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An Introduction to Statistics

An Introduction to Statistics
An Active Learning Approach

Second Edition
Additional resources:

March 2017 | 656 pages | SAGE Publications, Inc

The Second Edition takes a unique, active approach to teaching and learning introductory statistics that allows students to discover and correct their misunderstandings as chapters progress rather than at their conclusion. Empirically-developed, self-correcting activities reinforce and expand on fundamental concepts, targeting and holding students’ attention. Based on contemporary memory research, this learner-centered approach leads to better long-term retention through active engagement while generating explanations. Along with carefully placed reading questions, this edition includes learning objectives, realistic research scenarios, practice problems, self-test questions, problem sets, and practice tests to help students become more confident in their ability to perform statistics. 


About the Authors
1 Introduction to Statistics and Frequency Distributions
How to Be Successful in This Course  
Math Skills Required in This Course  
Why Do You Have to Take Statistics?  
Statistics and the Helping Professions  
Hypothesis Testing, Effect Size, and Confidence Intervals  
Testing Causal Hypotheses  
Populations and Samples  
Independent and Dependent Variables  
Scales of Measurement  
Discrete Versus Continuous Variables  
Graphing Data  
Shapes of Distributions  
Frequency Distribution Tables  
Overview of the Activity  
Chapter 1 Practice Test  
2 Central Tendency
Central Tendency  
Computing the Mean  
Find the Median  
Find the Mode  
Overview of the Activity  
Chapter 2 Practice Test  
3 Variability
Population Variability  
Steps in Computing a Population’s Standard Deviation  
Sample Variability  
Overview of the Activity  
Chapter 3 Practice Test  
4 z Scores
z for a Single Score  
Using X to Find Important “Cut Lines”  
z Scores and the Standard Normal Curve  
Example 1: Positive z Score  
Example 2: Negative z Score  
Example 3: Proportion Between Two z Scores  
Overview of the Activity  
Chapter 4 Practice Test  
5 The Distribution of Sample Means and z for a Sample Mean
Sampling and Sampling Error  
Distribution of Sample Means  
z for a Sample Mean  
Example: Computing and Interpreting the z for a Sample Mean  
Exact Probabilities Versus Probability Estimates  
Overview of the Activities  
Chapter 5 Practice Test  
6 Hypothesis Testing With z Scores
Introduction to Hypothesis Testing  
Hypothesis Testing With z for a Sample Mean Example (One-Tailed)  
What Does It Mean to Describe Something as “Statistically Significant”?  
Errors in Hypothesis Testing  
Hypothesis Testing Rules  
What Is a p Value?  
Why Statisticians “Fail to Reject the Null” Rather Than “Accept the Null”  
Why Scientists Say “This Research Suggests” Rather Than “This Research Proves”  
Overview of the Activities  
Chapter 6 Practice Test  
7 Single-Sample t Test
Single-Sample t Test  
Conceptual Information  
One-Tailed Single-Sample t Test Example  
Two-Tailed Single-Sample t Test Example  
Other Alpha Levels  
Overview of the Activity  
Chapter 7 Practice Test  
8 Estimation With Confidence Intervals
Three Statistical Procedures With Three Distinct Purposes  
Logic of Confidence Intervals  
Computing a Confidence Interval for a Population Mean  
Computing Confidence Intervals for a Mean Difference  
Reporting Confidence Intervals in APA Style  
Confidence Intervals for Effect Sizes  
Interpretations of Confidence Intervals  
Overview of the Activity  
Chapter 8 Practice Test  
9 Related Samples t Test
Repeated/Related Samples t Test  
Logic of the Single-Sample and Repeated/Related Samples t Tests  
Related Samples t (Two-Tailed) Example  
Related Samples t (One-Tailed) Example  
Statistical Results, Experimental Design, and Scientific Conclusions  
Overview of the Activities  
Chapter 9 Practice Test  
10 Independent Samples t Test
Independent Samples t  
Conceptual Formula for the Independent Samples t  
Two-Tailed Independent t Test Example  
One-Tailed Independent t Test Example  
Other Alpha Levels  
Overview of the Activities  
Chapter 10 Practice Test  
11 One-Way Independent Samples ANOVA
Independent Samples ANOVA  
An Example ANOVA Problem  
An Additional Note on ANOVAs: Family-Wise Error and Alpha Inflation  
Overview of the Activities  
Chapter 11 Practice Test  
12 Two-Factor ANOVA or Two-Way ANOVA
Purpose of the Two-Way ANOVA  
Describing Factorial Designs  
Logic of the Two-Way ANOVA  
Example of a Two-Way ANOVA  
Overview of the Activities  
Chapter 12 Practice Test  
13 Correlation and Regression
When to Use Correlations and What They Can Tell You  
Review of z Scores  
The Logic of Correlation  
Direction and Strength of Correlation Coefficients  
Computational Formulas  
Spearman’s (rs) Correlations  
Using Scatterplots Prior to Correlation Coefficients  
Alternative Use for Correlation  
Correlation and Causation  
Hypothesis Testing With Correlation  
Two-Tailed Pearson’s Correlation Example  
One-Tailed Pearson’s Correlation Example  
What If You Need to Do a Spearman’s Correlation?  
Confidence Intervals  
Overview of the Activities  
Chapter 13 Practice Test  
14 Goodness of Fit and Independence Chi-Square Statistics
Overview of Chi-Square  
Logic of the Chi-Square Test  
Comparing the Goodness-of-Fit Chi-Square and the Chi-Square for Independence  
Goodness-of-Fit Chi-Square Example  
Chi-Square for Independence  
Overview of the Activities  
Chapter 14 Practice Test  
Appendix A
Unit Normal Table (z Table)  
Appendix B
One-Tailed Probabilities t Table  
Two-Tailed Probabilities t Table  
Appendix C
F Table (a = .05)  
F Table (a = .01)  
Appendix D
The Studentized Range Statistic (q) Table  
Appendix E
One-Tailed Pearson’s Correlation Table  
Two-Tailed Pearson’s Correlation Table  
Appendix F
Spearman’s Correlation Table  
Appendix G
Fisher r to z Table  
Appendix H
Critical Values for Chi-Square  
Appendix I
Computing SSs for Factorial ANOVA  
Appendix J
Choosing Correct Test Statistics  


