Illuminating Statistical Analysis Using Scenarios and Simulations

This book presents the basic concepts of statistics and statistical inference using the dual mechanisms of scenarios and simulation.  This approach helps readers to develop key intuitions and deep understandings of statistical analysis.  For example, 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 easily be linked to traditional formulaic methods, and the author does not simply explain the connections, 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 topical coverage.  The book is comprised of a series of short, concise lessons that build upon each other and are intended to be read in order. The lessons cover a wide range of concepts and methods of classical (frequentist) statistics and inference, and appendices on Bayesian statistics and data mining methods are also included.  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. The simulation results also foreshadow the various mathematical formulas that underlie statistical analysis.  The book also addresses how simulation can serve as a robust statistical analysis method in its own right.  Topical coverage includes: sample proportions and the normal distribution; sample means and the normal distribution; multiple proportions and means (the x² and F distributions); linear associations (covariance, correlation, and regression); unruly scaled data; and statistical scenarios.