# Understanding Statistical Analysis and Modeling

- Robert Bruhl - University of Illinois at Chicago, USA

**Understanding Statistical Analysis and Modeling** is a text for graduate and advanced undergraduate students in the social, behavioral, or managerial sciences seeking to understand the logic of statistical analysis. Robert Bruhl covers all the basic methods of descriptive and inferential statistics in an accessible manner by way of asking and answering research questions. Concepts are discussed in the context of a specific research project and the book includes probability theory as the basis for understanding statistical inference. Instructions on using SPSS**^{®}** are included so that readers focus on interpreting statistical analysis rather than calculations. Tables are used, rather than formulas, to describe the various calculations involved with statistical analysis and the exercises in the book are intended to encourage students to formulate and execute their own empirical investigations.

Purpose: Making Sense of What We Observe |

Deciding How to Represent Properties of a Phenomenon |

Describing Differences or Explaining Differences Between Phenomena? |

Deciding How to Collect Observations |

1.0 Learning Objectives |

1.1 Motivation |

1.2 Representation and Modeling |

1.3 A Special Case: Investigating Subjective Behavior |

1.4 Reasons for an Empirical Investigation |

1.5 Summary |

1.6 Exercises |

1.7 Some Formal Terminology (Optional) |

2.0 Learning Objectives |

2.1 Motivation |

2.2 Instrumentation: Choosing a Tool to Assess a Property of Interest |

2.3 Limited Focus or Intent to Generalize |

2.4 Controlled or Natural Observations |

2.5 Applied Versus Pure Research |

2.6 Summary |

2.7 Exercises |

Organizing and Describing a Set of Observations |

Measuring the Variability in a Set of Observations |

Describing a Set of Observations in Terms of Their Variability |

3.0 Learning Objectives |

3.1 Motivation: Comparing, Sorting, and Counting |

3.2 Constructing a Sample Frequency Distribution for a “Qualitative” Property |

3.3 Constructing a Sample Frequency Distribution for an “Ordinal” Property |

3.4 Some Important Technical Notes |

3.5 Summary |

3.6 SPSS Tutorial |

3.7 Exercises |

4.0 Learning Objectives |

4.1 Motivation |

4.2 A Cautionary Note Regarding Quantitatively Assessed Properties |

4.3 Constructing a Sample Frequency Distribution for a Quantitative Property |

4.4 Identifying a Typical Phenomenon from a Set of Phenomena |

4.5 Assessing and Using the Median of a Set of Observations |

4.6 Assessing and Using the Mean of a Set of Observations |

4.7 Interpreting and Comparing the Mode, the Median, and the Mean |

4.8 Summary |

4.9 SPSS Tutorial |

4.10 Exercises |

5.0 Learning Objectives |

5.1 Motivation |

5.2 A Case Example: The Frequency Distribution Report |

5.3 The Range of a Set of Observations |

5.4 The Mean Absolute Difference |

5.5 The Variance and the Standard Deviation |

5.6 Interpreting the Variance and the Standard Deviation |

5.7 Comparing the Mean Absolute Difference and the Standard Deviation |

5.8 A Useful Note on Calculating the Variance |

5.9 A Note on Modeling and the Assumption of Variability |

5.10 Summary |

5.11 SPSS Tutorial |

5.12 Exercises |

5.13 The Method of Moments (Optional) |

5.14 A Distribution of “Squared Differences from a Mean” (Optional) |

6.0 Learning Objectives |

6.1 Motivation |

6.2 Executing the z-Transformation |

6.3 An Example |

6.4 Summary |

6.5 An Exercise |

Why Probability Theory? |

The Concept of a Probability |

Predicting Events Involving Two Coexisting Properties |

Sampling and the Normal Probability Model |

7.0 Learning Objectives |

7.1 Motivation |

7.2 Uncertainty, Chance, and Probabilit |

7.3 Selection Outcomes and Probabilities |

7.4 Events and Probabilities |

7.5 Describing a Probability Model for a Quantitative Property |

7.6 Summary |

7.7 Exercises |

8.0 Learning Objectives |

8.1 Motivation |

8.2 Probability Models Involving Coexisting Properties |

8.3 Models of Association, Conditional Probabilities, and Stochastic Independence |

8.4 Covariability in Two Quantitative Properties |

8.5 Importance of Stochastic Independence and Covariance in Statistical Inference |

8.6 Summary |

8.7 Exercises |

9.0 Learning Objectives |

9.1 Motivation |

9.2 Samples and Sampling |

9.3 Bernoulli Trials and the Binomial Distribution |

9.4 Representing the Character of a Population |

9.5 Predicting Potential Samples from a Known Population |

9.6 The Normal Distribution |

9.7 The Central Limit Theorem |

