Kottemann J. Illuminating Statistical Analysis Using Scenarios and Simulations

John Wiley & Sons, Inc., 2017. — 263 p. — ISBN: 9781119296331Features 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 analysisSample Proportions and the Normal Distribution
Evidence and Verdicts
Judging Coins I
Briefon Bell Shapes
Judging Coins II
Amount of Evidence I
Variance of Evidence I
Judging Opinion Splits I
Amount of Evidence II
Variance of Evidence II
Judging Opinion Splits II
It Has Been the Normal Distribution All Along
Judging Opinion Split Differences
Rescaling to Standard Errors
The Standardized Normal Distribution Histogram
The z-Distribution
Brief on Two-Tail Versus One-Tail
Brief on Type I Versus Type II Errors
Sample Means and the Normal Distribution
Scaled Data and Sample Means
Distribution of Random Sample Means
Amount of Evidence
Variance of Evidence
Homing in on the Population Mean I
Homing in on the Population Mean II
Homing in on the Population Mean III
Judging Mean Differences
Sample Size, Variance, and Uncertainty
The t-Distribution
Multiple Proportions and Means: The X²- and F-Distributions
Multiple Proportions and the X²- Distribution
Facing Degrees of Freedom
Multiple Proportions: Goodness of Fit
Two-Way Proportions: Homogeneity
Two-Way Proportions: Independence
Variance Ratios and the F-Distribution
Multiple Means and Variance Ratios: ANOVA
Two-Way Means and Variance Ratios: ANOVA
Linear Associations: Covariance, Correlation, and Regression
Covariance
Correlation
What Correlations Happen Just by Chance?
Judging Correlation Differences
Correlation with Mixed Data Types
A Simple Regression Prediction Model
Using Binomials Too
A Multiple Regression Prediction Model
Loose End I (Collinearity)
Loose End II (Squaring R)
Loose End III (Adjusting R-Squared)
Reality Strikes
Dealing with Unruly Scaled Data
Obstacles and Maneuvers
Ordered Ranking Maneuver
What Rank Sums Happen Just by Chance?
Judging Rank Sum Differences
Other Methods Using Ranks
Transforming the Scale of Scaled Data
Brief on Robust Regression
Brief on Simulation and Resampling
Review and Additional Concepts
For Part I
For Part II
For Part III
For Part IV
For Part V
Appendices
Data Types and Some Basic Statistics
Simulating Statistical Scenarios
Standard Error as Standard Deviation
Data Excerpt
Repeated Measures
Bayesian Statistics
Data Mining