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Understanding Statistical Analysis and Modeling
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Understanding Statistical Analysis and Modeling

November 2017 | 440 pages | SAGE Publications, Inc
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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.



 
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
Key features

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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