Design Keys for Multiphase Experiments

  • R. A. BaileyEmail author
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


Desmond Patterson introduced the design key in 1965 in the context of rotation experiments in agriculture. When there are many factors involved, the design key gives an algorithm for constructing the design and for keeping track of confounding. Here I extend the idea to multiphase experiments, using one design key for each phase.


  1. 1.
    Bailey, R.A.: Patterns of confounding in factorial designs. Biometrika 64, 597–603 (1977)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Bailey, R.A., Brien, C.J.: Randomization-based models for multitiered experiments: I. A chain of randomizations. Ann. Stat. (2016) (in press)Google Scholar
  3. 3.
    Brien, C.J., Bailey, R.A.: Multiple randomizations. J. R. Stat. Soc. Ser. B 68, 571–609 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Brien, C.J., Bailey, R.A.: Decomposition tables for experiments I. A chain of randomizations. Ann. Stat. 37, 4184–4213 (2009)zbMATHMathSciNetGoogle Scholar
  5. 5.
    Cheng, C.-S.: Theory of Factorial Design. Chapman and Hall, Boca Raton (2014)Google Scholar
  6. 6.
    Cheng, C.-S., Tsai, P.-W.: Templates for design key construction. Stat. Sin. 23, 1419–1436 (2013)zbMATHMathSciNetGoogle Scholar
  7. 7.
    Fisher, R.A.: The theory of confounding in factorial experiments in relation to the theory of groups. Ann. Eugen. 11, 341–353 (1942)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Kobilinsky, A.: Confounding in relation to duality of finite Abelian groups. Linear Algebra Appl. 70, 321–347 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Kobilinsky, A., Bouvier, A., Monod, H. planor: Generation of regular factorial designs. R package version 0.2–3. (2015)
  10. 10.
    Kobilinsky, A., Monod, H.: Experimental design generated by group morphisms: an introduction. Scand. J. Stat. 18, 119–134 (1991)zbMATHMathSciNetGoogle Scholar
  11. 11.
    Kobilinsky, A., Monod, H., Bailey, R.A.: Automatic generation of generalised regular factorial designs (2015, submitted for publication)Google Scholar
  12. 12.
    Patterson, H.D.: The factorial combination of treatments in rotation experiments. J. Agric. Sci. 65, 171–182 (1965)CrossRefGoogle Scholar
  13. 13.
    Patterson, H.D.: Generation of factorial designs. J. R. Stat. Soc. Ser. B 38, 175–179 (1976)zbMATHMathSciNetGoogle Scholar
  14. 14.
    Patterson, H.D., Bailey, R.A.: Design keys for factorial experiments. J. R. Stat. Soc. Ser. C 27, 335–343 (1978)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsUK

Personalised recommendations