Cover
Half Title Page
Title Page
Copyright
Dedication
Acknowledgments
Brief Contents
Introduction: You Do Not Need to Be a Statistician to Understand Statistics!
1. Identifying a Research Problem and Stating Hypotheses
2. Identifying the Independent and Dependent Variables in a Hypothesis
3. Measures of Dispersion and Measures of Relative Standing
4. Graphically Describing the Dependent Variable
5. Choosing the Right Statistical Test
6. The One-Sample t-Test
7. The Independent-Sample t-Test
8. The Dependent-Sample t-Test
9. Analysis of Variance and Multivariate Analysis of Variance
10. The Chi-Square Tests
11. The Correlational Procedures
Conclusion: Have We Accomplished What We Set Out to Do?
Appendix A. Area under the Normal Curve Table (Critical Values of z)
Appendix B. Critical Values of t
Appendix C. Critical Values of F When Alpha = .01
Appendix D. Critical Values of F When Alpha = .05
Appendix E. Critical Values of F When Alpha = .10
Appendix F. Critical Values of Chi-Square
Appendix G. Selecting the Right Statistical Test
Glossary
Answers to Quiz Time!
Index
About the Author
Extended Contents
Introduction: You Do Not Need to Be a Statistician to Understand Statistics!
A Little Background
Many Students Do Not Know What They’re Getting Into
A Few Simple Steps
Step 1: Identify the Problem
Step 2: State a Hypothesis
Step 3: Identify the Independent Variable
Step 4: Identify and Describe the Dependent Variable
Step 5: Choose the Right Statistical Test
Step 6: Use Data Analysis Software to Test the Hypothesis
So, What’s New in This Edition?
Summary
Do You Understand These Key Words and Phrases?
1. Identifying a Research Problem and Stating Hypotheses
Introduction
Step 1: Identify the Problem
Characteristics of a Good Problem Statement
Finding a Good Research Problem
The Problem Is Interesting to the Researcher
The Scope of the Problem Is Manageable by the Researcher
The Researcher Has the Knowledge, Time, and Resources Needed to Investigate the Problem
The Problem Can Be Researched through the Collection and Analysis of Numeric Data
Investigating the Problem Has Theoretical or Practical Significance
It Is Ethical to Investigate the Problem
Writing the Problem Statement
Problem Statements Must Be Clear and Concise
The Problem Statement Must Include All Variables to Be Considered
The Problem Statement Should Not Interject the Researcher’s Bias
Summary of Step 1: Identify the Problem
Step 2: State a Hypothesis
An Example of Stating Our Hypothesis
A Little More Detail
The Direction of Hypotheses
Using Directional Hypotheses to Test a “Greater Than” Relationship
Using Directional Hypotheses to Test a “Less Than” Relationship
Nondirectional Hypotheses
Hypotheses Must Be Testable via the Collection and Analysis of Data
Research versus Null Hypotheses
Stating Null Hypotheses for Directional Hypotheses
Issues Underlying the Null Hypothesis for Directional Research Hypotheses
Stating Null Hypotheses for Nondirectional Hypotheses
A Preview of Testing the Null Hypothesis
Where Does That Leave Us?
Statistical Words of Wisdom
Summary of Step 2: State a Hypothesis
Do You Understand These Key Words and Phrases?
Quiz Time!
Problem Statements
Case Studies
The Case of Distance Therapy
The Case of the New Teacher
The Case of Being Exactly Right
The Case of “Does It Really Work?”
The Case of Advertising
The Case of Learning to Speak
The Case of Kids on Cruises
2. Identifying the Independent and Dependent Variables in a Hypothesis
Introduction
Step 3: Identify the Independent Variable
Nonmanipulated Independent Variables
Another Way of Thinking about Nonmanipulated Independent Variables
Manipulated or Experimental Independent Variables
Levels of the Independent Variable
Summary of Step 3: Identify the Independent Variable
Step 4: Identify and Describe the Dependent Variable
Identifying Your Dependent Variable
What Type of Data Are We Collecting?
Interval Data
Data Types—What Is the Good News?
Summary of the Dependent Variable and Data Types
Measures of Central Tendency
The Mean, Median, and Mode—Measures of Central Tendency
The Mode
Using Statistical Software to Analyze Our Data
Summary of the First Part of Step 4: Identify and Describe the Dependent Variable
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
3. Measures of Dispersion and Measures of Relative Standing
Introduction
Measures of Dispersion
The Range
The Standard Deviation
The Variance
Measures of Relative Standing
Percentiles
Computing and Interpreting T-Scores
Stanines
Putting It All Together
Using SPSS for T-Scores and Stanines—Not So Fast!
