Catalogues of Some Useful Classes of Circular Designs in Blocks of Three Different Sizes to Control Neighbor Effects
Keywords:Neighbor Effects, CBNDs, CSBNDs, CQRNDs, CNSBNDs
Minimal neighbor designs minimize the bias raised due to the neighbor effects using the minimum number of experimental units. Minimal circular balanced and strongly balanced neighbour designs can be constructed only for odd v (number of treatments to be compared). For v even, minimal Quasi Rees and nearly strongly balanced neighbor designs are constructed. In this article, the construction procedures of these four classes are described. Catalogues of these designs in blocks of three different sizes are also presented which provide the readymade solution to the experimenters and researchers.
J.M. Azais. Design of experiments for studying intergenotypic competition. Journal of the Royal Statistical Society: Series B 49: 334-345 (1987).
J.M. Azais, R.A. Bailey, and H. Monod. A catalogue of efficient neighbor designs with border plots. Biometrics 49(4): 1252- 1261 (1993).
J. Kunert. Randomization of neighbour balanced designs. Biometrical Journal 42(1): 111-118 (2000).
J.S. Tomar, S. Jaggi, and C. Varghese. On totally balanced block designs for competition effects. Journal of Applied Statistics 32(1): 87-97 (2005).
D.H. Rees. Some designs of use in serology. Biometrics 23: 779-791 (1967).
B.L. Misra, Bhagwandas, and S.M. Nutan. Families of neighbor designs and their analysis Communications in Statistics - Simulation and Computation 20: 427-436 (1991).
D.A. Preece. Balanced Ouchterlony neighbor designs. Journal of Combinatorial Mathematics and Combinatorial Computing 15: 197-219 (1994).
N.K. Chaure, and B.L. Misra. On construction of generalized neighbor design. Sankhya Series B 58: 245-253 (1996).
S. Jaggi, V.K. Gupta, and J. Ashraf. On block designs partially balanced for neighbouring competition effects. Journal of Indian Statistical Association 44(1): 27-41 (2006).
S.M. Nutan. Families of proper generalized neighbor designs. Journal of Statistical Planning and Inference 137: 1681–1686 (2007).
R.G. Kedia, and B.L. Misra. On construction of generalized neighbor design of use in serology. Statistics and Probability Letters 18: 254-256 (2008).
R. Ahmed, M. Akhtar, and M.H. Tahir. Economical generalized neighbor designs of use in Serology. Computational Statistics and Data Analysis 53: 4584-4589 (2009).
I. Iqbal, M.H. Tahir, and S.S.A. Ghazali. Circular neighbor-balanced designs using cyclic shifts. Science in China Series A: Mathematics 52(10): 2243-2256 (2009).
M. Akhtar, R. Ahmed, and F. Yasmin. A catalogue of nearest neighbor balanced- designs in circular blocks of size five. Pakistan Journal of Statistics 26(2): 397- 405 (2010).
K.K.S. Meitei. Circular neighbour-balanced designs and one-sided circular neighbour-balanced designs. Sankhyā: The Indian Journal of Statistics, Series B 72: 175-188 (2010).
R. Ahmed, and M. Akhtar. Designs balanced for neighbor effects in circular blocks of size six. Journal of Statistical Planning and Inference 141: 687-691 (2011).
F. Shehzad, M. Zafaryab, and R. Ahmed. Minimal neighbor designs in circular blocks of unequal sizes. Journal of Statistical Planning and Inference 141: 3681-3685 (2011).
I. Iqbal, M.H. Tahir, M.L. Aggarwal, A. Ali, and I. Ahmed. Generalized neighbor designs with block size 3. Journal of Statistical Planning and Inference 142: 626-632 (2012).
N. Hamad, and M. Hanif. Non-directional two-dimensional neighbor designs. Pakistan Journal of Statistics 33(4): 269-276 (2017).
S. Jaggi, D.K. Pateria, C. Varghese, E. Varghese, and A. Bhowmik. A note on circular neighbour balanced designs. Communications in Statistics - Simulation and Computation 47: 2896-2905 (2018).
K.P. Singh. A neighbor balanced design and its optimal certainty contribution. Bulletin of Pure and Applied Sciences Section - E - Mathematics & Statistics 38E(2): 636-640 (2019).
K.K.S. Meitei. Universally Optimal One-sided Circular Neighbour-balanced Designs with k = 5. Calcutta Statistical Association Bulletin 72(2): 84-88 (2020).
A. Salam, R. Ahmed, M. Daniyal, and R.A. Berihan. Minimal circular nearly strongly-balanced neighbor designs when left and right neighbor effects are equal. Journal of Statistical Application and Probability 11(3): 883-891 (2021).
I. Iqbal. Construction of experimental design using cyclic shifts. Ph.D. Thesis, University of Kent at Canterbury, UK (1991).