Partially Neighbor Balanced Designs for Circular Blocks
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
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Author
Naqvi Hamad, Ghazi University, Dera Ghazi Khan, Pakistan
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Abstract
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.
Keywords
Non-Binary Blocks, Generalized 2-Neighbor Designs, Generalized 3-Neighbor Designs
To cite this article
Naqvi Hamad, Partially Neighbor Balanced Designs for Circular Blocks, American Journal of Theoretical and Applied Statistics. Vol. 3, No. 5, 2014, pp. 125-129. doi: 10.11648/j.ajtas.20140305.12
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