Partially balanced nested block designs based on 2-associate-class association schemes for test-control comparisons

References

• Banerjee, S., and S. Kageyama. 1990. Existence of α-resolvable nested incomplete block-designs. Utilitas Mathematica 38:237–43.
   Web of Science ®Google Scholar
• Banerjee, S., and S. Kageyama. 1993. Methods of constructing nested partially balanced incomplete block designs. Utilitas Mathematica 43:3–6.
   Web of Science ®Google Scholar
• Bechhofer, R. E., and A. C. Tamhane. 1981. Incomplete block designs for comparing treatments with a control: General theory. Technometrics 23(1):45–57.
   Web of Science ®Google Scholar
• Cheng, C. S. 1986. A method for constructing balanced incomplete-block designs with nested rows and columns. Biometrika 73(3):695–700. doi: 10.1093/biomet/73.3.695.
   Web of Science ®Google Scholar
• Clatworthy, W. H. 1973. Tables of two-associate-class partially balanced designs. National Bureau of Standards, Applied Mathematics Series No. 63. Washington, DC: National Bureau of Standards.
   Google Scholar
• Das, A., and S. Gupta. 1997. Optimal block designs for triallel cross experiments. Communications in Statistics - Theory and Methods 26(7):1767–77. doi: 10.1080/03610929708832011.
   Web of Science ®Google Scholar
• Dey, A., U. S. Das, and A. K. Banerjee. 1986. Construction of nested balanced incomplete block designs. Calcutta Statistical Association Bulletin 35(3–4):161–8. doi: 10.1177/0008068319860306.
   Google Scholar
• Gupta, S., and S. Kageyama. 1994. Optimal complete diallel crosses. Biometrika 81(2):420–4. doi: 10.1093/biomet/81.2.420.
   Web of Science ®Google Scholar
• Gupta, V. K., and R. Parsad. 2001. Block designs for comparing test treatments with control treatments-an overview. Statistics and Applications 3:133–46.
   Google Scholar
• Hedayat, A. S., and D. Majumdar. 1984. A-optimal incomplete block designs for test treatment - Control comparisons. Technometrics 26(4):363–70.
   Web of Science ®Google Scholar
• Homel, R. J., and J. Robinson. 1975. Nested partially balanced incomplete block designs. Sankhya B 37:201–10.
   Google Scholar
• Jacroux, M. 1986. On the determination and construction of MV-optimal block designs for comparing test treatments with a standard treatment. Journal of Statistical Planning and Inference 15:205–25. doi: 10.1016/0378-3758(86)90098-4.
   Web of Science ®Google Scholar
• Jacroux, M. 1987. Some MV-optimal block designs for comparing test treatments with a standard treatment. Sankhyā: The Indian Journal of Statistics Series B 49:239–61.
   Google Scholar
• Jacroux, M. 1988. Some further results on the MV-Optimality of block designs for comparing test treatments to a standard treatment. Journal of Statistical Planning and Inference 20(2):201–14. doi: 10.1016/0378-3758(88)90123-1.
   Web of Science ®Google Scholar
• Jacroux, M., and D. Majumdar. 1989. Optimal block designs for comparing test treatments with a control when k > v. Journal of Statistical Planning and Inference 23(3):381–96. doi: 10.1016/0378-3758(89)90080-3.
   Web of Science ®Google Scholar
• Jimbo, M., and S. Kuriki. 1983. Constructions of nested designs. Ars Combinatoria 16:275–85.
   Google Scholar
• Kageyama, S., and Y. Miao. 1997. Nested designs with block size five and subblock size two. Journal of Statistical Planning and Inference 64(1):125–39. doi: 10.1016/S0378-3758(96)00210-8.
   Web of Science ®Google Scholar
• Kageyama, S., J. Philip, and S. Banerjee. 1995. Some constructions of nested BIB and 2-associate PBIB designs under restricted dualization. Bulletin of the Faculty of School Education Hiroshima University, Part II 17:33–9.
   Google Scholar
• Majumdar, D. 1996. 27 Optimal and efficient treatment-control designs. Handbook of Statistics 13:1007–53.
   Google Scholar
• Mandal, B. N., R. Parsad, and S. Dash. 2020. Construction of A-optimal balanced treatment incomplete block designs: An algorithmic approach. Communications in Statistics - Simulation and Computation 49(6):1653–64. doi: 10.1080/03610918.2018.1508701.
   Web of Science ®Google Scholar
• Mandal, B. N., G. Singh, R. Parsad, and S. Dash. 2022. Nearly balanced treatment incomplete block designs. Journal of the Indian Society of Agricultural Statistics 76(2):79–84.
   Google Scholar
• Morgan, J. P., D. A. Preece, and D. H. Rees. 2001. Nested balanced incomplete block designs. Discrete Mathematics 231(1–3):351–89. doi: 10.1016/s0012-365x(00)00332-0.
   Web of Science ®Google Scholar
• Parsad, R. 2019. Construction of nested partially balanced incomplete block designs. Statistics and Applications 17(1):275–80.
   Web of Science ®Google Scholar
• Parsad, R., V. K. Gupta, and N. S. G. Prasad. 1995. On construction of A-efficient balanced test treatment incomplete block-designs. Utilitas Mathematica 47:185–90.
   Web of Science ®Google Scholar
• Parsad, R., V. K. Gupta, and R. Srivastava. 2007a. Designs for cropping systems research. Journal of Statistical Planning and Inference 137(5):1687–703. doi: 10.1016/j.jspi.2006.09.018.
   Web of Science ®Google Scholar
• Parsad, R., S. Kageyama, and V. K. Gupta. 2007b. Use of complementary property of block designs in PBIB designs. Ars Combinatoria 85:173–82.
   Web of Science ®Google Scholar
• Parsad, R., and S. K. Satpati. 2005. Nested block designs for comparing test treatments with a control. Utilitas Mathematica 68:271–81.
   Web of Science ®Google Scholar
• Philip, J., S. Banerjee, and S. Kageyama. 1997. Construction of nested t-associate PBIB designs under restricted dualization. Utilitas Mathematica 51:27–32.
   Web of Science ®Google Scholar
• Preece, D. A. 1967. Nested balanced incomplete block designs. Biometrika 54(3):479–86. doi: 10.1093/biomet/54.3-4.479.
   PubMed Web of Science ®Google Scholar
• Saha, G. M., A. Dey, and C. K. Midha. 1998. Construction of nested incomplete block designs. Calcutta Statistical Association Bulletin 48(3–4):195–206. doi: 10.1177/0008068319980307.
   Google Scholar
• Saka, A. J., B. L. Adeleke, and T. G. Jaiyeola. 2018. Coset-k2 nested balanced incomplete block designs of resolvable type. International Journal of Statistics and Applications 8(5):267–73. doi: 10.5923/j.statistics.20180805.05.
   Google Scholar
• Satpati, S. K., and R. Parsad. 2004. Construction and cataloguing of nested partially balanced incomplete block designs. Ars Combinatoria 73:299–309.
   Web of Science ®Google Scholar
• Vinayaka. 2022. On constructions of nested partially balanced incomplete block designs. Communications in Statistics - Simulation and Computation 1–8. doi: 10.1080/03610918.2022.2091144.
   Web of Science ®Google Scholar
• Vinayaka and R. Parsad. 2023. Resolvable and 2-replicate PBIB designs based on higher association schemes using polyhedra. Statistics and Applications 21(2):141–54.
   Web of Science ®Google Scholar