Design and Analysis of Experiments for Statistical Selection, Screening and Multiple Comparisons


Robert E. Bechhofer, Thomas J. Santner, and David M. Goldsman

J. Wiley & Sons, New York 1995

This is book is an introduction to the design and analysis of and Experiments for statistical selection and screening. It also introduces some elementary multiple comparison methods. It was written at the Masters level in Statistics and assumes the reader is familiar with classical experimental design.


The publication of ``A single-sample multiple decision procedure for ranking means of normal populations with known variances'' by the first author of this book together with work by Milton Sobel and Shanti S. Gupta began a steady stream of contributions to ``ranking and selection'' theory that constitutes well over 1000 articles and several theoretical books. Despite their potential practial appeal, very few of these methodologies have found their way into methodological textbooks and hence into usage. The intent with the present volume is to bridge this gap.

This book focusses on three types of procedures: selection procedures using the so-called indifference-zone approach, screening procedures using the subset approach, and to a much lesser extent, multiple comparison procedures involving normal means. Concerning selection procedures, this book presents methodologies that shows how these techniques can be applied to three probability models that play a central role in many statistical studies of experimental data. These are the univariate normal distribution where interest lies in the mean, the Bernoulli distribution where we are concerned with the ``success'' probabilities and the multinomial distribution where we study the probabilities associated with certain categories (events). Software is given to implement many of the procedures presented.

The literature contains procedures for many other statistical models; some of these are referenced in the notes presented at the end of each chapter. However, we do not consider detailed selection procedures for normal variances, means of Poisson distributions (or processes), or parameters of exponential or gamma distributions.


  1. The Rationale of Selection, Screening and Multiple Comparison
  2. Selecting the Best Treatment in a Single-Factor Normal Response Experiment Using the Indifference-Zone Approach
  3. Selecting a Subset Containing the Best Treatment in a Normal Response Experiment
  4. Multiple Comparison Approaches for Normal Response Experiments
  5. Problems Involving a Standard or a Control Treatment in Normal Response Experiments
  6. Selection Problems in Two-Factor Normal Response Experiments
  7. Selecting Best Treatments in Single-Factor Bernoulli Response Experiments
  8. Selection Problems for Categorical Response Experiments


  1. Relationships Among Critical Points and Notation
  2. Tables
  3. FORTRAN Programs

Scripts and Complements

FORTRAN Programs

The source programs can be opened (in Unix)

      gzip  bsg.tar.gz 
      tar -xf bsg.tar.gz 


Please contact the authors if you wish to report typos or errors.


Robert Bechhofer (1919--1996) was founding head of the the Department of Operations Research at Cornell University. He was Fellow of the American Statistical Association and of the Institute of Mathematical Statistics. Thomas Santner is Professor of Statistics at the Ohio State University. He is former Department Chair and former Director of the the Department's Statistical Consulting Service. His research interests are in the design and analysis of computer screening experiments, the spatial and spatial-temporal analysis of fMRI image data, and the design and analysis of experiments for selection and screening. He is a Fellow of the American Statistical Association and of the Institute of Mathematical Statistics. David Goldsman is Associate Professor of Industrial and Systems Engineering at Georgia Institute of Technology. His research interests include computer simulation with emphasis on statistical output analysis, applied probability and statistics, ranking and selection, time series analysis, reliability and life testing, and the application of these areas in industrial engineering.

Professor David Goldsman
Industrial and Systems Engineering
Georgia Institute of Technology
765 Ferst Drive
Atlanta, GA 30332-0205


Professor Thomas Santner
Department of Statistics
Ohio State University
1958 Neal Avenue
Columbus, OH 43210-1247


Last edited on 17 April 2003 by Thomas Santner