Illuminating Statistical Analysis Using Scenarios and Simulations

Features an integrated approach of statistical scenarios and simulations and aids 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 and seminars in statistics and statistical inference. The book also serves as a thought–provoking treatise for researchers, scientists, managers, and others with a keen interest in statistical analysis.  

Jeffrey E. Kottemann, PhD, 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 PhD in Systems and Quantitative Methods from the University of Arizona.  

 

Preface

Acknowledgements 

Part I:  Sample Proportions and the Normal Distribution 

Chapter  1: Evidence and Verdicts 

Chapter 2: Judging Coins I 

Chapter 3: Brief on Bell–Shapes 

Chapter 4: Judging Coins II 

Chapter 5: Amount of Evidence I 

Chapter 6: Variance of Evidence I 

Chapter 7: Judging Opinion Splits I 

Chapter 8: Amount of Evidence II 

Chapter 9: Variance of Evidence II 

Chapter 10: Judging Opinion Splits II 

Chapter 11: It s Been the Normal Distribution All Along 

Chapter 12: Judging Opinion Split Differences 

Chapter 13: Rescaling to Standard Errors 

Chapter 14: The Standardized Normal Distribution Histogram 

Chapter 15: The z Distribution 

Chapter 16: Brief on Two–Tail vs. One–Tail 

Chapter 17: Brief on Type I vs. Type II Errors 

Part II: Sample Means and the Normal Distribution

Chapter 18: Scaled Data and Sample Means 

Chapter 19: Distribution of Random Sample Means 

Chapter 20: Amount of Evidence 

Chapter 21: Variance of Evidence 

Chapter 22: Homing in on the Population Mean I 

Chapter 23: Homing in on the Population Mean II 

Chapter 24: Homing in on the Population Mean III 

Chapter 25: Judging Mean Differences 

Chapter 26: Sample Size, Variance, and Uncertainty 

Chapter 27: The t Distribution 

Part III: Multiple Proportions and Means: the X2 and F Distributions

Chapter 28: Multiple Proportions and the X2 Distribution 

Chapter 29: Facing Degrees of Freedom 

Chapter 30: Multiple Proportions: Goodness of Fit 

Chapter 31: Two–Way Proportions: Homogeneity 

Chapter 32: Two–Way Proportions: Independence 

Chapter 33: Variance Ratios and the F Distribution 

Chapter 34: Multiple Means and Variance Ratios: ANOVA 

Chapter 35: Two–Way Means and Variance Ratios: ANOVA 

Part IV: Linear Associations: Covariance, Correlation, and Regression 

Chapter 36: Covariance 

Chapter 37: Correlation 

Chapter 38: What Correlations Happen Just by Chance? 

Chapter 39: Judging Correlation Differences 

Chapter 40: Correlation with Mixed Data Types 

Chapter 41: A Simple Regression Prediction Model 

Chapter 42: Using Binomials Too 

Chapter 43: A Multiple Regression Prediction Model 

Chapter 44: Loose End I (Collinearity) 

Chapter 45: Loose End II (Squaring R) 

Chapter 46: Loose End III (Adjusting R Squared) 

Chapter 47: Reality Strikes 

Part V:  Dealing with Unruly Scaled Data 

Chapter 48: Obstacles and Maneuvers 

Chapter 49: Ordered Ranking Maneuver 

Chapter 50: What Rank Sums Happen Just By Chance? 

Chapter 51: Judging Rank Sum Differences

Chapter 52: Other Methods Using Ranks 

Chapter 53: Transforming the Scale of Scaled Data 

Chapter 54: Brief on Robust Regression 

Chapter 55: Brief on Simulation and Resampling 

Part VI: Review and Additional Concepts

Chapter 56: For Part I 

Chapter 57: For Part II 

Chapter 58: For Part III 

Chapter 59: For Part IV 

Chapter 60: For Part V 

Appendices 

A. Data Types and Some Basic Statistics

B. Simulating Statistical Scenarios 

C. Standard Error as Standard Deviation

D. Data Excerpt 

E. Repeated Measures 

F. Bayesian Statistics 

G. Data Mining 

Index

Jeffrey E. Kottemann, PhD, 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 PhD in Systems and Quantitative Methods from the University of Arizona.