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Preface

Chapter 1 An Introduction to Statistics and Research Design

The Two Branches of Statistics

Descriptive Statistics

Inferential Statistics

Distinguishing Between a Sample and a Population

How to Transform Observations into Variables

Discrete Observations

Continuous Observations

Variables and Research

Independent, Dependent, and Confounding Variables

Reliability and Validity

Introduction to Hypothesis Testing

Conducting Experiments to Control for Confounding Variables

Between-Groups Design versus Within-Groups Design

Correlational Research

Chapter 2 Frequency Distributions

Frequency Distributions

Frequency Tables

Grouped Frequency Tables

Histograms

Frequency Polygons

Shapes of Distributions

Normal Distributions

Skewed Distributions

Chapter 3 Visual Displays of Data

How to Lie with Visual Statistics

“The Most Misleading Graph Ever Published”

Techniques for Misleading with Graphs

Common Types of Graphs

Scatterplots

Line Graphs

Bar Graphs

Pictorial Graphs

Pie Charts

How to Build a Graph

Choosing the Appropriate Type of Graph

How to Read a Graph

Guidelines for Creating a Graph

The Future of Graphs

Chapter 4 Central Tendency and Variability

Central Tendency

Mean, the Arithmetic Average

Median, the Middle Score

Mode, the Most Common Score

How Outliers Affect Measures of Central Tendency

Which Measure of Central Tendency Is Best?

Measures of Variability

Range

Variance

Standard Deviation

Chapter 5 Sampling and Probability

Samples and Their Populations

Random Sampling

Convenience Sampling

The Problem with a Biased Sample

Random Assignment

Probability

Coincidence and Probability

Expected Relative-Frequency Probability

Independence and Probability

Inferential Statistics

Developing Hypotheses

Making a Decision About the Hypothesis

Type I and Type II Errors

Type I Errors

Type II Errors

Chapter 6 The Normal Curve, Standardization, and z Scores

The Normal Curve

Standardization, z Scores, and the Normal Curve

The Need for Standardization

Transforming Raw Scores into z Scores

Transforming z Scores into Raw Scores

Using z Scores to Make Comparisons

Transforming z Scores into Percentiles

The Central Limit Theorem

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Creating a Distribution of Means

