Stat Labs: Mathematical Statistics Through Applications
Deborah Nolan Terry Speed
To Ben and Sammy —D.N.
To Sally —T.P.S
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This book uses a model we have developed for teaching mathematical statistics through in-depth case studies. Traditional statistics texts have many small numerical examples in each chapter to illustrate a topic in statistical theory. Here, we instead make a case study the centerpiece of each chapter. The case studies, which we call labs, raise interesting scientific questions, and figuring out how to answer a question is the starting point for developing statistical theory. The labs are substantial exercises; they have nontrivial solutions that leave room for different analyses of the data. In addition to providing the framework and motivation for studying topics in mathematical statistics, the labs help students develop statistical thinking. We feel that this approach integrates theoretical and applied statistics in a way not commonly encountered in an undergraduate text.
The Student The book is intended for a course in mathematical statistics for juniors and seniors. We assume that students have had one year of calculus, including Taylor series, and a course in probability. We do not assume students have experience with statistical software so we incorporate lessons into our course on how to use the software.
Theoretical Content The topics common to most mathematical statistics texts can be found in this book, including: descriptive statistics, experimental design, sampling, estimation,
testing, contingency tables, regression, simple linear least squares, analysis of variance, and multiple linear least squares. Also found here are many selected topics, such as quantile plots, the bootstrap, replicate measurements, inverse regression, ecological regression, unbalanced designs, and response surface analysis. This book differs from a standard mathematical statistics text in three essential ways. The first way is in how the topic of testing is covered. Although we address testing in several chapters and discuss the z, t, and F tests as well as chi-square tests of independence and homogeneity, Fisher’s exact test, Mantel-Haenszel test, and the chi-square goodness of fit test, we do not cover all of the special cases of t tests that are typically found in mathematical statistics texts. We also do not cover nonparametric tests. Instead we cover more topics related to linear models. The second main difference is the depth of the coverage. We are purposefully brief in the treatment of most of the theoretical topics. The essential material is there, but details of derivations are often left to the exercises. Finally this book differs from a traditional mathematical statistics text in its layout. The first four sections of each chapter provide the lab’s introduction, data description, background, and suggestions for investigating the problem. The theoretical material comes last, after the problem has been fully developed. Because of this novel approach, we have included an Instructor’s Guide to Stat Labs, where we describe the layout of the chapters, the statistical content of each chapter, and ideas for how to use the book in a course. The design of Stat Labs is versatile enough to be used as the main text for a course, or as a supplement to a more theoretical text. In a typical semester, we cover about 10 chapters. The core chapters that we usually cover are Chapter 1 on descriptive statistics, Chapter 2 on simple random sampling, Chapter 4 on estimation and testing, and Chapter 7 on regression. Other chapters are chosen according to the interests of students. We give examples of semester courses for engineering, social science, and life science students in the Instructor’s Guide.
Acknowledgments This book has been many years in the making, and has changed shape dramatically in i