Stat Labs: Mathematical Statistics through Applications
uses a model we have developed for teaching mathematical statistics through
indepth case studies.
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
goodnessoffit tests

5  Taste testing experiment  design of experiments  contingency tables
chisquare tests of homogeneity & independence

6  HIV in hemophiliacs  Poisson counts and rates  confidence intervals for rates
MantelHaenszel 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

