Mathematical Statistics and Data Analysis Hardcover – 1 Jul 1994
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Rice tries to bridge the gap between theory and application, delivering enough theory that the student understands the logical foundation of the applied aspects they may have already discovered in previous courses. In my mind, this is the central theme of Rice's text - avoiding unnecessary and often pedantic details better left to graduate majors in statistics while filling in the background material that often left students of statistics uncertain about the amount of confidence to place in their analyses. Rice's text is not for those who fear rigour and logic. His introductions to new concepts are compact, impersonal, and often followed by terse propositions, definitions and laws that build logically as the text progresses. He includes numerous examples that are similarly terse; however, he never failed my litmus test for logical works, which is a demonstrable linkage between each example and some proposition, law or definition previously introduced.
The text commences with the most basic review of probability, progressing quickly to random variables, distributions, expected values and important derived distributions like the t, F and Chi-square. Students will discover how the tests they applied in the past are related to theory. This theme culminates in the section on Survey Sampling, in which sampling estimators and their assumptions are derived.
Rice has weaknesses that deserve mention. Some of the problems are tough, and Rice's impersonal approach emphasizes concepts over technique. I spent many hours reading and re-reading sections in the text before a useful approach to a problem came to me. Sections on least squares and ANOVA are the least useful; they are too compact to achieve the goal of bridging theory and application. This material is much better covered elsewhere. The decision theory and Baesian inference section suffers similarly, but given how little exposure most stats students get to this material is nevertheless useful.
If you're interested in learning the rigourous application of statistics but not theory, then Rice isn't for you. No matter what, you mustn't be afraid of challenges; Rice is impersonal and compact and won't make any excuses for you. If you want to understand the assumptions and limitations of the applied statistics you've already been practicing, however, I recommend Rice enthusiastically. He won't explain the assumptions, but he will arm you with the knowledge to do it yourself.
But then return. Return to this wonderfully complete and rigourous txt that offers challenging end of chapter exercises and insures that if you look something up, you will find it. The contents is vast, and each time you open it, you're likely to walk away with something new or something appreciated fully for the first time.
Misses the 5th star because of its list of errata, and because newer editions haven't been forthcoming. It could use one more revision.
Although the title contains the word "mathematical," the book has an eminently practical orientation. There is even an entire chapter devoted to descriptive statistics and graphical tools. A course making good use of this book will give the student a solid introduction to the art of data analysis.
This book may be too advanced for students without sufficient mathematical preparation. Such students might warm up first with Friedman et al. or Moore and McCabe.
The chief difference between the second and third editions seems to be that the latter gives somewhat more space to the Bayesian approach.
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