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Metrika

, Volume 41, Issue 1, pp 263–275 | Cite as

Robustness to the unavailability of data in block designs

  • W. I. Notz
  • D. C. Whittinghill
  • Y. Zhu
Article

Abstract

We present general results for finding or boundingtmaxB, the maximum number of arbitrary whole blocks of observations which can be removed from a block design, and still leave all of the elementary treatment contrasts estimable. The block sizes may be larger than the number of treatments. The results are applied to BBDs, reinforced BIBDs and BBDs, BTIBDs, and a series of variance balanced incomplete block designs with two block sizes. Also given for most of these designs, are results fortmax, the maximum number of arbitrary, scattered observations that can become unavailable, and still leave all of the elementary treatment contrasts estimable.

Key Words

BBD BTIBD block design reinforced design robustness 

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References

  1. Baksalary JK, Tabis Z (1987) Conditions for the robustness of block designs against the unavailability of data. J Statist Plann Inference 16:49–54Google Scholar
  2. Bechhofer RE, Tamhane AC (1981) Incomplete block designs for comparing treatments with a control: General theory. Techn 23:45–56Google Scholar
  3. Bhaumik DK, Whittinghill DC (1991) Optimality and robustness to the unavailability of blocks in block designs. J Roy Statist Soc Ser B 53:399–407Google Scholar
  4. Das A, Dhall SP (1988) Robustness of augmented BIB designs. Sankhya Ser B 50:376–381Google Scholar
  5. Das MN (1958) On reinforced incomplete block designs. J Ind Soc Agric Statist 10:73–77Google Scholar
  6. Ghosh S (1982) Robustness of BIBD against the unavailability of data. J Statist Plann Inference 6:29–32Google Scholar
  7. Ghosh S, Kageyama S, Mukerjee R (1992) Efficiency of connected binary block designs when a single observation is unavailable. Ann Inst Statist Math 44:593–603Google Scholar
  8. Ghosh S, Rao SB, Singhi NM (1983) On a robust property of PBIBD. J Statist Plann Inf 8:355–363Google Scholar
  9. Gupta VK, Srivastava R (1992) Investigations on robustness of block designs against missing observations. Sankhya Ser B 54: 100–105Google Scholar
  10. Heiligers B (1991) A note on connectedness of block designs. Metrika 38:377–381Google Scholar
  11. Kageyama S (1976) Constructions of balanced block designs. Util Math 9:209–229Google Scholar
  12. Kiefer J (1975) Balanced block designs and generalized Youden designs, I. Construction (Patchwork). Ann Stat 3:109–118Google Scholar
  13. Mukerjee R, Kageyama S (1990) Robustness of group divisible designs. Commun Statist Theor Meth 19:3189–3203Google Scholar
  14. Sathe YS, Satam MR (1992) Some more robust block designs against the unavailability of data. J Statist Plann Inf 30:93–98Google Scholar

Copyright information

© Physica-Verlag 1994

Authors and Affiliations

  • W. I. Notz
    • 1
  • D. C. Whittinghill
    • 1
  • Y. Zhu
    • 1
  1. 1.Department of StatisticsThe Ohio State UniversityColumbusUSA

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