A Personal Tribute to Milton Sobel: Selecting the Best Treatment

Abstract

The paper begins with a sketch of Milton Sobel's life and work, which is followed by a summary of his pioneering collaborations in selecting the best among k ≥2 populations. It takes us back to Bechhofer et al. (1954), where a path-breaking two-stage selection methodology was developed for normal populations with unknown means and a common but unknown variance.Every two-stage methodology begins with a pilot sample. However, no easy practical approach existed for determining an appropriate pilot size until recently. We have summarized two recent ideas to determine a pilot size.Then, the methodology of Bechhofer et al. (1954) is extended for situations where population variances are c 2 i 2 with 2 >0 being unknown but c i >0 being known, not all equal, i = 1 k ≥2 . This new methodology does not need any new statistical table for its implementation beyond what was required by the original 1954 methodology.Several illustrations are included from practical problems using real data. The paper ends with brief recollections of Milton Sobel and some personal thoughts.