Characterizations for Balance with Orthogonal Factorial Structure

  • Sudhir Gupta
  • Rahul Mukerjee
Part of the Lecture Notes in Statistics book series (LNS, volume 59)


This chapter considers factorial designs which are balanced and have orthogonal factorial structure (OFS). Such designs have been termed balanced factorial experiments by Shah (1958, 1960a). They are also known as balanced confounded designs according to the nomenclature of Nair and Rao (1948). The main result of this section, namely Theorem 3.1.1, gives an algebraic characterization for balance with OFS in the connected case. For equireplicate and proper designs, the ‘sufficiency’ part of this result was proved by Kurkjian and Zelen (1963), while the ‘necessity’ part was proved by Kshirsagar (1966). Gupta (1983a) considered extensions to designs that are not necessarily equireplicate or proper. The following definition and lemmas will be helpful.


Proper Design Association Scheme Balance Design Balance Incomplete Block Design Interaction Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Sudhir Gupta
    • 1
  • Rahul Mukerjee
    • 2
  1. 1.Division of Statistics, Department of Mathematical SciencesNorthern Illinois UniversityDeKalbUSA
  2. 2.Stat-Math Division, Indian Statistical InstituteCalcuttaIndia

Personalised recommendations