According to the description on the back of the book, Michael J. Panik's Advanced Statistics from an Elementary Point of View "captures the flavor of a course in mathematical statistics without imposing rigor for its own sake." Your reaction to that quotation will pretty well summarize your feelings towards the book, depending on whether or not you appreciate rigor "for its own sake." If all blurb-writers were this honest about their books, then there would be no need for MAA Reviews. This book covers a wide range of topics in statistics — it doesn't even define means or medians until the second chapter, but it ends with chapters about contingency tables and bivariate linear regressions. In between there are full chapters on parametric probability distributions, sampling, Chi-Square distributions, point estimation, and tests of parametric statistical hypotheses.
Panik's goal is to make the book very accessible, and in this goal he succeeds. His exposition is quite clear and I found it quite easy to follow his many examples. There are also a large number of exercises, many of which have solutions given and some of which seem quite interesting. Panik certainly does not impose much rigor, however, and many of the explanations were not as fleshed out or precise as I would have liked. While I imagine that many of my students would appreciate the lack of formal proofs throughout the book, I know that many others — and certainly most mathematicians or statisticians I know — would find this book highly deficient for this very reason. Panik preemptively addresses this issue in his introduction, pointing out that many of the theorems have their proofs developed in the exercises, but this reader was still disappointed.
Panik is an economist, and I imagine that his book would work well for a statistics course for economics majors — or for the similar courses in many of the departments on my campus that focus on actually using statistical techniques rather than on why they are true. But while it did indeed "capture the flavor" of a course I would want to see in a mathematics department, it would need quite a bit of extra meat to be substantial enough for the whole meal that I would want from a textbook.
Darren Glass (email@example.com) is an Assistant Professor at Gettysburg College.