# 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.

Learning Objectives |

Motivation |

Representation and Modeling |

A Special Case: Investigating Subjective Behavior |

Reasons for an Empirical Investigation |

Summary |

Exercises |

Some Formal Terminology |

Chapter 2. Methods of Quantitative Empirical Investigation |

Learning Objectives |

Motivation |

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

Limited Focus or Intent to Generalize |

Controlled or Natural Observations |

Applied versus Pure Research |

Summary |

Exercises |

Learning Objectives |

Motivation: Comparing, Sorting, and Counting |

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

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

Some Important Technical Notes |

Summary |

SPSS® Tutorial |

Exercises |

Learning Objectives |

Motivation |

A Cautionary Note Regarding Quantitatively Assessed Properties |

Constructing a Sample Frequency Distribution for a Quantitative Property |

Identifying a Typical Phenomenon from a Set of Phenomena |

Assessing and Using the Median of a Set of Observations |

Assessing and Using the Mean of a Set of Observations |

Interpreting and Comparing the Mode, Median, and Mean |

Summary |

SPSS® Tutorial |

Exercises |

Learning Objectives |

Motivation |

A Case Example: The Frequency Distribution Report |

The Range of a Set of Observations |

The Mean Absolute Difference |

The Variance and Standard Deviation |

Interpreting the Variance and Standard Deviation |

Comparing the Mean Absolute Difference and Standard Deviation |

A Useful Note on Calculating the Variance |

A Note on Modeling and the Assumption of Variability |

Summary |

SPSS® Tutorial |

Exercises |

The Method of Moments |

A Distribution of “Squared Differences from a Mean” |

Learning Objectives |

Motivation |

Executing the Z-Transformation |

An Example |

Summary |

An Exercise |

Learning Objectives |

Motivation |

Uncertainty, Chance, and Probability |

Selection Outcomes and Probabilities |

Events and Probabilities |

Describing a Probability Model for a Quantitative Property |

Summary |

Exercises |

Learning Objectives |

Motivation |

Probability Models Involving Co-Existing Properties |

Models of Association, Conditional Probabilities, and Stochastic Independence |

Co-Variability in Two Quantitative Properties |

Importance of Stochastic Independence and Co-Variance in Statistical Inference |

Summary |

Exercises |

Learning Objectives |

Motivation |

Samples and Sampling |

Bernoulli Trials and the Binomial Distribution |

Representing the Character of a Population |

Predicting Potential Samples from a Known Population |

The Normal Distribution |

The Central Limit Theorem |

Normal Sampling Variability and Statistical Significance |

Summary |

Exercises |

Learning Objectives |

Motivation |

Projecting the Occurrence of a Qualitative Property for a Population |

Projecting a Parameter of a Population from a Sample Statistic |

Some Notes on Sampling |

Summary |

Exercises |

Learning Objectives |

Motivation |

An Example |

An Extension: Testing the Statistical Significance of Population Proportions |

Summary |

SPSS® Tutorial |

Exercises |

Learning Objectives |

Motivation |

Comparing Sample Means Using the Central Limit Theorem |

The t-Test |

Summary |

SPSS® Tutorial |

Exercises |

Learning Objectives |

Motivation |

Variability and “Squared Differences” |

“Typical” Variability and the F-Statistic |

Summary |

SPSS® Tutorial |

Exercises |

Learning Objectives |

Motivation |

Assessing an Association as a Co-Variance |

Step One: Visual Interpretation with a Scatter-Plot |

Step Two: Assessing the Co-Variation as the Correlation Coefficient |

Step Three: Constructing a Linear Mathematical Model |

Step 4: Assessing the Usefulness of the Model |

Summary |

SPSS® Tutorial |

Exercises |

### Supplements

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

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

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

**Downloadable datasets**to accompany exercises and problems in the book**Solutions**to all exercises and problems**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**

HEOA Compliance

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**Available formats**

ISBN: 9781506317397 | Electronic Version | Suggested Retail Price: $66.00 | Bookstore Price: $52.80 |

ISBN: 9781506317410 | Paperback | Suggested Retail Price: $82.00 | Bookstore Price: $65.60 |

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