Chapter 1: A Gentle Introduction

How Much Math Do I Need to Do Statistics?

The General Purpose of Statistics: Understanding the World

Liberal and Conservative Statisticians

Descriptive and Inferential Statistics

Experiments Are Designed to Test Theories and Hypotheses

Eight Essential Questions of Any Survey or Study

On Making Samples Representative of the Population

Experimental Design and Statistical Analysis as Controls

The Language of Statistics

On Conducting Scientific Experiments

The Dependent Variable and Measurement

Measurement Scales: The Difference Between Continuous and Discrete Variables

Types of Measurement Scales

Rounding Numbers and Rounding Error

History Trivia: Achenwall to Nightingale

Key Terms, Symbols, and Definitions

Chapter 1 Practice Problems

Chapter 1 Test Yourself Questions

Chapter 2: Descriptive Statistics: Understanding Distributions of Numbers

The Purpose of Graphs and Tables: Making Arguments and Decisions

A Summary of the Purpose of Graphs and Tables

Shapes of Frequency Distributions

Grouping Data Into Intervals

Advice on Grouping Data Into Intervals

The Cumulative Frequency Distribution

Cumulative Percentages, Percentiles, and Quartiles

Nonnormal Frequency Distributions

On the Importance of the Shapes of Distributions

Additional Thoughts About Good Graphs Versus Bad Graphs

History Trivia: De Moivre to Tukey

Key Terms and Definitions

Chapter 2 Practice Problems

Chapter 2 Test Yourself Questions

Chapter 3: Statistical Parameters: Measures of Central Tendency and Variation

Measures of Central Tendency

Choosing Between Measures of Central Tendency

Uncertain or Equivocal Results

Correcting for Bias in the Sample Standard Deviation

How the Square Root of x2 Is Almost Equivalent to Taking the Absolute Value of x

The Computational Formula for Standard Deviation

The Sampling Distribution of Means, the Central Limit Theorem, and the Standard Error of the Mean

The Use of the Standard Deviation for Prediction

Practical Uses of the Empirical Rule: As a Definition of an Outlier

Practical Uses of the Empirical Rule: Prediction and IQ Tests

History Trivia: Fisher to Eels

Key Terms, Symbols, and Definitions

Chapter 3 Practice Problems

Chapter 3 Test Yourself Questions

Chapter 4: Standard Scores, the z Distribution, and Hypothesis Testing

The Classic Standard Score: The z Score and the z Distribution

More Practice on Converting Raw Data Into Z Scores

Interpreting Negative z Scores

Testing the Predictions of the Empirical Rule With the z Distribution

Why Is the z Distribution So Important?

How We Use the z Distribution to Test Experimental Hypotheses

More Practice With the z Distribution and T Scores

Summarizing Scores Through Percentiles

History Trivia: Karl Pearson to Egon Pearson

Key Terms and Definitions

Chapter 4 Practice Problems

Chapter 4 Test Yourself Questions

Chapter 5: Inferential Statistics: The Controlled Experiment, Hypothesis Testing, and the z Distribution

Hypothesis Testing in the Controlled Experiment

Hypothesis Testing: The Big Decision

How the Big Decision Is Made: Back to the z Distribution

The Parameter of Major Interest in Hypothesis Testing: The Mean

Nondirectional and Directional Alternative Hypotheses

A Debate: Retain the Null Hypothesis or Fail to Reject the Null Hypothesis

The Null Hypothesis as a Nonconservative Beginning

The Four Possible Outcomes in Hypothesis Testing

Significant and Nonsignificant Findings

Trends, and Does God Really Love the.05 Level of Significance More Than the.06 Level?

Directional or Nondirectional Alternative Hypotheses: Advantages and Disadvantages

Did Nuclear Fusion Occur?

Conclusions About Science and Pseudoscience

The Most Critical Elements in the Detection of Baloney in Suspicious Studies and Fraudulent Claims

Can Statistics Solve Every Problem?

History Trivia: Egon Pearson to Karl Pearson

Key Terms, Symbols, and Definitions

Chapter 5 Practice Problems

Chapter 5 Test Yourself Questions

Chapter 6: An Introduction to Correlation and Regression

Correlation: Use and Abuse

A Warning: Correlation Does Not Imply Causation

Another Warning: Chance Is Lumpy

Correlation and Prediction

The Four Common Types of Correlation

The Pearson Product–Moment Correlation Coefficient

Testing for the Significance of a Correlation Coefficient

Obtaining the Critical Values of the t Distribution

If the Null Hypothesis Is Rejected

Representing the Pearson Correlation Graphically: The Scatterplot

Fitting the Points With a Straight Line: The Assumption of a Linear Relationship

Interpretation of the Slope of the Best-Fitting Line

The Assumption of Homoscedasticity

The Coefficient of Determination: How Much One Variable Accounts for Variation in Another Variable: The Interpretation of r2

Quirks in the Interpretation of Significant and Nonsignificant Correlation Coefficients

Reading the Regression Line

The World is a Complex Place: Any Single Behavior is Most Often Caused by Multiple Variables

Final Thoughts About Regression Analyses: A Warning about the Interpretation of the Significant Beta Coefficients

Significance Test for Spearman’s r

Point-Biserial Correlation

Testing for the Significance of the Point-Biserial Correlation Coefficient

Testing for the Significance of Phi

History Trivia: Galton to Fisher

Key Terms, Symbols, and Definitions

Chapter 6 Practice Problems

Chapter 6 Test Yourself Questions

Chapter 7: The t Test for Independent Groups

The Statistical Analysis of the Controlled Experiment

One t Test but Two Designs

Assumptions of the Independent t Test

The Formula for the Independent t Test

You Must Remember This! An Overview of Hypothesis Testing With the t Test

What Does the t Test Do? Components of the t Test Formula

What If the Two Variances Are Radically Different From One Another?

