Resolvable Dichotomized Split-Set Partially Balanced   Incomplete Block Designs

Vinaykumar L.N.; Cini Varghese; Mohd Harun; Sayantani Karmakar

doi:10.56093/jisas.v77i02.171436

Authors

Vinaykumar L.N. The Graduate School, ICAR-Indian Agricultural Research Institute, New Delhi
Cini Varghese ICAR-Indian Agricultural Statistics Research Institute, New Delhi
Mohd Harun ICAR-Indian Agricultural Statistics Research Institute, New Delhi
Sayantani Karmakar ICAR-Indian Agricultural Statistics Research Institute, New Delhi

https://doi.org/10.56093/jisas.v77i02.171436

Keywords:

Association scheme; Resolvable; Canonical efficiency factor; Partially balanced incomplete block designs.

Abstract

A four-associate class association scheme named as Dichotomized Split-Set (DiSS) association scheme is defined for
number of treatments and a method for constructing Partially Balanced Incomplete Block (PBIB) designs based on this association scheme is developed. The proposed designs are cost effective in terms of resources as they require lesser replications. They are resolvable; hence they possess high application potential in areas like multi-site varietal trials where experimenters generally prefer incomplete block designs. The efficiency factors for these designs are computed in comparison to an orthogonal block design and are found to be quite high. For easy generation of these designs for any v = 2p(p - 1); p ≥ 3, an R package called “ResPBIBD” is developed.

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References

Bose, R.C. and Nair, K.R. (1939). Partially balanced incomplete block designs. Sankhya: Indian Journal of Statistics, 4(3), 337–372.

Bose, R.C. and Nair, K.R. (1962). Resolvable incomplete block designs with two replications. Sankhya: Indian Journal of Statistics – Series A, 24, 9–24.

Das, M.N. (1960). Circular designs. Journal of the Indian Society of Agricultural Statistics, 12, 46–56.

John, P.W.M. (1966). An extension of the triangular association scheme to three associate classes. Journal of the Royal Statistical Society: Series B (Methodological), 28(2), 361–365.

Parsad, R., Gupta, V.K., Batra, P.K., Satpati, S.K. and Biswas, P. (2007). Monograph on Alpha Designs. IASRI Publication, New Delhi.

Patterson, H.D. and Williams, E. (1976). A new class of resolvable incomplete block designs. Biometrika, 63(1), 83–92.

Raghavarao, D. (1960). A generalization of group divisible designs. The Annals of Mathematical Statistics, 31(3), 756–771.

Tharthare, S.K. (1965). Generalized right angular designs. The Annals of Mathematical Statistics, 36(5), 1535–1553.

Raghavarao, D. and Chandrasekhararao, K. (1964). Cubic designs. The Annals of Mathematical Statistics, 35(1), 389–397.

Rao, C.R. (1956). A general class of quasifactorial and related designs. Sankhya: Indian Journal of Statistics (1933–1960), 17(2), 165–174.

Roy, P.M. (1953). Hierarchical group divisible incomplete block designs with m associate classes. Science and Culture, 19, 210–211.

Saha, G.M., Dey, A. and Kulshreshtha, A.C. (1974). Circular designs – further results. Journal of the Indian Society of Agricultural Statistics, 26(1), 87–92.

Tharthare, S.K. (1963). Right angular designs. The Annals of Mathematical Statistics, 34(3), 1057–1067.

Varghese, C. and Sharma, V.K. (2004). A series of resolvable PBIB(3) designs with two replicates. Metrika, 60(3), 251–254.

Vinaykumar, L.N., Varghese, C., Harun, M. and Karmakav, S. (2022). ResPBIBD: "Resolvable partially balanced incomplete block designs (PBIBDs)". R package. https://cran.r-project.org/package=ResPBIBD

Williams, E.R., Patterson, H.D. and John, J.A. (1976). Resolvable designs with two replications. Journal of the Royal Statistical Society: Series B (Methodological), 38(3), 296–301.

Yates, F. (1936). A new method of arranging variety trials involving a large number of varieties. The Journal of Agricultural Science, 26(3), 424–455.