American Journal of Theoretical and Applied Statistics
Volume 3, Issue 5, September 2014, Pages: 125-129
Received: Jul. 16, 2014;
Accepted: Aug. 14, 2014;
Published: Aug. 30, 2014
Views 2726 Downloads 113
Naqvi Hamad, Ghazi University, Dera Ghazi Khan, Pakistan
A partially neighbor balanced design is a design in which for any fixed treatment, other treatments occur as neighbor λi times. This paper generates infinite series of one-dimensional partially neighbor balanced designs for v = n treatments. The blocks used in these designs are considered circular. Designs given here are partially balanced in terms of nearest neighbors and not necessarily in terms of variance. Binary and non-binary concepts have been used for the construction of designs. Theorem 1 generates binary generalized 2-neighbor designs and theorem 2 generates non-binary generalized 3-neighbor designs. These theorems generate designs for v = n treatments i.e., for odd and even number of treatments simultaneously. This concept remains relatively under-explored in the literature. The objective is to decrease error variance due to neighbor effect and reduce computational cost.
Partially Neighbor Balanced Designs for Circular Blocks, American Journal of Theoretical and Applied Statistics.
Vol. 3, No. 5,
2014, pp. 125-129.
Ahmed, R., Akhtar, M. and Tahir, M.H. (2009).Economical generalized neighbor designs for use in serology. Comput. Stat. and Data analysis 53: 4584-4589.
Azais, J. M., Bailey, R. A. and Monod, H. (1993). A catalogue of efficient neighbor-designs with border plots. Biometrics 49: 1252–1261.
Chaure, K. and Misra, B.L. (1996). On construction of generalized neighbor designs. Sankhya 58 (B, pt 2): 245–253.
Hamad, N., Zafaryab, M. and Hanif, M. (2010). Non-binary neighbor balance circular designs for v = 2n and λ = 2. J. Statist. Plann. Inference 140, 3013-3016.
Hwang, F. K., 1973. Constructions for some classes of neighbor designs. The Ann. Statist. 1(4): 786-790.
Kiefer, J., 1975. Construction and optimality of generalized Youden designs, in A Survey of Statistical Designs and Linear Models. : Srivastava, J. N. (Ed.), North-Holland, Amsterdam.
Kedia, R.G. and Misra, B.L. (2008).On construction of generalized neighbor design of use in serology. Statist. Prob. Letters 78: 254-256.
Misra, B.L. and Nutan, B. (1991). Families of neighbor designs and their analysis. Commun. Statist. Simul. Comput. 20 (2 and 3): 427–436.
Monod, H. (1992). Two factor neighbor designs in incomplete blocks for intercropping experiments. The Statistician 41(5): 487-497.
Nutan, S. M. (2007). Families of proper generalized neighbor designs. J. Statist. Plann. Inference 137: 1681-1686.
Preece, D.A. (1994). Balanced Ouchterlony neighbor designs. J. Combin. Math. Combin. Comput., 15, 197–219.
Rees, D.H. (1967). Some designs of use in serology. Biometrics 23: 779–791.