Characteristics of the Distribution of Means

Using the Central Limit Theorem to Make Comparisons with z Scores

Chapter 7 Hypothesis Testing with z Tests

The z Table

Raw Scores, z Scores, and Percentages

The z Table and Distributions of Means

The Assumptions and Steps of Hypothesis Testing

The Three Assumptions for Conducting Analyses

The Six Steps of Hypothesis Testing

An Example of the z Test

Chapter 8 Confidence Intervals, Effect Size, and Statistical Power

Confidence Intervals

Interval Estimates

Calculating Confidence Intervals with z Distributions

Effect Size

The Effect of Sample Size on Statistical Significance

What Effect Size Is

Cohen’s d

Meta-Analysis

Statistical Power

The Importance of Statistical Power

Five Factors That Affect Statistical Power

Chapter 9 The Single-Sample t Test and the Paired-Samples t Test

The t Distributions

Estimating Population Standard Deviation from a Sample

Calculating Standard Error for the t Statistic

Using Standard Error to Calculate the t Statistic

The Single-Sample t Test

The t Table and Degrees of Freedom

The Six Steps of the Single-Sample t Test

Calculating a Confidence Interval for a Single-Sample t Test

Calculating Effect Size for a Single-Sample t Test

The Paired-Samples t Test

Distributions of Mean Differences

The Six Steps of the Paired-Samples t Test

Calculating a Confidence Interval for a Paired-Samples t Test

Calculating Effect Size for a Paired-Samples t Test

Chapter 10 The Independent-Samples t Test

Conducting an Independent-Samples t Test

A Distribution of Differences Between Means

The Six Steps of the Independent-Samples t Test

Reporting the Statistics

Beyond Hypothesis Testing

Calculating a Confidence Interval for an Independent-Samples t Test

Calculating Effect Size for an Independent-Samples t Test

Chapter 11 One-Way ANOVA

Using the F Distributions with Three or More Samples

Type I Errors When Making Three or More Comparisons

The F Statistic as an Expansion of the z and t Statistics

The F Distributions for Analyzing Variability to Compare Means

The F Table

The Language and Assumptions for ANOVA

One-Way Between-Groups ANOVA

Everything About ANOVA but the Calculations

The Logic and Calculations of the F Statistic

Making a Decision

Beyond Hypothesis Testing for the One-Way Between-Groups ANOVA

R², the Effect Size for ANOVA

Post Hoc Tests

Tukey HSD

One-Way Within-Groups ANOVA

The Benefits of Within-Groups ANOVA

The Six Steps of Hypothesis Testing

Beyond Hypothesis Testing for the One-Way Within-Groups ANOVA

R², the Effect Size for ANOVA

Tukey HSD

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Chapter 12 Two-Way Between-Groups ANOVA

Two-Way ANOVA

Why We Use Two-Way ANOVA

The More Specific Vocabulary of Two-Way ANOVA

Two Main Effects and an Interaction

Understanding Interactions in ANOVA

Interactions and Public Policy

Interpreting Interactions

Conducting a Two-Way Between-Groups ANOVA

The Six Steps of Two-Way ANOVA

Identifying Four Sources of Variability in a Two-Way ANOVA

Effect Size for Two-Way ANOVA

Chapter 13 Correlation

The Meaning of Correlation

The Characteristics of Correlation

Correlation Is Not Causation

The Pearson Correlation Coefficient

Calculating the Pearson Correlation Coefficient

Hypothesis Testing with the Pearson Correlation Coefficient

Applying Correlation in Psychometrics

Reliability

Validity

Chapter 14 Regression

Simple Linear Regression

Prediction versus Relation

Regression with z Scores

Determining the Regression Equation

The Standardized Regression Coefficient and Hypothesis Testing with Regression

Interpretation and Prediction

Regression and Error

Applying the Lessons of Correlation to Regression

Regression to the Mean

Proportionate Reduction in Error

Multiple Regression

Understanding the Equation

Multiple Regression in Everyday Life

Chapter 15 Nonparametric Tests

Nonparametric Statistics

An Example of a Nonparametric Test

When to Use Nonparametric Tests

Chi-Square Tests

Chi-Square Test for Goodness of Fit

Chi-Square Test for Independence

Cramér’s V, the Effect Size for Chi Square

Graphing Chi-Square Percentages

Relative Risk

Ordinal Data and Correlation

When the Data Are Ordinal

The Spearman Rank-Order Correlation Coefficient

The Mann–Whitney U Test

Appendix A Reference for Basic Mathematics

A.1: Diagnostic Test: Skills Evaluation

A.2: Symbols and Notation: Arithmetic Operations

A.3: Order of Operations

A.4: Proportions: Fractions, Decimals, and Percentages

A.5: Solving Equations with a Single Unknown Variable

A.6: Answers to Diagnostic Test and Self-Quizzes

Appendix B Statistical Tables

B.1: The z Distribution

B.2: The t Distributions

B.3: The F Distributions

B.4: The Chi-Square Distributions

B.5: The q Statistic (Tukey HSD Test)

B.6: The Pearson Correlation Coefficient

B.7: The Spearman Correlation Coefficient

B.8A: Mann–Whitney U for a p Level of .05 for a One-Tailed Test

B.8B: Mann–Whitney U for a p Level of .05 for a Two-Tailed Test

B.9: Wilcoxon Signed-Ranks Test for Matched Pairs (T)

B.10: Random Digits

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Appendix C Solutions to Odd-Numbered End-of-Chapter Problems

Appendix D Solutions to Check Your Learning Problems

Appendix E Choosing the Appropriate Statistical Test

Category 1: Two Scale Variables

Category 2: Nominal Independent Variable(s) and a Scale Dependent Variable

Category 3: One or Two Nominal Variables

Category 4: At Least One Ordinal Variable

Appendix F Reporting Statistics

Overview of Reporting Statistics

Justifying the Study

Reporting Traditional Statistics

Reporting Newer Statistics

Appendix G Building Better Graphs Using Excel

Glossary

References

Index