Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes

Authors

  • Sajid Hussain The Islamia University of Bahawalpur, Bahawalpur
  • Jamshaid ul Hassan Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Abid Khan Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Hurria Ali Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Aqsa Safdar Department of Statistics, The Islamia University of Bahawalpur, Pakistan
  • Abdul Salam Department of Statistics, The Islamia University of Bahawalpur, Pakistan

DOI:

https://doi.org/10.21015/vtm.v11i2.1687

Abstract

Minimal circular weakly balanced neighbor designs (MCWBNDs) are efficient to controlneighbor effects for v even. MCWBNDs-II are designs where3v/2 unordered pairs of different treatments occur twice but remaining pairs occur once as neighbors, are not available for m (mod 4) ≡ 0& 3 in blocks of three different sizes with m = (v-2)/2 and v even. Here, some new generators are presented to develop cyclic shifts to get MCWBNDs-II in blocks of three different sizes.

References

Ahmed, R., & Akhtar, M. (2011). Designs balanced for neighbor effects in circular blocks of size six. Journal of Statistical Planning and Inference, 141, 687–691.

Akhtar, M., Ahmed, R., & Yasmin, F. (2010). A catalogue of nearest neighbor balanced-designs in circular blocks of size five. Pakistan Journal of Statistics, 20(2), 397–405.

Azais, J. M. (1987). Design of experiments for studying intergenotypic competition. Journal of the Royal Statistical Society: Series B, 49, 334–345.

Azais, J. M., Bailey, R. A., & Monod, H. (1993). A catalogue of efficient neighbor designs with border plots. Biometrics, 49(4), 1252–61.

Fardos, A., Salam, A., Hassan, J., Ali, H., Noreen, K., & Ahmed, R. (2023). Catalogues of some useful classes of circular designs in blocks of three different sizes to control neighbor effects. Proceedings of the Pakistan Academy of Sciences: A: Physical and Computational Sciences, 60(2), 29–38.

Hassan, J., Noreen, K., Rasheed, H. M. K., Ul Hassan, M., & Ahmed, R. (2023). Construction of circular quasi rees neighbor designs which can be converted into minimal circular balanced and strongly balanced neighbor designs. Communications in Statistics-Theory and Methods, 52(16), 5587–5605.

Hwang, F. K. (1973). Constructions for some classes of neighbor designs. Annals of Statistics, 1(4), 786–790.

Iqbal, I. (1991). Construction of experimental design using cyclic shifts (Doctoral dissertation, University of Kent at Canterbury, U.K.).

Iqbal, I., Tahir, M. H., & Ghazali, S. S. A. (2009). Circular neighbor-balanced designs using cyclic shifts. Science in China Series A: Mathematics, 52(10), 2243–2256.

James, A. T., & Wilkinson, G. N. (1971). Factorization of the residual operator and canonical decomposition of non-orthogonal factors in the analysis of variance. Biometrika, 58, 258–294.

Khalid, A., Shehzad, F., Ali, A., & Ahmed, R. (2019). Some important classes of neighbor balance designs in linear blocks of small sizes. Journal of King Saud University- Science, 30, 311–315.

Kunert, J. (2000). Randomization of neighbour balanced designs. Biometrical Journal, 42(1), 111–118.

Langton, S. (1990). Avoiding edge effects in agroforestry experiments: The use of neighbour-balanced designs and guard areas. Agroforestry Systems, 12, 173–185.

Mehmood, Q., Nadeem, M., Noreen, K., & Ahmed, R. (2022). Construction of generalized neighbor designs in circular blocks of two different sizes. The Nucleus, 59(1-4), 16–25.

Nadeem, M., Tahir, M. H., Ismail, M., Ahmed, R., & Iqbal, U. (2021). Some economical classes of minimal circular generalised neighbour designs. International Journal of Innovation, Creativity and Change, 15(8), 243–255.

Noreen, K., Omer, T., Hassan, J., Rasheed, H. M. K., & Ahmed, R. (2023a). Some new constructions of minimal efficient circular nearly strongly balanced neighbor designs. Journal of King Saud University- Science, 35, 1027–48.

Noreen, K., Rashid, M. S., Shehzad, F., Ul Hassan, M., Noreen, Z., Omer, T., & Ahmed, R. (2022). Algorithms to obtain generalized neighbor designs in minimal circular blocks. Communications in Statistics-Simulation and Computation, In Press.

Noreen, K., Tahir, M. H., Rasheed, M., Ul Hassan, M., & Ahmed, R. (2023b). Some important classes of non-directional minimal circular weakly balanced neighbor designs. Communications in Statistics-Simulation and Computation, In Press.

Pearce, S. C., Calinski, T., & Marshall, T. F. C. (1974). The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika, 61, 449–460.

Rasheed, H. M. K., Jabeen, R., Hussain, S., Shah, A., & Ahmed, R. (2019). Catalogues of efficient circular weakly balanced repeated measurements designs in periods of two different sizes. Aligarh Journal of Statistics, 39, 93–116.

Rasheed, M., Noreen, K., Ahmed, R., Tahir, M. H., & Jamal, F. (2022). Some useful classes of minimal weakly balanced neighbor designs in circular blocks of two different sizes. Communications in Statistics-Theory and Methods, 21(24), 8822–8839.

Rees, D. H. (1967). Some designs of use in serology. Biometrics, 23, 779–791.

Salam, A., Ahmed, R., Daniyal, M., Ismail, M., & Rehman, H. (2021). Some new constructions of minimal neighbour designs in circular blocks. International Journal of Innovation, Creativity and Change, 15(8), 435–456.

Shabbir, J., Hassan, J., Ul Hassan, M., Noreen, K., Hussain, S., & Ahmed, R. (2023). An algorithm coded with r to generate gn2-designs in circular blocks. VFAST Transaction on Mathematics, 11(2), 16–27.

Shahid, M. R., Ahmed, R., Shehzad, F., & Muhammad, Y. S. (2019). Development of some useful generators to obtain partially neighbor balanced designs. Journal of King Saud University-Science, 31, 24–26.

Shehzad, F., Zafaryab, M., & Ahmed, R. (2011). Minimal neighbor designs in circular blocks of unequal sizes. Journal of Statistical Planning and Inference, 141, 3681–3685.

Tomar, J. S., Jaggi, S., & Varghese, C. (2005). On totally balanced block designs for competition effects. Journal of Applied Statistics, 32(1), 87–97.

Williams, R. M. (1952). Experimental designs for serially correlated observations. Biometrika, 39, 151–167.

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Published

2023-12-31

How to Cite

Sajid Hussain, Jamshaid ul Hassan, Abid Khan, Hurria Ali, Aqsa Safdar, & Abdul Salam. (2023). Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes. VFAST Transactions on Mathematics, 11(2), 155–173. https://doi.org/10.21015/vtm.v11i2.1687