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*
*Notes*
**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*
*Notes*
**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*
*Notes*
**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*

*Notes*

**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*

*Notes*

**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

Probability Distributions

The Normal Distribution

Standardizing Variables and Calculating z-Scores

*Chapter Summary*
*Using Stata*
*Using SPSS*
*Practice Problems*
*Notes*
**Chapter 7** From Sample to Population

Repeating 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*
*Notes*
**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*
*Notes*
**Chapter 9** Differences between Samples and Populations

The Logic of Hypothesis Testing

Null Hypotheses (H_{0}) and Alternative Hypotheses (H_{a})

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*
*Notes*
**Chapter 10** Comparing Groups

Two-Sample Hypothesis Tests

The Logic of the Null and Alternative Hypotheses 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*
*Notes*
**Chapter 11** Testing Mean Differences among Multiple Groups

Comparing Variation within and between Groups

Hypothesis Testing Using ANOVA

Analysis of Variance Assumptions

The Steps of an ANOVA Test

Determining Which Means Are Different: Post-Hoc Tests

ANOVA Compared to Repeated t-Tests

*Chapter Summary*

*Using Stata*

*Using SPSS*

*Practice Problems*

*Notes*

**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*

*Notes*

**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*

*Notes*

**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 the Estimate

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*
*Notes*
**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**