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Illuminating Statistical Analysis Using Scenarios and Simulations

Book Description

 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.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright
  4. Preface
  5. Acknowledgements
  6. Part I: Sample Proportions and the Normal Distribution
    1. Chapter 1: Evidence and Verdicts
    2. Chapter 2: Judging Coins I
    3. Chapter 3: Brief on Bell Shapes
    4. Chapter 4: Judging Coins II
    5. Chapter 5: Amount of Evidence I
    6. Chapter 6: Variance of Evidence I
    7. Chapter 7: Judging Opinion Splits I
    8. Chapter 8: Amount of Evidence II
    9. Chapter 9: Variance of Evidence II
    10. Chapter 10: Judging Opinion Splits II
    11. Chapter 11: It Has Been the Normal Distribution All Along
      1. A Note on Stricter Thresholds for Type I Error
    12. Chapter 12: Judging Opinion Split Differences
    13. Chapter 13: Rescaling to Standard Errors
    14. Chapter 14: The Standardized Normal Distribution Histogram
    15. Chapter 15: The z-Distribution
    16. Chapter 16: Brief on Two-Tail Versus One-Tail
    17. Chapter 17: Brief on Type I Versus Type II Errors
      1. The Bigger Picture
  7. Part II: Sample Means and the Normal Distribution
    1. Chapter 18: Scaled Data and Sample Means
    2. Chapter 19: Distribution of Random Sample Means
    3. Chapter 20: Amount of Evidence
    4. Chapter 21: Variance of Evidence
      1. Variance and Standard Deviation
    5. Chapter 22: Homing in on the Population Mean I
    6. Chapter 23: Homing in on the Population Mean II
    7. Chapter 24: Homing in on the Population Mean III
    8. Chapter 25: Judging Mean Differences
    9. Chapter 26: Sample Size, Variance, and Uncertainty
    10. Chapter 27: The t-Distribution
  8. Part III: Multiple Proportions and Means: The X2- and F-Distributions
    1. Chapter 28: Multiple Proportions and the X2-Distribution
    2. Chapter 29: Facing Degrees of Freedom
    3. Chapter 30: Multiple Proportions: Goodness of Fit
      1. A Note on Using Chi-squared to Test the Distribution of a Scaled Variable
    4. Chapter 31: Two-Way Proportions: Homogeneity
    5. Chapter 32: Two-Way Proportions: Independence
    6. Chapter 33: Variance Ratios and the F-Distribution
    7. Chapter 34: Multiple Means and Variance Ratios: ANOVA
    8. Chapter 35: Two-Way Means and Variance Ratios: ANOVA
  9. Part IV: Linear Associations: Covariance, Correlation, and Regression
    1. Chapter 36: Covariance
    2. Chapter 37: Correlation
    3. Chapter 38: What Correlations Happen Just by Chance?
      1. Special Considerations: Confidence Intervals for Sample Correlations
    4. Chapter 39: Judging Correlation Differences
      1. Special Considerations: Sample Correlation Differences
    5. Chapter 40: Correlation with Mixed Data Types
    6. Chapter 41: A Simple Regression Prediction Model
    7. Chapter 42: Using Binomials Too
      1. Getting More Sophisticated #1
      2. Getting More Sophisticated #2
    8. Chapter 43: A Multiple Regression Prediction Model
      1. Getting More Sophisticated
    9. Chapter 44: Loose End I (Collinearity)
    10. Chapter 45: Loose End II (Squaring R)
    11. Chapter 46: Loose End III (Adjusting R-Squared)
    12. Chapter 47: Reality Strikes
  10. Part V: Dealing with Unruly Scaled Data
    1. Chapter 48: Obstacles and Maneuvers
    2. Chapter 49: Ordered Ranking Maneuver
    3. Chapter 50: What Rank Sums Happen Just by Chance?
    4. Chapter 51: Judging Rank Sum Differences
    5. Chapter 52: Other Methods Using Ranks
    6. Chapter 53: Transforming the Scale of Scaled Data
    7. Chapter 54: Brief on Robust Regression
    8. Chapter 55: Brief on Simulation and Resampling
  11. Part VI: Review and Additional Concepts
    1. Chapter 56: For Part I
    2. Chapter 57: For Part II
    3. Chapter 58: For Part III
    4. Chapter 59: For Part IV
    5. Chapter 60: For Part V
  12. Appendices
  13. A: Data Types and Some Basic Statistics
    1. Some Basic Statistics (Primarily for Scaled and Binomial Variables)
  14. B: Simulating Statistical Scenarios
    1. Random Variation
    2. General Guidelines
    3. Scenario-Specific Instructions
  15. C: Standard Error as Standard Deviation
  16. D: Data Excerpt
  17. E: Repeated Measures
  18. F: Bayesian Statistics
    1. A Note on Priors
    2. Getting More Sophisticated
  19. G: Data Mining
  20. Index
  21. End User License Agreement