Summary
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
4. Graphically Describing the Dependent Variable
Introduction
Graphical Descriptive Statistics
Graphically Describing Nominal Data
Pie Charts
Bar Charts
Graphically Describing Quantitative Data
Scatterplots
Histograms
Don’t Let a Picture Tell You the Wrong Story!
Summary of Graphical Descriptive Statistics
The Normal Distribution
Things That Can Affect the Shape of a Distribution of Quantitative Data
Summary of the Normal Distribution
Do You Understand These Key Words and Phrases?
Quiz Time!
5. Choosing the Right Statistical Test
Introduction
The Very Basics
The Central Limit Theorem
The Sampling Distribution of the Means
Summary of the Central Limit Theorem and the Sampling Distribution of the Means
How Are We Doing So Far?
Estimating Population Parameters Using Confidence Intervals
The Alpha Value
Type I and Type II Errors
Predicting a Population Parameter Based on a Sample Statistic Using Confidence Intervals
Pay Close Attention Here
Confidence Intervals for Alpha = .01 and Alpha = .10
Another Way to Think about z Scores in Confidence Intervals
Tying This All Together
Be Careful When Changing Your Alpha Values
Do We Understand Everything We Need to Know about Confidence Intervals?
Testing Hypotheses about a Population Parameter Based on a Sample Statistic
Making a Decision about the Certification Examination Scores
We Are Finally Going to Test Our Hypothesis!
Testing a One-Tailed Hypothesis
Testing a One-Tailed “Less Than” Hypothesis
Summarizing What We Just Said
Be Careful When Changing Your Alpha Values
The Heart of Inferential Statistics
Probability Values
A Few More Examples
Great News—We Will Always Use Software to Compute Our p Value
Step 5: Choose the Right Statistical Test
You Already Know a Few Things
A Couple of Notes about the Table
Summary of Step 5: Choose the Right Statistical Test
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas and Symbols?
Quiz Time!
6. The One-Sample t-Test
Introduction
Welcome to the Guinness Breweries
The t Distribution
Putting This Together
Determining the Critical Value of t
Degrees of Freedom
Be Careful Computing Degrees of Freedom
Let’s Get Back to Our Anxiety Hypothesis
Plotting Our Critical Value of t
The Statistical Effect Size of Our Example
Let’s Look at a Directional Hypothesis
Using the p Value
Check Your Mean Scores!
One More Time
Important Note about Software Packages
Let’s Use the Six-Step Model!
The Case of Slow Response Time
The Case of Stopping Sneezing
The Case of Growing Tomatoes
Summary
Do You Understand These Key Words and Phrases?
Do You Know These Formulas?
Quiz Time!
7. The Independent-Sample t-Test
Introduction
If We Have Samples from Two Independent Populations, How Do We Know If They Are Significantly Different from One Another?
The Sampling Distribution of Mean Differences
Calculating the t Value for the Independent-Sample t-Test
Pay Attention Here
Testing Our Hypothesis
The p Value
Note on Variance and the t-Test
The Statistical Effect Size of Our Example
Let’s Try Another Example
Remember the Effect Size
How Does This Work for a Directional Hypothesis?
Reminder—Always Pay Attention to the Direction of the Means!
The Case of the Cavernous Lab
The Case of the Report Cards
The Case of the Anxious Athletes
Putting the Independent-Sample t-Test to Work
Summary
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
The Case of the Homesick Blues
The Case of the Cold Call
The Case of the Prima Donnas
The Case of the Wrong Side of the Road
The Case of Workplace Satisfaction
The Case of the Flower Show
8. The Dependent-Sample t-Test
Introduction
That’s Great, but How Do We Test Our Hypotheses?
