpret statistical information and being able to say what it means. We include A Closer Look discussion in each chapter, advising students about the common errors and limitations in quantitative data collection and analysis. A new chapter feature for this eighth edition is Data at Work, profiling men and women who use data in their work settings and professions.

SPSS and GSS 2014.

IBM® SPSS® Statistics* is used throughout this book, although the use of computers is not required to learn from the text. Real data are used to motivate and make concrete the coverage of statistical topics. As a companion to the eighth edition’s SPSS demonstrations and exercises, we provide two GSS 2014 data sets on the study site at http://edge.sagepub.com/frankfort8e. SPSS exercises at the end of each chapter rely on variables from both data modules. There is ample opportunity for instructors to develop their own exercises using these data.

*SPSS is a registered trademark of International Business Machines Corporation.

Tools to Promote Effective Study.

Each chapter concludes with a list of Main Points and Key Terms discussed in that chapter. Boxed definitions of the Key Terms also appear in the body of the chapter, as do Learning Checks keyed to the most important points. Key Terms are also clearly defined and explained in the Glossary, another special feature in our book. Answers to all the Odd- Numbered Exercises and Learning Checks in the text are included at the end of the book, as well as on the study site at http://edge.sagepub.com/frankfort8e. Complete step-by- step solutions are provided in the instructor’s manual, available on the study site.

A Note About Rounding

Throughout this text and in ancillary materials, we followed these rounding rules: If the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up. If the number you are rounding is followed by 0, 1, 2, 3, or 4, do not change the number. For rounding long decimals, look only at the number in the place you are rounding to and the number that follows it.

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resources for review, study, and further exploration, keeping both instructors and students on the cutting edge of teaching and learning. SAGE edge content is open access and available on demand. Learning and teaching has never been easier!

SAGE edge for students provides a personalized approach to help students accomplish their coursework goals in an easy-to-use learning environment.

Mobile-friendly eFlashcards strengthen understanding of key terms and concepts. Mobile-friendly practice quizzes allow for independent assessment by students of their mastery of course material. A customized online action plan includes tips and feedback on progress through the course and materials, which allows students to individualize their learning experience. Web exercises and meaningful web links facilitate student use of Internet resources, further exploration of topics, and responses to critical thinking questions. EXCLUSIVE! Access to full-text SAGE journal articles that have been carefully selected to support and expand on the concepts presented in each chapter. Access to GSS 2014 data sets.

SAGE edge for instructors supports teaching by making it easy to integrate quality content and create a rich learning environment for students.

Test banks provide a diverse range of pre-written options as well as the opportunity to edit any question and/or insert personalized questions to effectively assess students’ progress and understanding. Sample syllabus provides a suggested model for instructors to use when creating the syllabi for their courses. Editable, chapter-specific PowerPoint® slides offer complete flexibility for creating a multimedia presentation for the course. EXCLUSIVE! Access to full-text SAGE journal articles have been carefully selected to support and expand on the concepts presented in each chapter to encourage students to think critically. Multimedia content includes web resources and web exercises that appeal to students with different learning styles. Lecture notes summarize key concepts by chapter to ease preparation for lectures and class discussions. Lively and stimulating ideas for class activities that can be used in class to reinforce active learning. Chapter-specific discussion questions help launch classroom interaction by prompting students to engage with the material and by reinforcing important content. A course cartridge provides easy LMS (Learning Management System) integration.

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Acknowledgments

We are both grateful to Jerry Westby, Series Editor for SAGE Publications, for his commitment to our book and for his invaluable assistance through the production process.

Many manuscript reviewers recruited by SAGE provided invaluable feedback. For their thoughtful comments to the eighth edition, we thank

Andrew S. Fullerton, Oklahoma State University David A. Gay, University of Central Florida Dr. Lindsey Peterson, Mississippi State University Heather Macpherson Parrott, Long Island University-Post Christopher Donoghue, Montclair State University S. Michael Gaddis, The Pennsylvania State University Jann W. MacInnes, University of Florida Laura Sullivan, Brandeis University Warren Waren, Texas A&M University Joe Weinberg, University of Southern Mississippi

For their comments to the seventh edition, we thank

Walter F. Carroll, Bridgewater State University Andrew S. Fullerton, Oklahoma State University David A. Gay, University of Central Florida Judith G. Gonyea, Boston University Megan Henly, University of New Hampshire Patricia A. Jaramillo, The University of Texas at San Antonio Brett Lehman, Louisiana State University James W. Love, California State University, Fullerton Kay Kei-Ho Pih, California State University, Northridge

For their comments to the sixth edition, we thank

Diane Balduzy, Massachusetts College of Liberal Arts Ellen Berg, California State University–Sacramento Robert Carini, University of Louisville Melissa Evans-Andris, University of Louisville Meredith Greif, Georgia State University Kristen Kenneavy, Ramapo College Dave Rausch, West Texas A&M University Billy Wagner, California State University–Channel Islands Kevin Yoder, University of North Texas

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For their comments to the fifth edition, we thank

Anna A. Amirkhanyan, The American University Robert Carini, University of Louisville Patricia Case, University of Toledo Stanley DeViney, University of Maryland Eastern Shore David Gay, University of Central Florida Dusten R. Hollist, University of Montana Ross Koppel, University of Pennsylvania Benny Marcus, Temple University Matt G. Mutchler, California State University Dominguez Hills Mahasin C. Owens-Sabir, Jackson State University Dave Rausch, West Texas A&M University Kevin Yoder, University of North Texas

We are grateful to Jessica Miller and Kelly DeRosa for guiding the book through the production process. We would also like to acknowledge Laura Kirkhuff, Krishna Pradeep Joghee, and the rest of the SAGE staff for their assistance on this edition.

We extend our deepest appreciation to Michael Clark for his fine editing and data work. Among his many contributions, Michael would relate our revision goals to his student experience, reminding us of how students can learn and successfully master this material.

Chava Frankfort-Nachmias would like to thank and acknowledge her friends and colleagues for their unending support; she also would like to thank her students:

I am grateful to my students at the University of Wisconsin–Milwaukee, who taught me that even the most complex statistical ideas can be simplified. The ideas presented in this book are the products of many years of classroom testing. I thank my students for their patience and contributions.

Finally, I thank my partner, Marlene Stern, for her love and support.