Robustness of connected balanced block designs

  • Sanpei Kageyama


It is well known that the connected incomplete block designs with the highest intrablock efficiency factors are balanced. In a connected balanced block (BB) design, every elementary contrast is estimated with the same variance. If a treatment is lost in a connected BB design, then the residual design is not balanced for the most part. In this paper, an upper bound and a lower bound for efficiency of a residual design are derived with some illustrations. Moreover, from these discussions it is conceivable that the loss of efficiency even in the unbalanced case is, in general, small.


Block Design Original Design Efficiency Factor Balance Incomplete Block Design Balance Structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Conniffe, D. and Stone, J. (1974). The efficiency factor of a class of incomplete block designs.Biometrika,61, 633–636.MathSciNetCrossRefGoogle Scholar
  2. [2]
    John, P. W. M. (1976). Robustness of balanced incomplete block designs,Ann. Statist.,4, 960–962.MathSciNetCrossRefGoogle Scholar
  3. [3]
    Kageyama, S. (1974). Reduction of associate classes for block designs and related combinatorial arrangements,Hiroshima Math. J.,4, 527–618.MathSciNetzbMATHGoogle Scholar
  4. [4]
    Kageyama, S. (1976). Constructions of balanced block designs,Utilitas Math.,9, 209–229.MathSciNetzbMATHGoogle Scholar
  5. [5]
    Raghavarao, D. (1971).Constructions and Combinatorial Problems in Design of Experiments, Wiley, New York.zbMATHGoogle Scholar
  6. [6]
    Roy, J. (1958). On the efficiency factor of block designs,Sankhyã,19, 181–188.zbMATHGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1980

Authors and Affiliations

  • Sanpei Kageyama
    • 1
  1. 1.Hiroshima UniversityHiroshimaJapan

Personalised recommendations