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Journal of Statistical Theory and Practice

, Volume 1, Issue 3–4, pp 417–426 | Cite as

Square Lattice Designs in Incomplete Split-plot Designs

  • Shinji Kuriki
  • Kiyoaki Nakajima
Article

Abstract

We construct an incomplete split-plot design by the semi-Kronecker product of two resolvable designs. We use any resolvable design for the treatments of whole-plots and a square lattice design for the treatments of subplots. We give the stratum efficiency factors for such incomplete split-plot designs, which have the general balance property.

AMS Subject Classification

62K15 62K10 05B05 

Keywords

Square lattice designs Resolvable designs Incomplete split-plot designs General balance property Stratum efficiency factors 

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References

  1. Bhargava, R.P., Shah, K.R., 1975. Analysis of some mixed models for block and split-plot designs. Annals of the Institute of Statistical Mathematics, 27, 365–375.MathSciNetCrossRefGoogle Scholar
  2. Houtman, A.M., Speed, T.P., 1983. Balance in designed experiments with orthogonal block structure. The Annals of Statistics, 11, 1069–1085.MathSciNetCrossRefGoogle Scholar
  3. John, J.A., 1987. Cyclic designs. Chapman and Hall, New York.CrossRefGoogle Scholar
  4. John, J.A., Williams, E.R., 1995. Cyclic and computer generated designs. Chapman and Hall, New York.CrossRefGoogle Scholar
  5. Khatri, C.G., Rao, C.R., 1968. Solutions to some functional equations and their applications to characterization of probability distributions. Sankhyā, A 30, 167–180.MathSciNetMATHGoogle Scholar
  6. Mejza, I., Kuriki, S., Mejza, S., 2001. Balanced square lattice designs in split-block designs. Colloquium Biomet-ryczne, 31, 97–103.MATHGoogle Scholar
  7. Mejza, I., Mejza, S., 1984. Incomplete split plot designs. Statistics & Probability Letters, 2, 327–332.MathSciNetCrossRefGoogle Scholar
  8. Mejza, I., Mejza, S., 1996. Incomplete split-plot designs generated by GDPBIBD(2). Calcutta Statistical Association Bulletin, 46, 117–127.MathSciNetCrossRefGoogle Scholar
  9. Mejza, S., 1987. Experiments in incomplete split-plot designs. In Pukkila, T. Puntanen, S. (Eds.), Proceeding of Second International Tampere Conference in Statistics, University of Tampere, 575–584.Google Scholar
  10. Nelder, J.A., 1965a. The analysis of randomized experiments with orthogonal block structure. I. Block structure and the null analysis of variance. Proceedings of the Royal Society. London, A 283, 147–162.MathSciNetCrossRefGoogle Scholar
  11. Nelder, J.A., 1965b. The analysis of randomized experiments with orthogonal block structure. II. Treatment structure and the general analysis of variance. Proceedings of the Royal Society. London, A 283, 163–178.MathSciNetCrossRefGoogle Scholar
  12. Ozawa, K., Kuriki, S., 2006. Incomplete split-plot designs generated from α-resolvable designs. Statistics & Probability Letters, 76, 1245–1254.MathSciNetCrossRefGoogle Scholar
  13. Ozawa, K., Mejza, S., Jimbo, M., Mejza, I., Kuriki, S., 2004. Incomplete split-plot designs generated by some resolvable balanced designs. Statistics & Probability Letters, 68, 9–15.MathSciNetCrossRefGoogle Scholar
  14. Pearce, S.C., Caliński, T., Marshall, T.F. de C., 1974. The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika, 61, 449–460.MathSciNetCrossRefGoogle Scholar
  15. Rees, H.D., 1969. The analysis of variance of some non-orthogonal designs with split-plot. Biometrika, 56, 43–54.CrossRefGoogle Scholar
  16. Robinson, J., 1967a. Incomplete split-plot designs. Biometrics, 21, 793–802.MathSciNetCrossRefGoogle Scholar
  17. Robinson, J., 1967b. Blocking in incomplete split-plot designs. Biometrika, 57, 347–350.CrossRefGoogle Scholar
  18. Whitaker, D., Williams, E.R., John, J.A., 2002. A package for the computer generation of experimental designs, CycDesigN Ver. 2.0. CSIRO, Canberra.Google Scholar

Copyright information

© Grace Scientific Publishing 2007

Authors and Affiliations

  • Shinji Kuriki
    • 1
  • Kiyoaki Nakajima
    • 1
  1. 1.Department of Mathematical Sciences, Graduate School of EngineeringOsaka Prefecture UniversityOsakaJapan

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