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Statistics
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."

 

 
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

 
Summary

 
History Trivia: Achenwall to Nightingale

 
Key Terms, Symbols, and Definitions

 
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

 
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

 
SPSS Lesson 2

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

 
Choosing Between 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, Symbols, and Definitions

 
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

 
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 and Definitions

 
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?

 
Probability

 
History Trivia: Egon Pearson to Karl Pearson

 
Key Terms, Symbols, and Definitions

 
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

 
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

 
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, Symbols, and Definitions

 
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 and Definitions

 
Chapter 7 Practice Problems

 
Chapter 7 Test Yourself Questions

 
SPSS Lesson 7

 
 
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

 
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 and Definitions

 
Chapter 9 Practice Problems

 
Chapter 9 Test Questions

 
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

 
Warning!

 
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, Symbols, and Definitions

 
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 and Definitions

 
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 and Definitions

 
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, Symbols, and Definitions

 
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
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

 
SPSS Lesson 15

 
 
Chapter 16: Other Statistical Parameters and Tests
Big Data

 
Health Science Statistics

 
Additional Statistical Analyses and Multivariate Statistics

 
A Summary of Multivariate Statistics

 
Coda

 
Key Terms and Definitions

 
Chapter 16 Practice Problems

 
Chapter 16 Test Yourself Questions

 

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

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Frederick L. Coolidge

Frederick L. Coolidge (Ph.D.) received his B.A., M.A., and Ph.D. in Psychology at the University of Florida. He completed a two-year postdoctoral fellowship in clinical neuropsychology at Shands Teaching Hospital in Gainesville, Florida. He has been awarded three Fulbright Fellowships to India (1987, 1992, and 2005). He has also won three teaching awards at the University of Colorado (1984, 1987, and 1992), including the lifetime title of University of Colorado Presidential Teaching Scholar. In 2005, he received the University of Colorado at Colorado Springs College of Letters, Arts, and Sciences’ Outstanding Research and Creative Works... More About Author

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ISBN: 9781506368436
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