Rowman & Littlefield Publishers

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**Nancy Whittier** is Sophia Smith Professor of Sociology at Smith College. She has taught statistics and research methods for 25 years, and also teaches classes on gender, sexuality, and social movements. She is the author of *Frenemies: Feminists, Conservatives, and Sexual Violence *(Oxford University Press, 2018), *The Politics of Child Sexual Abuse: Emotions, Social Movements, and the State*(Oxford University Press, 2009) and numerous articles on social movements, gender, and sexual violence.

**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, inequality in higher education.

**Howard J. Gold** is Professor of Government at Smith College. He has taught statistics for 30 years, and also teaches courses on American elections, public opinion and the media, and political behavior. His research focuses on public opinion, partisanship, and voting behavior.

Preface

About the Authors

**Chapter 1 Introduction **

Why Study Statistics?

Research Questions and the Research Process

Pinning Things Down: Variables and Measurement

Units of Analysis

Measurement Error: Validity and Reliability

Levels of Measurement

Causation: Independent and Dependent Variables

Getting the Data: Sampling and Generalizing

*Sampling Methods *

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

*Big Data*

Growth Mindset and Math Anxiety

**Using This Book**

Statistical Software

Chapter Summary

Using Stata

Using SPSS

Practice Problems

**Chapter 2 Getting to Know Your Data**

Frequency Distributions

Percentages and Proportions

Cumulative Percentage and Percentile

Percent Change

Rates and Ratios

*Rates*

Ratios

Working with Frequency Distribution Tables

*Missing Values*

Simplifying Tables by Collapsing Categories

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

*Bar Graphs and Pie Charts *

Histograms

Stem-and-Leaf-Plots

Frequency Polygons

Time Series Charts

Comparing Two Groups On the Same Variable Using Tables, Graphs, and Charts

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 3 Examining Relationships between Two Variables**

Cross-Tabulations and Relationships between Variables

*Independent and Dependent Variables*

Column, Row, and Total Percentages

Interpreting the Strength of Relationships

Interpreting the Direction of Relationships

Graphical Representations of Bivariate Relationships

Chapter Summary

Using Stata

Using SPSS

Practice Problems

**Chapter 4 Typical Values in a Group**

What Does It Mean to Describe What Is Typical?

Mean

Median

Mode

Finding the Mode, Median, and Mean in Frequency Distributions

Choosing the Appropriate Measure of Central Tendency

Median Versus Mean Income

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 5 The Diversity of Values in a Group**

Range

Interquartile Range

Standard Deviation

Using the Standard Deviation to Compare Distributions

Comparing Apples and Oranges

Skewed Versus Symmetric Distributions

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

Chapter 6 Probability and the Normal Distribution

The Rules of Probability

*The Addition Rule*

The Complement Rule

*The Multiplication Rule with Independence*

*The Multiplication Rule without Independence*

Applying the Multiplication Rule with Independence to the “Linda” and “Birth-Order” Probability Problems

The Normal Distribution

Standardizing Variables and Calculating Z-Scores

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 7 From Sample to Population**

Repeated Sampling, Sample Statistics, and the Population Parameter

Sampling Distributions

Finding the Probability of Obtaining A Specific Sample Statistic

*Estimating the Standard Error from a Known Population Standard Deviation*

Finding and Interpreting the Z-Score for Sample Means

Finding and Interpreting the Z-Score for Sample Proportions

The Impact of Sample Size On the Standard Error

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 8 Estimating Population Parameters**

Inferential Statistics and the Estimation of Population Parameters

Confidence Intervals Manage Uncertainty Through Margins of Error

Certainty and Precision of Confidence Intervals

Confidence Intervals for Proportions

*Constructing a Confidence Interval for Proportions: Examples*

Confidence Intervals for Means

*The t-Distribution*

Calculating Confidence Intervals for Means: Examples

The Relationship Between Sample Size and Confidence Interval Range

The Relationship Between Confidence Level and Confidence Interval Range

Interpreting Confidence Intervals

How Big a Sample?

