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Design and Analysis of Experiments for Statistical Selection, Screening, and Multiple Comparisons (Wiley Series in Probability and Statistics)

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Robert Bechhofer along with Milton Sobel pioneered the concept of rank and selecting the population with the largest mean or a subset of populations with the largest means. This is a practical alternative to the usual analysis of variance and multiple contrasts approach (ANOVA). ANOVA methods just determine if there are differences among populations but researchers are often interested in knowing which population has the largest (best) mean. Ranking and selection procedures consider the selection of the population with the best mean or a ranking of the populations based on the means. It is formulated in a way to pick the right populatiion (i.e. the one with the largest population mean) or subset of populations based on either maximizing the probability of correct selection or by use of indifference zones in hypothesis testing. This material has been covered in Bechhofer's treatise with Kiefer and Sobel in 1968, the text by Gupta and Panchapakesan in 1979 and Gibbons, Olkin and Sobel in 1977. This text is an update on the theory and applications and differs from the previous texts in that it also considers issues of statistical design.
The theory has been well developed over a period of the past 30 years but has not been taught in applied statistics course and inspite of its practicality it is not applied nealry as much as the analysis of variance even though it is sometimes more appropriate. This has been a frustration for Bechhofer and his colleagues. This book is another attempt to get the methods more widely known and used. Part of the problem is the lack of software. Tables as provided in the text can be exceedingly complex. The authors provide FORTRAN programs to carry out the procedures. Unfortunately in today's computing environment it will take inclusion in major statistical software packages to get these methods the usage that they probably deserve.

The text is authoritative and well-written. It could be used for an intermediate level statistics course in ranking and selection methods and designs. It is an excellent reference source. Unfortunately Bechhofer has since past away so it is now the job of his colleagues and students to promote these methods.