Relatorio Estatistica

Stat Labs: Mathematical
Statistics Through
Applications

Deborah Nolan
Terry Speed

Springer

To Ben and Sammy
—D.N.

To Sally
—T.P.S

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Preface

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 toillustrate 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
ofthe 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,

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Preface

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 bookdiffers 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 specialcases 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 theexercises.
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 toStat 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
ondescriptive 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...