Assumptions for Confidence Intervals

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 9 Differences between Samples and Populations**

The Logic of Hypothesis Testing

*Null Hypotheses (H0) and Alternative Hypotheses (Ha)*

One-Tailed and Two-Tailed Tests

Hypothesis Tests for Proportions

*The Steps of the Hypothesis Test*

One-Tailed and Two-Tailed Tests

Hypothesis Tests for Means

*Example: Testing a Claim about a Population Mean*

Error and Limitations: How Do We Know We are Correct?

*Type I and Type II Errors*

What Does Statistical Significance Really Tell Us? Statistical and Practical Significance

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 10 Comparing Groups**

Two-Sample Hypothesis Tests

*The Logic of the Null Hypothesis and Alternative Hypothesis in Two-Sample Tests*

Notation for Two-Sample Tests

The Sampling Distribution for Two-Sample Tests

Hypothesis Tests for Differences Between Means

Confidence Intervals for Differences Between Means

Hypothesis Tests for Differences Between Proportions

Confidence Intervals for Differences Between Proportions

Statistical and Practical Significance in Two-Sample Tests

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 11 Testing Mean Differences among Multiple Groups**

Comparing Variation Within and Between Groups

Hypothesis Testing Using Anova

Analysis of Variance Assumptions

Determining Which Means are Different: Post-Hoc Tests

Anova Compared to RepeateD t-Tests

**Chapter Summary **

Using Stata

Using SPSS

Practice Problems

**Chapter 12 Testing the Statistical Significance of Relationships in Cross-Tabulations**

The Logic of Hypothesis Testing with Chi-Square

The Steps of a Chi-Square Test

Size and Direction of Effects: Analysis of Residuals

Example: Gender and Perceptions of Health

Assumptions of Chi-Square

Statistical Significance and Sample Size

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 13 Ruling Out Competing Explanations for Relationships between Variables**

Criteria for Causal Relationships

Modeling Spurious Relationships

Modeling Non-Spurious Relationships

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

**Chapter 14 Describing Linear Relationships between Variables**

Correlation Coefficients

*Calculating Correlation Coefficients*

Scatterplots: Visualizing Correlations

Regression: Fitting a Line to a Scatterplot

The “Best-Fitting” Line

Slope and Intercept

*Calculating the Slope and Intercept*

Goodness-of-Fit Measures

*R-Squared (r*^{2}*)*

*Standard Error of Prediction*

Dichotomous (“Dummy”) Independent Variables

Multiple Regression

Statistical Inference for Regression

*The F-Statistic*

Standard Error of the Slope

Assumptions of Regression

**Chapter Summary**

Using Stata

Using SPSS

Practice Problems

Solutions to Odd Numbered Practice Problems

Glossary

Appendix A Normal Table

Appendix B Table of t-Values

Appendix C F-Table, for Alpha = .05

Appendix D Chi-Square Table

Appendix E Selected List of Formulas

Appendix F Choosing Tests for Bivariate Relationships

Index

View samples chapters of the __Front Matter__, __Chapter 1__, __Chapter 3__, and __Chapter 9__.

- Stata and SPSS explanations and examples in every chapter.

- Statistics analysis taught in the way it is used in the social sciences.

- Real world applications integrated throughout the chapters.

- Research on the teaching and learning of quantitative material incorporated into the content.

- Multiple types of practice problems provided both in the text and on the open access Companion Website.

- Instructor and student ancillaries written by the authors.

**FOR STUDENTS**

Accompanying the text is an open-access

Companion Website designed to reinforce the main topics and help you master key vocabulary and concepts through flashcards and self-graded quizzes.

**FOR PROFESSORS**

Ancillary Materials are available for this title. For access to these

__professor use only__ materials, please

Sign-In if you are a registered user, or

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**Instructor's Manual.** For each chapter, this valuable resource provides a variety of tools such as lecture outlines, student learning objectives, discussion questions, and other resources to simplify classroom preparation.

**Test Bank.** The Test Bank includes a variety of test questions and is available in either Word or PDF formats. For every chapter in the text, the Test Bank includes a complete test with a variety of question types, including multiple choice, true false, and essay formats.

**Lecture Notes.** The Lecture Notes provide the tables and figures from the text.