#
An Introduction to Statistics
An Active Learning Approach

- Kieth A. Carlson - Valparaiso University, USA
- Jennifer R. Winquist - Valparaiso University, USA

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.

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 |

SPSS |

Overview of the Activity |

Chapter 1 Practice Test |

Central Tendency |

Computing the Mean |

Find the Median |

Find the Mode |

SPSS |

Overview of the Activity |

Chapter 2 Practice Test |

Population Variability |

Steps in Computing a Population’s Standard Deviation |

Sample Variability |

SPSS |

Overview of the Activity |

Chapter 3 Practice Test |

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 |

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 |

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 |

Single-Sample t Test |

Conceptual Information |

One-Tailed Single-Sample t Test Example |

Two-Tailed Single-Sample t Test Example |

Other Alpha Levels |

SPSS |

Overview of the Activity |

Chapter 7 Practice Test |

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 |

SPSS |

Overview of the Activity |

Chapter 8 Practice 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 |

SPSS |

Overview of the Activities |

Chapter 9 Practice 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 |

SPSS |

Overview of the Activities |

Chapter 10 Practice Test |

Independent Samples ANOVA |

An Example ANOVA Problem |

An Additional Note on ANOVAs: Family-Wise Error and Alpha Inflation |

SPSS |

Overview of the Activities |

Chapter 11 Practice Test |

Purpose of the Two-Way ANOVA |

Describing Factorial Designs |

Logic of the Two-Way ANOVA |

Example of a Two-Way ANOVA |

SPSS |

Overview of the Activities |

Chapter 12 Practice Test |

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 |

SPSS |

Overview of the Activities |

Chapter 13 Practice Test |

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 |

SPSS |

Overview of the Activities |

Chapter 14 Practice Test |

Unit Normal Table (z Table) |

One-Tailed Probabilities t Table |

Two-Tailed Probabilities t Table |

F Table (a = .05) |

F Table (a = .01) |

The Studentized Range Statistic (q) Table |

One-Tailed Pearson’s Correlation Table |

Two-Tailed Pearson’s Correlation Table |

Spearman’s Correlation Table |

Fisher r to z Table |

Critical Values for Chi-Square |

Computing SSs for Factorial ANOVA |

Choosing Correct Test Statistics |

### Supplements

** 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**offer complete flexibility for creating a multimedia presentation for the course^{®}slides **Lecture notes**summarize key concepts by chapter to ease preparation for lectures and class discussions

__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*

**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*

**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.

**Counseling, School & Educational Psychology Dept., SUNY At Buffalo**