Abstract
A simple method of construction of three series of optimal block designs for complete diallel cross method (4) has been presented by using nested balanced incomplete block designs of Dey et al. (Calcutta Statist. Assoc. Bull. 35, 161–167 1986). The proposed designs are different from Gupta and Choi (Communication in Statistics-Theory and Methods 27(11), 2827–2835 1998) and Das et al. (Statistics and Probability Letters 36, 427–436 1998)’s designs in parametric values. From the proposed designs we have also derived three series of optimal row–column designs for complete diallel cross method (4) and three series of A–optimal row–column designs for complete diallel cross method (2), respectively. By using the proposed method, we have also obtained some more designs of the above types from nested balanced incomplete block designs of Morgan et al. (Discrete Mathematics 231, 351–389 2001). Tables of these optimal /A-optimal designs have been provided. Illustration of the layouts of the proposed designs along with their analysis has been provided.
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References
Aggarwal, K.R. (1974). Analysis of Li(s) and triangular designs. Journal of the Indian Society for Agricultural Statistics 26, 3–13.
Bose, R. (1939). On the construction of balanced incomplete block designs. Ann Eugen 9, 353–399.
Das, A., Dey, A. and Dean, A.M. (1998). Optimal designs for diallel cross experiments. Statistics and Probability Letters 36, 427–436.
Dey, A., Das, U.S. and Banerjee, A.K. (1986). Construction of nested balanced incomplete block designs. Calcutta Statist. Assoc. Bull. 35, 161–167.
Dey, A. and Midha, C.K. (1996). Optimal designs for diallel crosses. Biometrika 83, 2, 484–489.
Griffing, B. (1956). Concepts of general and specific combining ability in relation to diallel crossing system. Aus. J. Biol. Sci. 9, 463–493.
Gupta, S. and Choi, K. (1998). Optimal row-column designs for complete diallel crosses. Communication in Statistics-Theory and Methods 27, 11, 2827–2835.
Hedayat, A.S., Jacroux, M. and Majumdar, D. (1988). Optimal Designs for Comparing Test Treatments with Controls. Statistical Science 3, 4, 462–491.
Kiefer, J. (1975). Construction and optimality of generalized Youden designs. North Hollond, Amsterdam, Srivastava J. N. (ed.), p. 333–353.
Morgan, J.P., Preece, D.A. and Rees, D.H (2001). Nested balanced incomplete block designs. Discrete Mathematics 231, 351–389.
Parsad, R., Gupta, V.K. and Gupta, S. (2005). Optimal Designs for Diallel and Double Cross Experiments. Utilitas Mathematica 68, 11–32.
Preece, D.A. (1967). Nested balanced incomplete block design. Biometrika 54, 479–486.
Sharma, M.K. and Fanta, S. (2011). Optimal Block Designs For CDC experiments LXIX no. 3, 2, 297–307.
Sharma, R.J. (1998). Statistical and Biometrical Techniques in Plant Breeding, New Age International Publication (p) Limited. Publishers, New Delhi.
Singh, M., Gupta, S. and Parsad, R. (2012). Genetic crosses experiments. Wiley, New York, Hinkelmann K (ed.), p. 1–71.
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Sharma, M.K., Tadesse, M. Optimal Block and Row–Column Designs for CDC Methods. Sankhya B 79, 278–291 (2017). https://doi.org/10.1007/s13571-016-0126-6
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DOI: https://doi.org/10.1007/s13571-016-0126-6