50
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Orthogonal arrays and designs for partial triallel crosses

ORCID Icon, &
Pages 125-134 | Received 08 Dec 2017, Accepted 30 Sep 2018, Published online: 21 Dec 2018

References

  • Arora, B. S., and K. R. Aggarwal. 1984. Confounded trialllel experiments and their applications. Sankhya B 46:54–63.
  • Arora, B. S., and K. R. Aggarwal. 1989. Triallel experiments with reciprocal effects. Journal of the Indian Society of Agricultural Statistics 41:91–103.
  • Bose, R. C. 1939. On the construction of balanced incomplete block designs. Annals of Eugenics 9(4):353–99.
  • Bose, R. C., and K. A. Bush. 1952. Orthogonal arrays of strength 2 and three. The Annals of Mathematical Statistics 23(4):508–24.
  • Bose, R. C., S. S. Shrikhande, and E. T. Parker. 1960. Further results on construction of mutually orthogonal Latin squares and falsity of Euler’s conjecture. Canadian Journal of Mathematics 12:189–203.
  • Ceranka, B., H. Chudzik, A. Dobek, and H. Kielczewska. 1990. Estimation of parameters for triallel crosses compared in block designs. Statistics and Applications 2:27–35.
  • Cheng, C. S. 1978. Optimality of certain asymmetrical experimental designs. The Annals of Statistics 6(6):1239–61.
  • Das, A., and S. Gupta. 1997. Optimal block designs for triallel cross experiments. Communications in Statistics - Theory and Methods 26(7):1767–77.
  • Dey, A., and C. K. Midha. 1996. Optimal designs for diallel crosses. Biometrika 83(2):484–9.
  • Gupta, S., and S. Kageyama. 1994. Optimal complete diallel crosses. Biometrika 81(2):420–4.
  • Hinkelmann, K. 1965. Partial triallel crosses. Sankhya A27:173–96.
  • Hinkelmann, K. 1975. A survey of statistical design and linear models. 243–269. Amsterdam: North Hollond.
  • Kiefer, J. 1975. Construction and optimality of generalized Youden designs. In A survey of statistical design and linear models, ed. J. N. Srivastava, 333–353. Amsterdam: North Hollond.
  • Nair, K. R., and C. R. Rao. 1948. Confounding in asymmetrical factorial experiments. Journal of the Royal Statistical Society 10:109–31.
  • Narain, P. 1990. Statistical genetics. New Delhi: Wiley Eastern Limited.
  • Ponnuswamy, K. N., and M. R. Srinivasan. 1991. Construction of partial triallel crosses (ptc) using a class of balanced incomplete block designs (BIBD). Communications in Statistics - Theory and Methods 20(10):3315–3323.
  • Rao, C. R. 1946. Difference sets and combinatorial arrangements derivable from finite geometries. Proceedings of the National Academy of Sciences 12:123–35.
  • Rao, C. R. 1946b. Hypercubes of strength “d” leading to confounded designs in factorial experiments. Bulletin of the Calcutta Mathematical Society 28:67–8.
  • Rao, C. R. 1947. Factorial experiments derivable from combinatorial arrangements of array. Journal of the Royal Statistical Society 9(1):128–39.
  • Rao, C. R. 1949. On a class of arrangements. Proceedings of the Edinburgh Mathematical Society 8(3):119–25.
  • Rao, C. R. 1973. Some combinatorial problems of arrays and application to design of experiments. In A survey to design of experiments, Chapter 29, pp 349–359. North Holland.
  • Rawlings, J. O., and C. C. Cockerham. 1962. Triallel analysis. Crop Science 2(3):228–31.
  • Ray-Chaudhuri, D. R., and R. M. Wilson. 1971. Solution of Kirkman’s school girl problem. Proceedings of Symposia in Pure Mathematics, Combinatorics. American Mathematical Society, Providence, RI. 19:187–203.
  • Ray-Chaudhuri, D. K., and R. M. Wilson. 1973. The Existence of resolvable designs. In A Survey of Combinatorial Theory. ed. J. N. Srivastava, 361–375. North-Holland , Amesterdam.
  • Sharma, M. K., A. Asedewoin, and M. Bisrat. 2011. Optimal partial triallel cross designs. Model Assisted Statistics and Applications 6:1–8.
  • Sharma, M. K., and S. Fanta. 2012. Optimal PartialTriallel cross. JISAS 66(2):289–94.
  • Subbarayan, A. 1992. On the applications of pure cyclic triple system for plant breeding experiments. Journal of Applied Statistics 19(4):489–500.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.