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Illuminating statistical analysis using scenarios and simulations / Jeffrey E Kottemann, Ph.D.

By: Kottemann, Jeffrey E.
Call number: QA276 K676 2017 Material type: TextTextPublisher: Hoboken, New Jersey : John Wiley & Sons, Inc., [2017]Description: xi, 297 pages : illustrations. ; 25 cm.Content type: text Media type: unmediated Carrier type: volumeISBN: 9781119296331 (cloth) ; 1119296331 (cloth) ; 9781119296362 (epub)Subject(s): Mathematical statistics | Distribution (Probability theory)DDC classification: 519.5
Contents:
Illuminating Statistical Analysis Using Scenarios and Simulations; Contents; Preface; Acknowledgements; Part I: Sample Proportions and the Normal Distribution; 1: Evidence and Verdicts; 2: Judging Coins I; 3: Brief on Bell Shapes; 4: Judging Coins II; 5: Amount of Evidence I; 6: Variance of Evidence I; 7: Judging Opinion Splits I; 8: Amount of Evidence II; 9: Variance of Evidence II; 10: Judging Opinion Splits II; 11: It Has Been the Normal Distribution All Along; A Note on Stricter Thresholds for Type I Error; 12: Judging Opinion Split Differences; 13: Rescaling to Standard Errors.
14: The Standardized Normal Distribution Histogram15: The z-Distribution; 16: Brief on Two-Tail Versus One-Tail; 17: Brief on Type I Versus Type II Errors; The Bigger Picture; Part II: Sample Means and the Normal Distribution; 18: Scaled Data and Sample Means; 19: Distribution of Random Sample Means; 20: Amount of Evidence; 21: Variance of Evidence; Variance and Standard Deviation; 22: Homing in on the Population Mean I; 23: Homing in on the Population Mean II; 24: Homing in on the Population Mean III; 25: Judging Mean Differences; 26: Sample Size, Variance, and Uncertainty.
27: The t-DistributionPart III: Multiple Proportions and Means: The X- and F-Distributions; 28: Multiple Proportions and the X2-Distribution; 29: Facing Degrees of Freedom; 30: Multiple Proportions: Goodness of Fit; A Note on Using Chi-squared to Test the Distribution of a Scaled Variable; 31: Two-Way Proportions: Homogeneity; 32: Two-Way Proportions: Independence; 33: Variance Ratios and the F-Distribution; 34: Multiple Means and Variance Ratios: ANOVA; 35: Two-Way Means and Variance Ratios: ANOVA; Part IV: Linear Associations: Covariance, Correlation, and Regression; 36: Covariance.
37: Correlation38: What Correlations Happen Just by Chance?; Special Considerations: Confidence Intervals for Sample Correlations; 39: Judging Correlation Differences; Special Considerations: Sample Correlation Differences; 40: Correlation with Mixed Data Types; 41: A Simple Regression Prediction Model; 42: Using Binomials Too; Getting More Sophisticated #1; Getting More Sophisticated #2; 43: A Multiple Regression Prediction Model; Getting More Sophisticated; 44: Loose End I (Collinearity); 45: Loose End II (Squaring R); 46: Loose End III (Adjusting R-Squared); 47: Reality Strikes.
Part V: Dealing with Unruly Scaled Data48: Obstacles and Maneuvers; 49: Ordered Ranking Maneuver; 50: What Rank Sums Happen Just by Chance?; 51: Judging Rank Sum Differences; 52: Other Methods Using Ranks; 53: Transforming the Scale of Scaled Data; 54: Brief on Robust Regression; 55: Brief on Simulation and Resampling; Part VI: Review and Additional Concepts; 56: For Part I; 57: For Part II; 58: For Part III; 59: For Part IV; 60: For Part V; Appendices; A: Data Types and Some Basic Statistics; Some Basic Statistics (Primarily for Scaled and Binomial Variables)
Summary: "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" -- From the publisher.
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Includes index.

Illuminating Statistical Analysis Using Scenarios and Simulations; Contents; Preface; Acknowledgements; Part I: Sample Proportions and the Normal Distribution; 1: Evidence and Verdicts; 2: Judging Coins I; 3: Brief on Bell Shapes; 4: Judging Coins II; 5: Amount of Evidence I; 6: Variance of Evidence I; 7: Judging Opinion Splits I; 8: Amount of Evidence II; 9: Variance of Evidence II; 10: Judging Opinion Splits II; 11: It Has Been the Normal Distribution All Along; A Note on Stricter Thresholds for Type I Error; 12: Judging Opinion Split Differences; 13: Rescaling to Standard Errors.

14: The Standardized Normal Distribution Histogram15: The z-Distribution; 16: Brief on Two-Tail Versus One-Tail; 17: Brief on Type I Versus Type II Errors; The Bigger Picture; Part II: Sample Means and the Normal Distribution; 18: Scaled Data and Sample Means; 19: Distribution of Random Sample Means; 20: Amount of Evidence; 21: Variance of Evidence; Variance and Standard Deviation; 22: Homing in on the Population Mean I; 23: Homing in on the Population Mean II; 24: Homing in on the Population Mean III; 25: Judging Mean Differences; 26: Sample Size, Variance, and Uncertainty.

27: The t-DistributionPart III: Multiple Proportions and Means: The X- and F-Distributions; 28: Multiple Proportions and the X2-Distribution; 29: Facing Degrees of Freedom; 30: Multiple Proportions: Goodness of Fit; A Note on Using Chi-squared to Test the Distribution of a Scaled Variable; 31: Two-Way Proportions: Homogeneity; 32: Two-Way Proportions: Independence; 33: Variance Ratios and the F-Distribution; 34: Multiple Means and Variance Ratios: ANOVA; 35: Two-Way Means and Variance Ratios: ANOVA; Part IV: Linear Associations: Covariance, Correlation, and Regression; 36: Covariance.

37: Correlation38: What Correlations Happen Just by Chance?; Special Considerations: Confidence Intervals for Sample Correlations; 39: Judging Correlation Differences; Special Considerations: Sample Correlation Differences; 40: Correlation with Mixed Data Types; 41: A Simple Regression Prediction Model; 42: Using Binomials Too; Getting More Sophisticated #1; Getting More Sophisticated #2; 43: A Multiple Regression Prediction Model; Getting More Sophisticated; 44: Loose End I (Collinearity); 45: Loose End II (Squaring R); 46: Loose End III (Adjusting R-Squared); 47: Reality Strikes.

Part V: Dealing with Unruly Scaled Data48: Obstacles and Maneuvers; 49: Ordered Ranking Maneuver; 50: What Rank Sums Happen Just by Chance?; 51: Judging Rank Sum Differences; 52: Other Methods Using Ranks; 53: Transforming the Scale of Scaled Data; 54: Brief on Robust Regression; 55: Brief on Simulation and Resampling; Part VI: Review and Additional Concepts; 56: For Part I; 57: For Part II; 58: For Part III; 59: For Part IV; 60: For Part V; Appendices; A: Data Types and Some Basic Statistics; Some Basic Statistics (Primarily for Scaled and Binomial Variables)

"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" -- From the publisher.

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