Traditional statistics texts have many small numerical examples in each chapter to illustrate a topic in mathematical statistics. Here, we instead make a case study the centerpiece of each chapter. The case studies, which we call labs, raise interesting scientific questions, and by figuring out how to answer these questions we develop statistical theory.
The labs are substantial exercises. Data are provided to address the questions; the solutions are nontrivial and leave room for different analyses. They provide the framework and motivation for the topics in mathematical statistics and they help students develop statistical thinking.
This approach integrates mathematical statistics 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
on how to use the software into our course.
Statistical Topics
This book covers the standard topics found in most mathematical statistics
texts.
| Chapter | Main Topic | Additional topics |
| 1 - Infant health | descriptive statistics | quantile plots
normal approximation |
| 2 - Video games | simple random sampling | confidence intervals
bootstrap |
| 3 - Radon in households | stratified sampling | optimal allocation
parametric bootstrap |
| 4 - Patterns in DNA | estimation and testing | maximum likelihood
goodness-of-fit tests |
| 5 - Taste testing experiment | design of experiments | contingency tables
chi-square tests of homogeneity & independence |
| 6 - HIV in hemophiliacs | Poisson counts and rates | confidence intervals for rates
Mantel-Haenszel test |
| 7 - Crab growth patterns | regression | correlation
prediction residuals |
| 8 - Instrument calibration | Simple linear models | replicate measurements
transformations confidence bands |
| 9 - Voting behavior | ecological regression | weighted regression |
| 10 - Infant health | multiple regression | model checking
geometry of least squares indicator variables |
| 11 - Genetically altered mice | analysis of variance | quantile plots
ANOVA table balanced and unbalanced designs |
| 12 - Helicopter design | response surface analysis | factorial design
interactions |
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