Incomplete block designs for comparing treatments wth a control: General theory

Robert E. Bechhofer*, Ajit C. Tamhane

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


In this paper we develop a theory of optimal incomplete block designs for comparing several treatments with a control. This class of designs is appropriate for comparing simultaneously p ≥ 2 test treatments with a control treatment (the so-called multiple comparisons with a control (MCC) problem) when the observations are taken in incomplete blocks of common size k < p + 1. For this problem we propose a new general class of incomplete block designs that are balanced with respect to (wrt) test treatments. We shall use the abbreviation BTIB to refer to such designs. We study their structure and give some methods of construction. A procedure for making exact joint confidence statements for this multiple comparisons problem is described. By using a new concept of admissibility of designs, it is shown how “inferior” designs can be eliminated from consideration, and attention limited to a small class of BTIB designs that can be constructed from so-called generator designs in the minimal complete class of such designs. Some open problems concerning construction of BTIB designs are posed.

Original languageEnglish (US)
Pages (from-to)45-57
Number of pages13
Issue number1
StatePublished - Feb 1981


  • Admissible designs
  • Balanced treatment incomplete block (btib) designs
  • Generator designs
  • Multiple comparisons with a control
  • Optimal designs

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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