Generators to Construct an Efficient Generalized Class of Minimal Circular Neighbor Designs

  • Sajid Hussain Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Jamshaidul Hassan Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Hurria Ali Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Abdul Salam Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Muhammad Rasheed Department of Statistics, The Islamia University of Bahawalpur, Pakistan
Keywords: circular block, minimal design, neighbor balanced design, strongly balanced neighbor design, neighbor effect

Abstract

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A design that is robust to neighbor effects is one that can protect against the neighbor effects. In situations where minimal circular balanced neighbor designs (MCBNDs) cannot be constructed, minimal circular weakly balanced neighbor designs-I (MCWBNDs-I) are preferred, which is an efficient generalized class. MCWBNDs-I are neighbor designs in which v/2 pairs of distinct treatments appear twice as neighbors, while the remaining pairs appear once. New generators are developed in this study to obtain MCWBNDs-I in blocks of three different sizes.

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References

Azais JM. Design of experiments for studying intergenotypic competition. J Royal Stat Soc. 1987;49(3):334–345. https://doi.org/10.1111/j.2517-6161.1987.tb01704.x

Kunert J. Randomization of neighbour balanced designs. Biometric J. 2000;42(1):111–118. https://doi.org/10.1002/(SICI)1521-4036(200001)42:1%3C111::AID-BIMJ111%3E3.0.CO;2-L

Tomar JS, Jaggi S, Varghese C. On totally balanced block designs for competition effects. J App Stat. 2005;32(1):87–97. https://doi.org/10.1080/0266476042000305177

Rees DH. Some designs of use in serology. Biometrics. 1967;23(4):779–791. https://doi.org/10.2307/2528428

Azaïs JM, Bailey RA, Monod H. A catalogue of efficient neighbor-designs with border plots. Biometrics. 1993;49(4):1252–1261. https://doi.org/10.2307/2532269

Hwang FK. Constructions for some classes of neighbor designs. Ann Stat. 1973;1(4):786–790. https://www.jstor.org/stable/2958325

Cheng CS. Construction of optimal balanced incomplete block designs for correlated observations. Ann Stat. 1983;11(1),240–246. https://doi.org/10.1214/aos/1176346074

Iqbal I, Tahir MH, Ghazali SSA. Circular neighbor-balanced designs using cyclic shifts. Sci China Series A:Math. 2009;52(10):2243–2256. https://doi.org/10.1007/s11425-009-0063-1

Akhtar M, Ahmed R, Yasmin F. A catalogue of nearest neighbor balanced designs in circular blocks of size five. Pak J Stat. 2010;26(2):e397.

Shehzad F, Zafaryab M, Ahmed R. Some series of proper generalized neighbor designs. J Stat Plan Infer. 2011;141(12):3808–3818. https://doi.org/10.1016/j.jspi.2011.06.016

Ahmed R, Akhtar M. Designs balanced for neighbor effects in circular blocks of size six. J Stat Plan Inf. 2011;141(2):687–691. https://doi.org/10.1016/j.jspi.2010.07.018

Ahmed R, Akhtar M. Construction of neighbor balanced designs in linear blocks. Commun. Stat-Theory Methods. 2011;40(17):1–8. https://doi.org/10.1080/03610926.2010.493278

Shahid MR, Zakria M, Shehzad F, Ahmed, R. Some important classes of generalized neighbor designs in linear blocks. Commun Stat-Simul Comp. 2017;46(3):1991–1997. https://doi.org/10.1080/03610918.2015.1026990

Shahid MR, Ahmed R, Shehzad F, Muhammad YS. Development of some useful generators to obtain partially neighbor balanced designs. J King Saud Uni Sci. 2019;31(1):24–26. https://doi.org/10.1016/j.jksus.2017.07.009

Misra BL, Nutan B. Families of neighbor designs and their analysis. Commun Stat-Simul Comp. 1991;20(2-3):427–436. https://doi.org/10.1080/03610919108812963

Chaure NK, Misra BL. On construction of generalized neighbor designs. Sankhya: Indian J Stat Ser B.1996;58(2):245–253.

Mishra NS. Families of proper generalized neighbor designs. J Stat Plan Infer. 2007;13(5):1681–1686. https://doi.org/10.1016/j.jspi.2006.09.017

Kedia RG, Misra BL. On construction of generalized neighbor design of use in serology. Stat Probab Lett. 2008;78(3):254–256. https://doi.org/10.1016/j.spl.2007.05.030

Ahmed R, Akhtar M, Tahir MH. Economical generalized neighbor designs of use in Serology. Comp Stat Data Anal. 2009;53(12):4584–4589. https://doi.org/10.1016/j.csda.2009.05.019

Zafarya M, Shehzad F, Ahmed R. Proper generalized neighbor designs in circular blocks. J Stat Plan Infer. 2010;140(11):3498–3504. https://doi.org/10.1016/j.jspi.2010.05.021

Iqbal I, Tahir MH, Aggarwal ML, Ali A, Ahmed, I. Generalized neighbor designs with block size 3. J Stat Plan Infer. 2012;142(3):626–632. https://doi.org/10.1016/j.jspi.2011.08.015

Ahmed R, Akhtar M. Designs partially balanced for neighbor effects. Aligarh J Stat. 2012;32:41–53.

Noreen K, Tahir MH, Rasheed M, Hassan MU, Ahmed R. Some important classes of non-directional minimal circular weakly balanced neighbor designs. Commun Stat-Simul Comp. 2023:1–10. https://doi.org/10.1080/03610918.2023.2196382

Iqbal I. Construction of Experimental Designs Using Cyclic Shifts [dissertation]. University of Kent at Canterbury,UK: 1991.

Pearce SC, Calinski T, Marshall TD. The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika. 1974;61(3):449–460. https://doi.org/10.1093/biomet/61.3.449

James AT, Wilkinson GN. Factorization of the residual operator and canonical decomposition of non-orthogonal factors in the analysis of variance. Biometrika. 1971;58(2):279–294. https://doi.org/10.1093/biomet/58.2.279

Divecha J, Gondaliya J. Construction of minimal balanced Cross over designs having good efficiency of separability. Elect J Stat. 2014;8(2):2923–2936. https://doi.org/10.1214/14-EJS979

Published
2024-03-15
How to Cite
1.
Hussain S, Jamshaidul Hassan, Hurria Ali, Abdul Salam, Muhammad Rasheed. Generators to Construct an Efficient Generalized Class of Minimal Circular Neighbor Designs. Sci Inquiry Rev. [Internet]. 2024Mar.15 [cited 2024May19];8(1):61-4. Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/4905
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Orignal Article