Characteristics of Dispersed Latin Squares

Authors

  • S. Z. Mahfooz University of Hafr Albatin, KSA
  • Y. Khan Univeristy of Hafr Albatin, KSA

DOI:

https://doi.org/10.71330/thenucleus.2019.585

Abstract

Experimental designs widely use Latin squares for controlled testing to understand causal processes.
Among many existing Latin squares for a given order, a design of experiment may need a specific Latin
square that offers its treatments (symbols) scattered at the desired locations. There is a need to study
systematic dispersion of symbols in Latin squares to assist effective research designs. This paper
describes the attributes and applications of one of such designs known as Latin square of diamond
dispersed pattern

Author Biographies

S. Z. Mahfooz, University of Hafr Albatin, KSA

Assistant Prof, Computer Science & Engineering

Y. Khan, Univeristy of Hafr Albatin, KSA

Assistant Prof, Mathematics

References

References [1] B. Durakovic, "Design of experiments application, concepts, examples: State of the art", Periodicals of Engineering and Natural Sciences, vol. 5, no. 3, p. 421-439, 2017. [2] S. Aoki and A. Takemura, “Design and analysis of fractional factorial experiments from the viewpoint of computational algebraic statisticsâ€, Journal of Statistical Theory and Practice, vol. 6, pp. 147-161, 2012. https://doi.org/10.1080/15598608.2012.647556. [3] D.R. Cox, "A remark on Systematic Latin Squares", Journal of the Royal Statistical Society, vol. 41, no. 3, pp. 388-389, 1979, https://doi.org/10.1111/j.2517-6161.1979.tb01093.x. [4] A. Hedayat, “A complete solution to the existence and non-existence of Knut Vik designs and orthogonal Knut Vik designsâ€, Journal of Combinational Theory, vol. 22, pp. 331-337, 1978. [5] S.Z. Mahfooz and M. Akhlaq, “Latin Squares of Diamond Dispersed Patternâ€, International Journal of Applied Computational Mathematics, vol. 3, pp. 81-89, 2017. [6] R.A. Fisher, "The arrangement of field experiments", Journal of Ministry of Agriculture of Great Britain, vol. 33, pp. 503-513, 1926.

F.G. Giesbrecht and M.L. Gumpertz, "Planning, construction and statistical analysis of comparative experiments", John Wiley & Sons, Inc., April 2004.

U. Saint-Mont, “Randomization does not help much, comparability doesâ€, Journal Public Library of Science (PloS), vol. 10, no. 7, 2015, https://doi.org/10.1371/journal.pone.0132102.

V. Dabbaghian and Tiankuang Wu, “Constructing non-cyclic pandiagonal Latin squares of prime ordersâ€, Journal of Discrete Algorithms, vol. 30, pp. 70-77, Jan 2015.

S.Z. Mahfooz and Bo Hu, “Diamond dispersed pattern in FMO for error resilient H.264/AVC video communicationâ€, Journal of Mianyang Normal University, vol. 11, pp. 101-106, 2011.

M. Abdaoui, "Strategies for avoiding cheating and preserving academic integrity in tests", Alkhitab w el-Tawassol Journal, vol. 4, pp. 1-9, 2018.

J. Ramberg and B. Modin, "School effectiveness and student cheating: Do students’ grades and moral standards matter for this relationship?", Social Psychology of Education, vol. 22, pp. 517-538, 2019.

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Published

12-06-2020

How to Cite

[1]
S. Z. Mahfooz and Y. Khan, “Characteristics of Dispersed Latin Squares”, The Nucleus, vol. 56, no. 4, pp. 131–136, Jun. 2020.

Issue

Vol. 56 No. 4 (2019)

Section

Articles

License

For all articles published in The Nucleus, copyright is retained by the authors. Articles are licensed under an open access licence [CC Attribution 4.0] meaning that anyone may download and read the paper for free. In addition, the article may be reused and quoted provided that the original published version is cited properly.