Efficient Neighbor Designs Weakly Balanced in Circular Blocks of Three Different Sizes
DOI:
https://doi.org/10.21015/vtm.v11i2.1687Abstract
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.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC-By) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
This work is licensed under a Creative Commons Attribution License CC BY