Independence versus Dependence
Computing the t Value for a Dependent-Sample t-Test
Testing a One-Tailed “Greater Than” Hypothesis
The Effect Size for a Dependent-Sample t-Test
Testing a One-Tailed “Less Than” Hypothesis
Testing a Two-Tailed Hypothesis
Let’s Move Forward and Use Our Six-Step Model
Step 1: Identify the Problem
Step 2: State a Hypothesis
Step 3: Identify the Independent Variable
Step 4: Identify and Describe the Dependent Variable
Step 5: Choose the Right Statistical Test
Step 6: Use Data Analysis Software to Test the Hypothesis
The Case of the Unexcused Students
Step 1: Identify the Problem
Step 2: State a Hypothesis
Step 3: Identify the Independent Variable
Step 4: Identify and Describe the Dependent Variable
Step 5: Choose the Right Statistical Test
Step 6: Use Data Analysis Software to Test the Hypothesis
The Case of Never Saying Never
Step 1: Identify the Problem
Step 2: State a Hypothesis
Step 3: Identify the Independent Variable
Step 4: Identify and Describe the Dependent Variable
Step 5: Choose the Right Statistical Test
Step 6: Use Data Analysis Software to Test the Hypothesis
Just in Case—A Nonparametric Alternative
Summary
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
The Case of Technology and Achievement
The Case of Worrying about Our Neighbors
The Case of SPAM
The Case of “We Can’t Get No Satisfaction”
The Case of “Winning at the Lottery”
9. Analysis of Variance and Multivariate Analysis of Variance
Introduction
Understanding the ANOVA
The Different Types of ANOVAs
One-Way ANOVA
Factorial ANOVA
Multivariate ANOVA (MANOVA)
Assumptions of the ANOVA
Random Samples
Independence of Scores
Normal Distribution of Data
Homogeneity of Variance
Calculating the ANOVA
Descriptive Statistics
The Total Variance
The Total Sum of Squares
The Between Sum of Squares
The Within Sum of Squares
Computing the Degrees of Freedom
Computing the Mean Square
Computing the F Value
The F Distribution
Determining the Area under the Curve for F Distributions
The p Value for an ANOVA
Effect Size for the ANOVA
Testing a Hypothesis Using the ANOVA
The Case of Multiple Means of Math Mastery
The Post-Hoc Comparisons
Multiple-Comparison Tests
Always Observe the Means!
The Case of Seniors Skipping School
The Case of Quality Time
The Case of Regional Discrepancies
The Factorial ANOVA
The Case of Age Affecting Ability
Interpreting the Interaction p Value
The Case of the Coach
The Multivariate ANOVA (MANOVA)
Assumptions of the MANOVA
Using the MANOVA
The Case of Balancing Time
Summary
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
The Case of Degree Completion
The Case of Seasonal Depression
The Case of Driving Away
The Case of Climbing
The Case of Employee Productivity
10. The Chi-Square Tests
Introduction
The One-Way Chi-Square Test
The Factorial Chi-Square Test (the Chi-Square Test of Independence)
Computing the Chi-Square Statistic
The Chi-Square Distribution
What about the Post-Hoc Test?
Working with an Even Number of Expected Values
The Case of the Belligerent Bus Drivers
The Case of the Irate Parents
The Chi-Square Test of Independence
Computing Chi-Square for the Test of Independence
Computing Expected Values for the Test of Independence
Computing the Chi-Square Value for the Test of Independence
Determining the Degrees of Freedom for the Test of Independence
We Are Finally Going to Test Our Hypothesis
Using SPSS to Check What We Just Computed
The Case of Corporal Punishment
Post-Hoc Tests Following the Chi-Square
The Case of Type of Instruction and Learning Style
Summary
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
The Case of Prerequisites and Performance
The Case of Getting What You Asked For
The Case of Money Meaning Nothing
The Case of Equal Opportunity
11. The Correlational Procedures
Introduction
Understanding the Idea of Correlations
Interpreting Pearson’s r
A Word of Caution
An Even More Important Word of Caution!
A Nonparametric Correlational Procedure
The p Value of a Correlation
The Case of the Absent Students
Another Example: The Case against Sleep
The Case of Height versus Weight
The Case of Different Tastes
Once We Have a Linear Relationship, What Can We Do with It?
Linear Regression
The Regression Equation
Computing the Slope
Computing the Intercept
Why Wasn’t It Exactly Right?
Using the Six-Step Model: The Case of Age and Driving
Summary
Do You Understand These Key Words and Phrases?
Do You Understand These Formulas?
Quiz Time!
The Case of “Like Father, Like Son”
The Case of “Can’t We All Just Get Along?”
The Case of More Is Better
The Case of More Is Better Still
Conclusion: Have We Accomplished What We Set Out to Do?
Statistics in a New Light
A Limited Set of Statistical Techniques
The Use of Statistical Software Packages
A Straightforward Approach
At Long Last
Appendix A. Area under the Normal Curve Table (Critical Values of z)
Appendix B. Critical Values of t
Appendix C. Critical Values of F When Alpha = .01
Appendix D. Critical Values of F When Alpha = .05
Appendix E. Critical Values of F When Alpha = .10
Appendix F. Critical Values of Chi-Square
Appendix G. Selecting the Right Statistical Test
Glossary
Answers to Quiz Time!
Index
About the Author