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Statistical Intervals: A Guide for Practitioners (Wiley Series in Probability and Statistics)

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Gerald Hahn has spent many years in industry working for the General Electric Company. He and Bill Meeker have written this very unique book that provides an up-to-date treatment of statistical methods for interval estimation.
In most introductory courses students are taught about statistical confidence intervals. However, there are many other types of statistical intervals that are appropriate for particular applications. Most students, particularly engineering students, only learn about confidence intervals and hence they apply them whenever they need a statistical interval. But often they are wrong because the problem really calls for a prediction interval or a tolerance interval. This circumstance is what motivated these authors to write this book.

The techniques are standard and are covered in other statistical texts. However, this is the only book with statistical intervals as its theme. It provides the methods and the context for using the various intervals and more importantly makes the distinctions that help the students overcome possible confusion. This is an excellent practical reference. Its many tables make it a great reference book. On many occasions I have needed Gaussian tolerance intervals or sometimes nonparametric tolerance intervals. I go to the tables in this book first. It also includes some discussion of bootstrap confidence intervals and other asymptotic approaches in Chapter 12 where Bayesian intervals are also introduced. Chapter 13 concentrates on 9 case studies and the appropriate intervals to be used in each case. Other practical issues such as determining the sample size requirements for precise statistical intervals are also discussed in various chapters.

"Statistical Intervals" has for years been a valuable tool in my professional work, which focuses on environmental statistics. Hahn & Meeker's discussion of how to interpret various intervals--confidence, tolerance, prediction--first opened my eyes to the ubiquity and utility of these techniques. I since have found it worthwhile to have a working knowledge of them all; that would scarcely have been possible without having such a handy reference.

The tables are getting dog-eared and gray from use, especially A-12 (factors for computing Normal distribution one-sided tolerance bounds), in testimony to the frequency I refer to them. The book also contains extensive graphics for estimating intervals and for determining sample sizes: these typically obviate any need to refer to tables or do the computations. There are some neat formulas, clearly described, that one can easily implement in a spreadsheet. These all appear in other texts and journal articles, but having them all in one place, well organized, makes them particularly worthwhile.

This is, indeed, a reference: a statistical "cookbook" if you will (intended in a positive sense, not perjoratively!). This means you will find little theoretical justification for any of the material. For each technique expect to find a clear definition, lucid descriptions, discussions of how to use any supporting formulas, graphs, or tables, all followed by a clear worked example. Of course there's an extensive bibliography if your theoretical curiosity is piqued.

One common technique you will not find (although it is mentioned and references provided) is computing statistical intervals for linear regression analysis. This subject, however, is covered well in other books (such as Draper and Smith's Applied Regression Analysis), so the omission does no harm and helps keep the book to a manageable 400 pages or so.

There are some obscure applications you will not find, in part because they were only under development at the time this book was written. For instance, there is a specialized (but widely applied) theory of "k best of m" prediction limits that is used in groundwater monitoring. For such specialized applications you will have to go elsewhere (such as Robert Gibbons' book on "Statistical Methods for Groundwater Monitoring"). Nevertheless, Hahn and Meeker do a very good job of covering the most widely used applications of statistical intervals.

I do not recollect ever finding a mathematical error or even a typographical error. Over the years I have also checked, and completely verified, the entries in several of the key tables. All in all, this book is remarkably clean and error free.

(This review is based on the 1991 edition; I do not know whether there have been further editions.)

A fantastic book! It was published just as I had finished collecting all the journal articles I could find on statistical intervals. (Years ago, Meeker told me that he and Gerry were thinking of writing a second edition, but apparently it didn't happen.) I did find an error: On p.131, expression 7.7, the first inequality is incorrect. I believe that it should read m/(y+1)>= (n|x)F... for the lower bound.

There is FREE software for calculating some of these intervals. See the index page http://www.public.iastate.edu/~wqmeeker/StInt/

My one disappointment about the book is that it omits some equations/algorithms for estimating some statistical intervals, offering instead graphs and tables. In these cases, if one wishes to extend or modify a result, one must either find the original source article or derive the missing equations/algorithms oneself, using the tables and graphs to check one's work.

Finally, note that for many intervals, use of results based on an assumption of normality (or other underlying distribution) will yield poorer estimates (less tight statistical bound estimates) than will the use of distribution-free methods. This is true even if one's data appears to be normally distributed and tests for non-normality do not reject the normality assumption.

-Stephen B. Cohen, Ph.D.