Preface
Acknowledgments
About the Author
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
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
Non-normal Frequency Distributions
On the Importance of the Shapes of Distributions
Additional Thoughts About Good Graphs Versus Bad Graphs
History Trivia: De Moivre to Tukey
Chapter 2 Practice Problems
Chapter 2 Test Yourself Questions
Chapter 3: Statistical Parameters: Measures of Central Tendency and Variation
Measures of Central Tendency
Choosing Among 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
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
Converting z Scores to Other Types of Standard 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
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
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
Final Thoughts About Multiple 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
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
Chapter 7 Practice Problems
Chapter 7 Test Yourself Questions
Chapter 8: The t Test for Dependent Groups
Variations on the Controlled Experiment
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
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
Chapter 9 Practice Problems
Chapter 9 Test Yourself Questions
Chapter 10: After a Significant ANOVA: Multiple Comparison Tests
Conceptual Overview of Tukey’s Test
Computation of Tukey’s HSD Test
What to Do If the Number of Error Degrees of Freedom Is Not Listed in the Table of Tukey’s q Values
Determining What It All Means
On the Importance of Nonsignificant Mean Differences
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
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
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
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 and Other Nonparametric Tests
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
Chapter 15 Practice Problems
Chapter 15 Test Yourself Questions
Chapter 16: Other Statistical Topics, Parameters, and Tests
Health Science Statistics
Additional Statistical Analyses and Multivariate Statistics
A Summary of Multivariate Statistics
Chapter 16 Practice Problems
Chapter 16 Test Yourself Questions
Appendix A: z Distribution
Appendix B: t Distribution
Appendix C: Spearman’s Correlation
Appendix D: Chi-Square ?2 Distribution
Appendix E: F Distribution
Appendix F: Tukey’s Table
Appendix G: Mann–Whitney U Critical Values
Appendix H: Wilcoxon Signed-Rank Test Critical Values
Appendix I: Answers to Odd-Numbered Test Yourself Questions
Glossary
References
Index