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A Gentle Introduction

Fourth Edition

January 2020 | 536 pages | SAGE Publications, Inc

The Fourth Edition of Statistics: A Gentle Introduction shows students that an introductory statistics class doesn’t need to be difficult or dull. This text minimizes students’ anxieties about math by explaining the concepts of statistics in plain language first, before addressing the math. Each formula within the text has a step-by-step example to demonstrate the calculation so students can follow along. Only those formulas that are important for final calculations are included in the text so students can focus on the concepts, not the numbers. A wealth of real-world examples and applications gives a context for statistics in the real world and how it helps us solve problems and make informed choices.

New to the Fourth Edition are sections on working with big data, new coverage of alternative non-parametric tests, beta coefficients, and the "nocebo effect," discussions of p values in the context of research, an expanded discussion of confidence intervals, and more exercises and homework options under the new feature "Test Yourself."


Included with this title:

The password-protected Instructor Resource Site (formally known as SAGE Edge)
offers access to all text-specific resources, including a test bank and editable, chapter-specific PowerPoint® slides. Learn more.
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

What Is a Statistician?

Liberal and Conservative Statisticians

Descriptive and Inferential Statistics

Experiments Are Designed to Test Theories and Hypotheses

Oddball Theories

Bad Science and Myths

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

Operational Definitions

Measurement Error

Measurement Scales: The Difference Between Continuous and Discrete Variables

Types of Measurement Scales

Rounding Numbers and Rounding Error

Statistical Symbols


History Trivia: Achenwall to Nightingale

Key Terms

Chapter 1 Practice Problems

Chapter 1 Test Yourself Questions

SPSS Lesson 1

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

Graphical Cautions

Frequency Distributions

Shapes of Frequency Distributions

Grouping Data Into Intervals

Advice on Grouping Data Into Intervals

The Cumulative Frequency Distribution

Cumulative Percentages, Percentiles, and Quartiles

Stem-and-Leaf Plot

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

Key Terms

Chapter 2 Practice Problems

Chapter 2 Test Yourself Questions

SPSS Lesson 2

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

Choosing Among Measures of Central Tendency

Klinkers and Outliers

Uncertain or Equivocal Results

Measures of Variation

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 Variance

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

Some Further Comments

History Trivia: Fisher to Eels

Key Terms

Chapter 3 Practice Problems

Chapter 3 Test Yourself Questions

SPSS Lesson 3

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

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

Calculating z Scores

More Practice on Converting Raw Data Into z Scores

Converting z Scores to Other Types of Standard Scores

The z Distribution

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

Chapter 4 Practice Problems

Chapter 4 Test Yourself Questions

SPSS Lesson 4

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

Significance Levels

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?

Baloney Detection

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

Chapter 5 Practice Problems

Chapter 5 Test Yourself Questions

SPSS Lesson 5

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

Linear Regression

Reading the Regression Line

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

Spearman’s Correlation

Significance Test for Spearman’s r

Ties in Ranks

Point-Biserial Correlation

Testing for the Significance of the Point-Biserial Correlation Coefficient

Phi (F) Correlation

Testing for the Significance of Phi

History Trivia: Galton to Fisher

Key Terms

Chapter 6 Practice Problems

Chapter 6 Test Yourself Questions

SPSS Lesson 6

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?

A Computational Example

Marginal Significance

The Power of a Statistical Test

Effect Size

The Correlation Coefficient of Effect Size

Another Measure of Effect Size: Cohen’s d

Confidence Intervals

Estimating the Standard Error

History Trivia: Gosset and Guinness Brewery

Key Terms

Chapter 7 Practice Problems

Chapter 7 Test Yourself Questions

SPSS Lesson 7

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

Key Terms

Chapter 8 Practice Problems

Chapter 8 Test Yourself Questions

SPSS Lesson 8

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

The F Ratio

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

ANOVA Designs

ANOVA Assumptions

Pragmatic Overview

What a Significant ANOVA Indicates

A Computational Example

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

Chapter 9 Practice Problems

Chapter 9 Test Questions

Chapter 9 Test Yourself Questions

SPSS Lesson 9

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

Final Results of ANOVA

Quirks in Interpretation

Tukey’s With Unequal Ns

Key Terms

Chapter 10 Practice Problems

Chapter 10 Test Yourself Questions

SPSS Lesson 10

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

Assumptions of the One-Factor Repeated-Measures ANOVA

Computational Example

Determining Effect Size in ANOVA

Key Terms

Chapter 11 Practice Problems

Chapter 11 Test Yourself Questions

SPSS Lesson 11

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

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

Computational Example

Key Terms

Chapter 12 Practice Problems

Chapter 12 Test Yourself Problems

SPSS Lesson 12

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?

Main Effect: Age Levels

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

Final Summary

Writing Up the Results Journal Style

Language to Avoid

Exploring the Possible Outcomes in a Two-Factor ANOVA

Determining Effect Size in a Two-Factor ANOVA

History Trivia: Fisher and Smoking

Key Terms

Chapter 13 Practice Problems

Chapter 13 Test Yourself Questions

SPSS Lesson 13

Chapter 14: Factorial ANOVA: Additional Designs
The Split-Plot Design

Overview of the Split-Plot ANOVA

Computational Example

Two-Factor ANOVA: Repeated Measures on Both Factors Design

Overview of the Repeated-Measures ANOVA

Computational Example

Key Terms and Definitions

Chapter 14 Practice Problems

Chapter 14 Test Yourself Questions

SPSS Lesson 14

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

Key Terms

Chapter 15 Practice Problems

Chapter 15 Test Yourself Questions

SPSS Lesson 15

Chapter 16: Other Statistical Topics, Parameters, and Tests
Big Data

Health Science Statistics

Additional Statistical Analyses and Multivariate Statistics

A Summary of Multivariate Statistics


Key Terms

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


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Statistics is generally not a dynamic topic. But Coolidge is able to break it down in a way that is manageable. His discussion of each type of analyses is easily accessed by the table of contents and accurately depicted in the index. This is especially important for this generation of learners who want easy access to the specific information that is necessary without waiting through extraneous concepts. Coolidge also describes contemporary and specific examples of how miss use of data can have an impact in real world circumstances. This is beneficial because it makes a true connection with the power that a statistical researcher holds.

Dr. Lynn DeSpain
Regis University

It is the only book on the market that covers important advanced techniques such as repeated measures ANOVA and multiple regressions, using SPSS.

Abby Heckman Coats
Westminster College, Fulton, Missouri

The book is written to address a broad range of student ability. It is helpful to students without a strong background in mathematics.

Andrew Zekeri
Department of Psychology and Sociology, Tuskegee University

Adopted as a recommended text for students interested in diving more deeply into some of the concepts we cover (all too briefly) in a refresher course for incoming Masters of Public Policy students.

Mr Ian Adams
Political Science Dept, University Of Utah
January 31, 2020

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