New generators for minimal circular generalised neighbour designs in blocks of two different sizes

Muhammad Nadeem; Khadija Noreen; M. Kashif Rasheed; Rashid Ahmed; Mahmood Ul Hassan

doi:10.59170/stattrans-2023-021

New generators for minimal circular generalised neighbour designs in blocks of two different sizes

Muhammad Nadeem Department of Statistics, The Islamia University of Bahawalpur, Pakistan ORCID:https://orcid.org/0000-0002-4034-3564 , Khadija Noreen Department of Statistics, The Islamia University of Bahawalpur, Pakistan ORCID:https://orcid.org/0000-0002-0377-0030 , M. Kashif Rasheed Department of Statistics, The Islamia University of Bahawalpur, Pakistan ORCID:https://orcid.org/0000-0002-5965-7803 , Rashid Ahmed Department of Statistics, The Islamia University of Bahawalpur ORCID:https://orcid.org/0000-0001-9703-7296 , Mahmood Ul Hassan Department of Statistics, Stockholm University, Stockholm, Sweden ORCID:https://orcid.org/0000-0003-2889-0263 Statistics in Transition new series, vol. 24, 2023, 2, pages: 85-92 Published online: 15 March 2023 DOI 10.59170/stattrans-2023-021 Citation: Nadeem, M., Noreen, K., Rasheed, M. K., Ahmed, R., Ul Hassan, M., 2023. New generators for minimal circular generalised neighbour designs in blocks of two different sizes. Statistics in Transition new series, 24(2), pp. 85-92. https://doi.org/10.59170/stattrans-2023-021

480 Views 36 Downloads

ARTICLE

(English) PDF

ABSTRACT

Minimal neighbour designs (NDs) are used when a response of a treatment (direct effect) is affected by the treatment(s) applied in the neighbouring units. Minimal generalised NDs are preferred when minimal NDs cannot be constructed. Through the method of cyclic shifts (Rule I), the conditions for the existence of minimal circular generalised NDs are discussed, in which v/2 unordered pairs do not appear as neighbours. Certain generators are also developed to obtain minimal circular generalised NDs in blocks of two different sizes, where k2 = 3, 4 and 5. All these designs are constructed using i sets of shifts for k1 and two for k2.

KEYWORDS

direct effects, neighbour effects, method of cyclic shifts, generalised NDs, GN2-designs.

REFERENCES

Ahmed, R., Akhtar, M. and Tahir, M. H., (2009). Economical generalized neighbor designs of use in Serology. Computational Statistics and Data Analysis, 53, pp. 4584–4589.

Ahmed, R., Akhtar, M., (2012). Designs partially balanced for neighbor effects. Aligarh Journal of Statistics, 32, pp. 41–53.

Chaure, N. K., Misra, B. L., (1996). On construction of generalized neighbor design. Sankhya Series B, 58, pp. 45–253.

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

Iqbal, I., Tahir, M. H., Aggarwal, M. L., Ali, A. and Ahmed, I. (2012). Generalized neighbor designs with block size 3. Journal of Statistical Planning and Inference, 142, pp. 626–632.

Kedia, R. G., Misra, B. L., (2008). On construction of generalized neighbor design of use in serology. Statistics and Probability Letters, 18, pp. 254–256.

Misra, B. L., Bhagwandas and Nutan S. M., (1991). Families of neighbor designs and their analysis, Communications in Statistics - Simulation and Computation, 20, pp. 427–436.

Nutan, S. M., (2007). Families of Proper Generalized Neighbor Designs. Journal of Statistical Planning and Inference, 137, pp. 1681–1686.

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

Shehzad, F., Zafaryab, M. and Ahmed, R., (2011). Some series of proper generalized neighbor designs. Journal of Statistical Planning and Inference, 141, pp. 3808–3818.

Zafaryab, M., Shehzad, F. and Ahmed, R., (2010). Proper generalized neighbor designs in circular blocks. Journal of Statistical Planning and Inference, 140, pp. 3498–3504.