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Understanding Statistical Analysis and Modeling


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Table of Contents

Introduction Acknowledgments About the Author PART I. RESEARCH DESIGN 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 PART II. DESCRIPTIVE STATISTICS 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 PART III. STATISTICAL INFERENCE AND PROBABILITY 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 PART IV. TOOLS FOR MAKING STATISTICAL INFERENCES 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 Index

About the Author

Robert Bruhl is the author of the statistics textbook Understanding Statistical Analysis and Modeling for Sage (2018). He is currently Clinical Professor in the Department of Political Science, where his primary focus is on policy analysis and research design. Included in his specialties are economic history, voter behavior, and Congressional behavior. Most recently, he has focused his attention on political marketing and campaigns, and has presented papers on this subject both nationally and internationally. He has also contributed his expertise to both local, national, and international media. Prior to his appointment at UIC, he taught at DePaul University in their Public Service Graduate Program, and before entering the academic world, he enjoyed a fifteen-year career in the private sector, and held various positions in management consulting, marketing, and business planning. He has a B.A. degree (Phi Beta Kappa) in Mathematics from Northwestern University, an M.S. degree in Computer and Communication Sciences from the University of Michigan, an M.B.A. in Business Economics from the University of Chicago, and a Ph.D. (Phi Kappa Phi) in Public Policy Analysis from the University of Illinois at Chicago. He is currently at work on a book describing the political and economic development of the English-American Colonies, with a focus on the effect this development had on the U.S. Constitution.


"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

"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

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

-- Brian Frederick

"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

"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.

"This book provides a thorough introduction to statistics. End-of-chapter exercises and SPSS (R) tutorials will greatly enhance students' abilities to transfer skills learned in the classroom to real-world problems."

-- Christopher Larimer

"Functional and straightforward. A comprehensive introduction to statistics!"

-- Derrick Bryan

"This is a remarkable book that integrates examples, SPSS (R) 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

"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

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