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Understanding Statistical Analysis and Modeling

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.

About the Author
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

Chapter 1. “Why” Conduct Research, and “Why” Use Statistics?
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)

Chapter 2. Methods of Quantitative Empirical Investigation
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

Chapter 3. The Frequency Distribution Report: Organizing a Set of Observations
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

Chapter 4. The Mode, the Median, and the Mean: Describing a Typical Value of a Quantitative Property Observed for a Set of Phenomena
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

Chapter 5. The Variance and the Standard Deviation: Describing the Variability Observed for a Quantitative Property of a Set of Phenomena
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)

Chapter 6. The z-Transformation and Standardization: Using the Standard Deviation to Compare Observations
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

Chapter 7. The Concept of a Probability
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

Chapter 8. Coexisting Properties and Joint Probability Models
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

Chapter 9. Sampling and the Normal Probability Model
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

Chapter 10. Estimation Studies: Inferring the Parameters of a Population from the Statistics of a Sample
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

Chapter 11. Chi-Square Analysis: Investigating a Suspected Association Between Two Qualitative Properties
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

Chapter 12. The t-Test of Statistical Significance: Comparing a Quantitative Property Assessed for Two Different Groups
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

Chapter 13. Analysis of Variance: Comparing a Quantitative Property Assessed for Several Different Groups
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

Chapter 14. Correlation Analysis and Linear Regression: Assessing the Covariability of Two Quantitative Properties
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



Instructor Site

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.
Student Study Site

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.”

Scott Comparato
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.”

Robert J. Eger III
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.”

Brian Frederick
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.”

Benjamin C. Ngwudike
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.”

John David Rausch, Jr.
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.”

Christopher Larimer
Political Science, University of Northern Iowa

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

Derrick Bryan
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."

Prachi Kene
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.”

Michael Raisinghani
Management, Texas Woman’s University
Key features


  • A motivation section begins each chapter explaining why the topics are important, and how these topics answer research questions.
  • SPSS® tutorials guide readers through the process of using SPSS® to conduct each type of statistical analysis.
  • Every example of using a statistical procedure begins with a research question and ends by answering that research question to show readers why that statistical result matters.
  • For non-mathematical readers, tables are used to describe statistical calculations because they are easier to follow than formulas.
  • Non-parametric statistical procedures are included for those in the social sciences and business fields.

Sage College Publishing

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