Instructor Teaching Site

SAGE edge for Instructors supports teaching by making it easy to integrate quality content and create a rich learning environment for students.

  • Test banks provide a diverse range of pre-written options as well as the opportunity to edit any question and/or insert personalized questions to effectively assess students’ progress and understanding
  • Sample course syllabi for semester and quarter courses provide suggested models for structuring one’s course
  • Editable, chapter-specific PowerPoint® slides offer complete flexibility for creating a multimedia presentation for the course
  • Lecture notes summarize key concepts by chapter to ease preparation for lectures and class discussions
Student Study Site

SAGE edge for Students provides a personalized approach to help students accomplish their coursework goals in an easy-to-use learning environment.

  • Mobile-friendly eFlashcards strengthen understanding of key terms and concepts
  • Mobile-friendly practice quizzes allow for independent assessment by students of their mastery of course material
  • A  customized online action plan includes tips and feedback on progress through the course and materials, which allows students to individualize their learning experience
  • Learning objectives reinforce the most important material

“The text is the most thorough I have seen as far as going through examples. After this text, students are almost guaranteed to be able to complete these statistical measures on their own.”

Elizabeth Axel, Adelphi University

Elizabeth Axel
Adelphi University

“The most impressive feature of the text is the manner in which it invites the student to interact with and digest the material covered in each chapter.”

Lyon Rathbun, University of Texas, Brownsville

Lyon Rathbun
University of Texas, Brownsville

This is perhaps the most student friendly intro to statistics book I've had the pleasure of reading. I work with students from the social sciences and before learning can begin, fear must be put to rest. This text presents statistical terms in small chunks to alleviate fear and even perhaps to begin a love affair with the language of statistics.

Daniel Smith
Counseling, School & Educational Psychology Dept., SUNY At Buffalo
March 24, 2017

Sample Materials & Chapters

Chapter 1

Chapter 3

Chapter 10

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ISBN: 9781483378732