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Statistical Papers

, Volume 39, Issue 1, pp 41–60 | Cite as

Modifying and using Yates' algorithm

  • Hans Riedwyl
Articles

Abstract

It is well known that Yates' algorithm can be used to estimate the effects in a factorial design. We develop a modification of this algorithm and call it modified Yates' algorithm and its inverse. We show that the intermediate steps in our algorithm have a direct interpretation as estimated level-specific mean values and effects. Also we show how Yates' or our modified algorithm can be used to construct the blocks in a 2 k factorial design and to generate the layout sheet of a 2 k−p fractional factorial design and the confounding pattern in such a design. In a final example we put together all these methods by generating and analysing a 26-2 design with 2 blocks.

Key words

Yates' algorithm 2k factorial design fractional factorial design 

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References

  1. Box, G.E.P., Hunter, W.G. and Hunter, J.S. (1978),Statistics for Experimenters, New York: John Wiley.zbMATHGoogle Scholar
  2. Daniel, C. (1976),Applications of Statistics to Industrial Experimentation, New York: John Wiley.zbMATHGoogle Scholar
  3. Lorenzen, T.J. and Anderson, V.L. (1993),Design of Experiments—A No-Name Approach, New York: Dekker.zbMATHGoogle Scholar
  4. Montgomery, D.C. (1991),Design and Analysis of Experiments, third edition, New York: John Wiley.zbMATHGoogle Scholar
  5. National Bureau of Standards (1957),Fractional Factorial Experimental Designs for Factors at Two Levels (National Bureau of Standards Applied Mathematics Series, Vol. 48), Washington DC: U.S. Government Printing Office.Google Scholar
  6. Yates, F. (1935), “Complex Experiments”,Journal of the Royal Statistical Society, Ser. B, 2, 181–223Google Scholar

Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  • Hans Riedwyl
    • 1
  1. 1.Institute of Mathematical Statistics and Actuarial ScienceUniversity of BerneBernSwitzerland

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