Construction of Generalized Neighbor Designs in Circular Blocks of Two Different Sizes
Neighbor balanced designs are used in experiments where neighbor effects may arise. These designs ensure that treatment comparisons will be less affected by the neighbor effects. Experimenters always prefer minimal designs but minimal circular neighbor designs cannot be constructed for even v, where v is number of treatments to be compared. Therefore, for v even, minimal circular generalized neighbor designs (MGNDs) should be used which are considered to be the good alternate to the minimal neighbor designs. In this article, some generators are developed to obtain MCGNDs in which 3v/2 unordered pairs of distinct treatments appear twice as neighbors while others appear once. Catalogues of the designs provide readymade solutions to the experimenters and researchers. The proposed designs catalogues are also compiled from the generators developed in this study for v (even) ≤ 100.
D.H. Rees, “Some designs of use in serology”, Biometrics, vol. 23, pp. 779-791, 1967.
J.M. Azais, R.A. Bailey and H. Monod, “A catalogue of efficient neighbor designs with border plots”, Biometrics, vol. 49, no. 4, pp.1252-61, 1993.
I. Iqbal, M.H. Tahir and S.S.A. Ghazali, “Circular neighbor-balanced designs using cyclic shifts”, Sci. China Math., vol. 52, no. 10, pp. 2243-2256, 2009.
M. Akhtar, R. Ahmed and F. Yasmin, “A catalogue of nearest neighbor balanced-designs in circular blocks of size five”, Pakistan J. Statist., vol. 26, no. 2, pp.397-405, 2010.
R. Ahmed and M. Akhtar, “Designs balanced for neighbor effects in circular blocks of size six”, J. Stat. Plan. Inference, vol. 141, pp. 687-691, 2011.
F. Shehzad, M. Zafaryab and R. Ahmed, “Minimal neighbor designs in circular blocks of unequal sizes”, J. Stat. Plan. Inference, vol. 141, pp. 3681-3685, 2011.
B.L. Misra, Bhagwandas and S.M. Nutan, “Families of neighbor designs and their analysis”, Commun. Stat. Simul. Comput., vol. 20, pp. 427-436, 1991.
N.K. Chaure and B.L. Misra, “On construction of generalized neighbor design”, Sankhya B, vol. 58, pp. 45-253, 1996.
S.M. Nutan, “Families of proper generalized neighbor designs”, J. Stat. Plan. Inference, vol. 137, pp. 1681-1686, 2007.
R.G. Kedia and B.L. Misra, “On construction of generalized neighbor design of use in serology”, Statist. Probab. Lett., vol. 18, pp. 254-256, 2008.
R. Ahmed, M. Akhtar and M.H. Tahir, “Economical generalized neighbor designs of use in Serology”, Comput. Stat. Data Anal, vol. 53, pp. 4584-4589, 2009.
M. Zafaryab, F. Shehzad and R. Ahmed, “Proper generalized neighbor designs in circular blocks”, J. Stat. Plan. Inference, vol. 140, pp. 3498-3504, 2010.
F. Shehzad, M. Zafaryab and R. Ahmed, “Some series of proper generalized neighbor designs”, J. Stat. Plan. Inference, vol. 141, pp. 3808-3818, 2011.
I. Iqbal, M.H. Tahir, M.L. Aggarwal, A. Ali and R. Ahmed, “Generalized neighbor designs with block size 3”, J. Stat. Plan. Inference, vol. 142, pp. 626-632, 2012.
I. Iqbal, “Construction of experimental design using cyclic shifts”, Ph.D. Thesis, University of Kent at Canterbury, U.K, 1991.