Partially Neighbor Balanced Designs for Circular Blocks

Naqvi Hamad

doi:doi:10.11648/j.ajtas.20140305.12

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Partially Neighbor Balanced Designs for Circular Blocks

Naqvi Hamad

Published in American Journal of Theoretical and Applied Statistics (Volume 3, Issue 5)

Received: 16 July 2014 Accepted: 14 August 2014 Published: 30 August 2014

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 3, Issue 5)
DOI	10.11648/j.ajtas.20140305.12
Page(s)	125-129
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Non-Binary Blocks, Generalized 2-Neighbor Designs, Generalized 3-Neighbor Designs

References

[1]	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.
[2]	Azais, J. M., Bailey, R. A. and Monod, H. (1993). A catalogue of efficient neighbor-designs with border plots. Biometrics 49: 1252–1261.
[3]	Chaure, K. and Misra, B.L. (1996). On construction of generalized neighbor designs. Sankhya 58 (B, pt 2): 245–253.
[4]	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.
[5]	Hwang, F. K., 1973. Constructions for some classes of neighbor designs. The Ann. Statist. 1(4): 786-790.
[6]	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.
[7]	Kedia, R.G. and Misra, B.L. (2008).On construction of generalized neighbor design of use in serology. Statist. Prob. Letters 78: 254-256.
[8]	Misra, B.L. and Nutan, B. (1991). Families of neighbor designs and their analysis. Commun. Statist. Simul. Comput. 20 (2 and 3): 427–436.
[9]	Monod, H. (1992). Two factor neighbor designs in incomplete blocks for intercropping experiments. The Statistician 41(5): 487-497.
[10]	Nutan, S. M. (2007). Families of proper generalized neighbor designs. J. Statist. Plann. Inference 137: 1681-1686.
[11]	Preece, D.A. (1994). Balanced Ouchterlony neighbor designs. J. Combin. Math. Combin. Comput., 15, 197–219.
[12]	Rees, D.H. (1967). Some designs of use in serology. Biometrics 23: 779–791.

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Naqvi Hamad. (2014). Partially Neighbor Balanced Designs for Circular Blocks. American Journal of Theoretical and Applied Statistics, 3(5), 125-129. https://doi.org/10.11648/j.ajtas.20140305.12

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Naqvi Hamad. Partially Neighbor Balanced Designs for Circular Blocks. Am. J. Theor. Appl. Stat. 2014, 3(5), 125-129. doi: 10.11648/j.ajtas.20140305.12

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Naqvi Hamad. Partially Neighbor Balanced Designs for Circular Blocks. Am J Theor Appl Stat. 2014;3(5):125-129. doi: 10.11648/j.ajtas.20140305.12

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@article{10.11648/j.ajtas.20140305.12,
  author = {Naqvi Hamad},
  title = {Partially Neighbor Balanced Designs for Circular Blocks},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {5},
  pages = {125-129},
  doi = {10.11648/j.ajtas.20140305.12},
  url = {https://doi.org/10.11648/j.ajtas.20140305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140305.12},
  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.},
 year = {2014}
}

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TY  - JOUR
T1  - Partially Neighbor Balanced Designs for Circular Blocks
AU  - Naqvi Hamad
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140305.12
DO  - 10.11648/j.ajtas.20140305.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 125
EP  - 129
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140305.12
AB  - 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.
VL  - 3
IS  - 5
ER  -

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Author Information

Naqvi Hamad

Ghazi University, Dera Ghazi Khan, Pakistan

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APA Style

Naqvi Hamad. (2014). Partially Neighbor Balanced Designs for Circular Blocks. American Journal of Theoretical and Applied Statistics, 3(5), 125-129. https://doi.org/10.11648/j.ajtas.20140305.12

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ACS Style

Naqvi Hamad. Partially Neighbor Balanced Designs for Circular Blocks. Am. J. Theor. Appl. Stat. 2014, 3(5), 125-129. doi: 10.11648/j.ajtas.20140305.12

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AMA Style

Naqvi Hamad. Partially Neighbor Balanced Designs for Circular Blocks. Am J Theor Appl Stat. 2014;3(5):125-129. doi: 10.11648/j.ajtas.20140305.12

Copy | Download

@article{10.11648/j.ajtas.20140305.12,
  author = {Naqvi Hamad},
  title = {Partially Neighbor Balanced Designs for Circular Blocks},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {3},
  number = {5},
  pages = {125-129},
  doi = {10.11648/j.ajtas.20140305.12},
  url = {https://doi.org/10.11648/j.ajtas.20140305.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20140305.12},
  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.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Partially Neighbor Balanced Designs for Circular Blocks
AU  - Naqvi Hamad
Y1  - 2014/08/30
PY  - 2014
N1  - https://doi.org/10.11648/j.ajtas.20140305.12
DO  - 10.11648/j.ajtas.20140305.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 125
EP  - 129
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20140305.12
AB  - 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.
VL  - 3
IS  - 5
ER  -

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