The Power of a Statistical Test

The Correlation Coefficient of Effect Size

Another Measure of Effect Size: Cohen’s d

Estimating the Standard Error

History Trivia: Gosset and Guinness Brewery

Key Terms and Definitions

Chapter 7 Practice Problems

Chapter 7 Test Yourself Questions

Chapter 8: The t Test for Dependent Groups

Assumptions of the Dependent t Test

Why the Dependent t Test May Be More Powerful Than the Independent t Test

How to Increase the Power of a t Test

Drawbacks of the Dependent t Test Designs

One-Tailed or Two-Tailed Tests of Significance

Hypothesis Testing and the Dependent t Test: Design 1

Design 1 (Same Participants or Repeated Measures): A Computational Example

Design 2 (Matched Pairs): A Computational Example

Design 3 (Same Participants and Balanced Presentation): A Computational Example

History Trivia: Fisher to Pearson

Key Terms and Definitions

Chapter 8 Practice Problems

Chapter 8 Test Yourself Questions

Chapter 9: Analysis of Variance (ANOVA): One-Factor Completely Randomized Design

A Limitation of Multiple t Tests and a Solution

The Equally Unacceptable Bonferroni Solution

The Acceptable Solution: An Analysis of Variance

The Null and Alternative Hypotheses in ANOVA

The Beauty and Elegance of the F Test Statistic

How Can There Be Two Different Estimates of Within-Groups Variance?

What a Significant ANOVA Indicates

Degrees of Freedom for the Numerator

Degrees of Freedom for the Denominator

Determining Effect Size in ANOVA: Omega-Squared (w2)

Another Measure of Effect Size: Eta (h)

History Trivia: Gosset to Fisher

Key Terms and Definitions

Chapter 9 Practice Problems

Chapter 9 Test Yourself Questions

Chapter 10: After a Significant Analysis of Variance: Multiple Comparison Tests

Conceptual Overview of Tukey’s Test

Computation of Tukey’s HSD Test

What to Do If the Error Degrees of Freedom Are Not Listed in the Table of Tukey’s q Values

Determining What It All Means

On the Importance of Nonsignificant Mean Differences

Key Terms, Symbols, and Definitions

Chapter 10 Practice Problems

Chapter 10 Test Yourself Questions

Chapter 11: Analysis of Variance (ANOVA): One-Factor Repeated-Measures Design

The Repeated-Measures ANOVA

Assumptions of the One-Factor Repeated-Measures ANOVA

Determining Effect Size in ANOVA

Key Terms and Definitions

Chapter 11 Practice Problems

Chapter 11 Test Yourself Questions

Chapter 12: Factorial ANOVA: Two-Factor Completely Randomized Design

The Most Important Feature of a Factorial Design: The Interaction

Fixed and Random Effects and In Situ Designs

The Null Hypotheses in a Two-Factor ANOVA

Assumptions and Unequal Numbers of Participants

Key Terms and Definitions

Chapter 12 Practice Problems

Chapter 12 Test Yourself Problems

Chapter 13: Post Hoc Analysis of Factorial ANOVA

Main Effect Interpretation: Gender

Why a Multiple Comparison Test Is Unnecessary for a Two-Level Main Effect, and When Is a Multiple Comparison Test Necessary?

Multiple Comparison Test for the Main Effect for Age

Warning: Limit Your Main Effect Conclusions When the Interaction Is Significant

Multiple Comparison Tests

Interpretation of the Interaction Effect

Writing Up the Results Journal Style

Exploring the Possible Outcomes in a Two-Factor ANOVA

Determining Effect Size in a Two-Factor ANOVA

History Trivia: Fisher and Smoking

Key Terms, Symbols, and Definitions

Chapter 13 Practice Problems

Chapter 13 Test Yourself Questions

Chapter 14: Factorial ANOVA: Additional Designs

Overview of the Split-Plot ANOVA

Two-Factor ANOVA: Repeated Measures on Both Factors Design

Overview of the Repeated-Measures ANOVA

Key Terms and Definitions

Chapter 14 Practice Problems

Chapter 14 Test Yourself Questions

Chapter 15: Nonparametric Statistics: The Chi-Square Test

Overview of the Purpose of Chi-Square

Overview of Chi-Square Designs

Chi-Square Test: Two-Cell Design (Equal Probabilities Type)

The Chi-Square Distribution

Assumptions of the Chi-Square Test

Chi-Square Test: Two-Cell Design (Different Probabilities Type)

Interpreting a Significant Chi-Square Test for a Newspaper

Chi-Square Test: Three-Cell Experiment (Equal Probabilities Type)

Chi-Square Test: Two-by-Two Design

What to Do After a Chi-Square Test Is Significant

When Cell Frequencies Are Less Than 5 Revisited

Other Nonparametric Tests

History Trivia: Pearson and Biometrika

Key Terms, Symbols, and Definitions

Chapter 15 Practice Problems

Chapter 15 Test Yourself Questions

Chapter 16: Other Statistical Parameters and Tests

Health Science Statistics

Additional Statistical Analyses and Multivariate Statistics

A Summary of Multivariate Statistics

Key Terms and Definitions

Chapter 16 Practice Problems

Chapter 16 Test Yourself Questions