Illuminating Statistical Analysis Using Scenarios and Simulations

Preface

The goal of this book is to help people develop an assortment of key intuitions about statistics and inference and use those intuitions to make sense of statistical analysis methods in a conceptual as well as a practical way. Moreover, I hope to engender good ways of thinking about uncertainty. The book is comprised of a series of short, concise chapters that build upon each other and are best read in order. The chapters cover a wide range of concepts and methods of classical (frequentist) statistics and inference. (There are also appendices on Bayesian statistics and on data mining techniques.)

Examining computer simulation results is central to our investigation. Simulating pollsters, for example, who survey random people for responses to an agree or disagree opinion question not only mimics reality but also has the added advantage of being able to employ 1000 independent pollsters simultaneously. The results produced by such simulations provide an eye-opening 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.

Mathematics used in the book involves basic algebra. Of particular relevance is interpreting the relationships found in formulas. Take, for example, . As increases, ...