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Understanding Statistical Analysis and Modeling

Understanding Statistical Analysis and Modeling

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December 2017 | 440 pages | SAGE Publications, Inc

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
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.

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ISBN: 9781506317410