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An Introduction to Statistics

An Introduction to Statistics
An Active Learning Approach

Second Edition

December 2016 | 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
April 25, 2017
Key features
  • Enhanced activity questions, with most questions using a fixed-choice format, provide better feedback to students to identify areas of improvement.
  • Streamlined organization combines hypothesis testing and assessing statistical assumptions to help students recognize that different statistical tests analyze different types of variables.
  • Expanded coverage of effect sizes includes all pairwise comparisons (including ANOVAs).
  • Incorporation of confidence intervals into all t-test chapters includes explanations and activities.
  • More instruction on writing results using APA style, particularly in the t-test and ANOVA chapters, gives readers confidence to convey their data.
  • A decision tree at the end of the book helps students choose the correct statistical tool for hypothesis testing.
  • Chapter-ending practice tests provide students with more opportunities for practice.
  • Integrative assignments in the related t, independent t, one-way ANOVA, and correlation chapters reinforce the different information researchers obtain from significance tests, effect sizes, and confidence intervals, encouraging students to think like researchers.


  • Embedded reading questions and empirically developed activities in each chapter help students extract key concepts and enable them to learn by doing.
  • Detailed, step-by-step instructions include annotated explanations for conducting statistical procedures with SPSS.   
  • Carefully developed scenarios, problem sets, and quiz questions in each chapter help students test their knowledge and master the material
  • Online self-test reviews help reinforce student understanding and long-term retention. 

Sample Materials & Chapters

Chapter 1

Chapter 3

Chapter 10

For instructors

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