Illuminating Statistical Analysis Using Scenarios and Simulations

Jeffrey E. Kottemann

• Publisher: Wiley
• Year: 2017
• ISBN:
  9781119296362
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Features an integrated approach of statistical scenarios and simulations to aid readers in developing key intuitions needed to understand the wide ranging concepts and methods of statistics and inference

Illuminating Statistical Analysis Using Scenarios and Simulations presents the basic concepts of statistics and statistical inference using the dual mechanisms of scenarios and simulations. This approach helps readers develop key intuitions and deep understandings of statistical analysis. Scenario-specific sampling simulations depict the results that would be obtained by a very large number of individuals investigating the same scenario, each with their own evidence, while graphical depictions of the simulation results present clear and direct pathways to intuitive methods for statistical inference. These intuitive methods can then be easily linked to traditional formulaic methods, and the author does not simply explain the linkages, but rather provides demonstrations throughout for a broad range of statistical phenomena. In addition, induction and deduction are repeatedly interwoven, which fosters a natural "need to know basis" for ordering the topic coverage.

Examining computer simulation results is central to the discussion and provides an illustrative way to (re)discover the properties of sample statistics, the role of chance, and to (re)invent corresponding principles of statistical inference. In addition, the simulation results foreshadow the various mathematical formulas that underlie statistical analysis.

In addition, this book:

• Features both an intuitive and analytical perspective and includes a broad introduction to the use of Monte Carlo simulation and formulaic methods for statistical analysis

• Presents straight-forward coverage of the essentials of basic statistics and ensures proper understanding of key concepts such as sampling distributions, the effects of sample size and variance on uncertainty, analysis of proportion, mean and rank differences, covariance, correlation, and regression

• Introduces advanced topics such as Bayesian statistics, data mining, model cross-validation, robust regression, and resampling

• Contains numerous example problems in each chapter with detailed solutions as well as an appendix that serves as a manual for constructing simulations quickly and easily using Microsoft® Office Excel®

Illuminating Statistical Analysis Using Scenarios and Simulations is an ideal textbook for courses, seminars, and workshops in statistics and statistical inference and is appropriate for self-study as well. The book also serves as a thought-provoking treatise for researchers, scientists, managers, technicians, and others with a keen interest in statistical analysis.

Jeffrey E. Kottemann, Ph.D., is Professor in the Perdue School at Salisbury University. Dr. Kottemann has published articles in a wide variety of academic research journals in the fields of business administration, computer science, decision sciences, economics, engineering, information systems, psychology, and public administration. He received his Ph.D. in Systems and Quantitative Methods from the University of Arizona.

Part I
Sample Proportions and the Normal Distribution

1
Evidence and Verdicts

Before we focus in on using statistics as evidence to be used in making judgments, let's take a look at a widely used “verdict outcomes framework.” This general framework is useful for framing judgments in a wide range of situations, including those encountered in statistical analysis.

Anytime we use evidence to arrive at a judgment, there are four generic outcomes possible, as shown in Table 1.1. Two outcomes correspond to correct judgments and two correspond to incorrect judgments, although we rarely know whether our judgments are correct or incorrect. Consider a jury trial in U.S. criminal court. Ideally, the jury is always correct, judging innocent defendants not guilty and judging guilty defendants guilty. Evidence is never perfect, though, and so juries will make erroneous judgments, judging innocent defendants guilty or guilty defendants not guilty.

Table 1.1 Verdict outcomes framework.

In U.S. criminal court, the presumption is that a defendant is innocent until “proven” guilty. Further, convention in U.S. criminal court has it that we are more afraid of punishing an innocent person (type I error) than we are of letting a guilty person go unpunished (type II error). Because of this fear, the threshold for a guilty verdict is set high: “Beyond a reasonable doubt.” So, convicting an innocent person should be a relatively unlikely outcome. In U.S. criminal court, we are willing to have a greater chance of letting a guilty person go unpunished than we are of punishing an innocent person. In short, we need to be very sure before we reject the presumption of innocence and render a verdict of guilty in U.S. criminal court.

We can change the relative chances of the two types of error by changing the threshold. Say we change from “beyond a reasonable doubt” to “a preponderance of evidence.” The former is the threshold used in U.S. criminal court, and the latter is the threshold used in U.S. civil court. Let's say that the former corresponds to being 95% sure before judging a defendant guilty and that the latter corresponds to being 51% sure before judging a defendant guilty. You can imagine cases where the same evidence results in different verdicts in criminal and civil court, which indeed does happen. For example, say that the evidence leads to the jury being 60% sure o...

Table of contents

• Cover
• Title Page
• Copyright
• Preface
• Acknowledgements
• Part I: Sample Proportions and the Normal Distribution
• Part II: Sample Means and the Normal Distribution
• Part III: Multiple Proportions and Means: The X2- and F-Distributions
• Part IV: Linear Associations: Covariance, Correlation, and Regression
• Part V: Dealing with Unruly Scaled Data
• Part VI: Review and Additional Concepts
• Appendices
• Index
• End User License Agreement