A Study on 2-Part Balanced Incomplete Block Design

Naziru Muhammad; Jamilu Garba; Abdulkarim Muhammad

doi:10.56919/usci.2223.001

Authors

Naziru Muhammad Department of Statistics, Ahmadu Bello University, Zaria, Kaduna, Nigeria. https://orcid.org/0000-0003-3991-3096
Dr. Jamilu Garba Department of Statistics, Ahmadu Bello University, Zaria, Kaduna, Nigeria. https://orcid.org/0000-0002-1077-358X
Abdulkarim Muhammad Department of Computer Science, Ahmadu Bello University, Zaria https://orcid.org/0000-0002-9436-3683

DOI:

https://doi.org/10.56919/usci.2223.001

Keywords:

Balanced Incomplete Block Design, Additive Model, ANOVA table, Model Parameters, Orthogonal Design, Adjusted Sum of Squares

Abstract

Multi-part Balanced Incomplete Block Designs is a combination of many orthogonal balanced incomplete block designs in the same block. The design has been used to study cancer trials with medical centers as blocks. Various design layouts has been constructed for a restricted number of cancer types and drugs. However, parameter estimation, hypothesis testing, and model building for the constructed design layouts have not being considered. Based on the foregoing, we proposed additive model for the design (2-part Balanced Incomplete Block Designs) and estimated its parameters using the least square method. The parameter estimation precipitated to the formation of ANOVA table which paved way for the hypothesis testing procedure.

References

Alawode, O. A., Bamiduro, T. A., and Eludire, A. A. (2012). Some Balanced Incomplete Block Designs (BIBDs) from Lotto Designs (LDs). International Journal of Mathematical and Computational Sciences, 6(8):1194–1197. https://doi.org/10.5281/zenodo.1327794

Bailey, R. A. and Cameron, P. J. (2019). Multi-Part Balanced Incomplete-Block Designs. Statistical Papers, 60(2):55–76. https://doi.org/10.1007/s00362-018-01071-x

Mason, R. L., Gunst, R. F., and Hess, J. L. (2003). Statistical Design and Analysis of Experiments: with Applications to Engineering and Science. John Wiley & Sons. ISBN: 9780471372165. Retrieved from http://onlinelibrary.wiley.com/doi/book/10.1002/0471458503

Mills, S. E. (2014). STAT5505 Design of Experiments. Citeseer, 5203 Herzberg Bldg., School of Mathematics and Statistics, Carleton. Retrieved from http://mathstat.carleton.ca/~smills/2014-15/STAT5505/lecture14.pdf

A Study on 2-Part Balanced Incomplete Block Design

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