9.8 Normal Sampling Variability and Statistical Significance |

9.9 Summary |

9.10 Exercises |

Estimation Studies |

Association Studies |

10.0 Learning Objectives |

10.1 Motivation |

10.2 Estimating the Occurrence of a Qualitative Property for a Population |

10.3 Estimating the Occurrences of a Quantitative Property for a Population |

10.4 Some Notes on Sampling |

10.5 SPSS Tutorial |

10.6 Summary |

10.7 Exercises |

11.0 Learning Objectives |

11.1 Motivation |

11.2 An Example |

11.3 An Extension: Testing the Statistical Significance of Population Proportions |

11.4 Summary |

11.5 SPSS Tutorial |

11.6 Exercises |

12.0 Learning Objectives |

12.1 Motivation |

12.2 An Example |

12.3 Comparing Sample Means Using the Central Limit Theorem (Optional) |

12.4 Comparing Sample Means Using the t-Test |

12.5 Summary |

12.6 SPSS Tutorial |

12.7 Exercises |

13.0 Learning Objectives |

13.1 Motivation |

13.2 An Example |

13.3 The F-Test |

13.4 A Note on Sampling Distributions (Optional) |

13.5 Summary |

13.6 SPSS Tutorial |

13.7 Exercises |

14.0 Learning Objectives |

14.1 Motivation |

14.2 An Example |

14.3 Visual Interpretation with a Scatter Plot (Optional) |

14.4 Assessing an Association as a Covariance |

14.5 Regression Analysis: Representing a Correlation as a Linear Mathematical Model |

14.6 Assessing the Explanatory Value of the Model |

14.7 Summary |

14.8 SPSS Tutorial |

14.9 Exercises |

### Supplements

Password-protected **Instructor Resources** include the following:

- Editable, chapter-specific Microsoft®
**PowerPoint® slides**offer complete flexibility in easily creating a multimedia presentation for your course. **Sample syllabi**help you prepare a course using*Understanding Statistical Analysis and Modeling.***Extra exercises**including solutions reinforce the key concepts of each chapter and can be used as**test questions.**- All
**figures and tables**from the book available for download.

The open-access** Student Study Site** includes the following:

**Solutions**to selected exercises and problems from the book**EXCLUSIVE!**Access to multimedia from the**SAGE Research Methods****platform**featuring videos with the author

“This is a well-thought out and designed text that gives students an open and accessible introduction to the concepts and techniques necessary for conducting social science research.”

**Political Science, Southern Illinois University**

“This book presents the opportunity for those teaching statistics to present probability theory in a non-intrusive manner, allowing students to move beyond their fears of probability theory and access one of the most important aspects of really understanding statistics.”

**Financial Management, Naval Postgraduate School**

“This text takes a refreshing approach to presenting statistical concepts in a methodologically rigorous yet meaningful way that students will intuitively grasp.”

**Political Science, Bridgewater State University**

“This text has a competitive edge over similar textbooks. I strongly recommend it to students who want to have a clear understanding of how to develop good research questions and select statistical techniques appropriate in answering the research questions.”

**Educational Leadership, Jackson State University**

“Readers will be surprised how much they are learning about statistics and statistical analysis as they read this book. The author presents mathematical concepts by first starting with the familiar and gently guiding the reader in more unfamiliar territory.”

**Political Science, West Texas A&M University**

“This book provides a thorough introduction to statistics. End-of-chapter exercises and SPSS**^{®}** tutorials will greatly enhance students' abilities to transfer skills learned in the classroom to real-world problems.”

**Political Science, University of Northern Iowa**

“Functional and straightforward. A comprehensive introduction to statistics!”

**Sociology, Morehouse College**

“This is a remarkable book that integrates examples, SPSS**^{®}** tutorials, and exercises. The chapters provide an in-depth analysis of the key concepts. This book is an essential resource for advanced-level undergraduate students and graduate students in the study of statistical analysis."

**Counseling, Educational Leadership and School Psychology, Rhode Island College**

“An enjoyable read. The book has the potential to promote numeracy among the general public, and serve as a resource in statistics education.”

**Management, Texas Woman’s University**

### Sample Materials & Chapters

Chapter 14: Correlation Analysis and Linear Regression_Assessing the Co-Variabil