International Journal of Statistics and Applications
p-ISSN: 2168-5193 e-ISSN: 2168-5215
2018; 8(5): 267-273
doi:10.5923/j.statistics.20180805.05
A. J. Saka^{1}, B. L. Adeleke^{2}, T. G. Jaiyeola^{1}
^{1}Department of Mathematics, Obafemi Awolowo University, Ile Ife, Nigeria
^{2}Department of Statistics, University of Ilorin, Ilorin, Nigeria
Correspondence to: A. J. Saka, Department of Mathematics, Obafemi Awolowo University, Ile Ife, Nigeria.
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Copyright © 2018 The Author(s). Published by Scientific & Academic Publishing.
This work is licensed under the Creative Commons Attribution International License (CC BY).
http://creativecommons.org/licenses/by/4.0/
This paper presents, a new method of constructing nested balanced incomplete block designs (NBIBDs) of resolvable type called Coset-k^{2}, using an algebraic notion, of the left coset type. The class of NBIBDs that was constructed for treatments arranged in ‘b’ blocks of size each with and other parameters of the design are expressed as Indeed, the parameters of the design for any given number of treatments, v, are specified with ease even before the full designs are constructed. Also, fewer numbers of blocks are required when compared with the designs of comparable sizes. Designs that are constructed in this paper are appropriate for experiments where extraneous factors of two types if they exist can be eliminated, evaluated and controlled.
Keywords: Coset, Resolvable Designs, Incomplete Block Designs, Nested Designs and Nested Balanced Incomplete Block Designs
Cite this paper: A. J. Saka, B. L. Adeleke, T. G. Jaiyeola, Coset-k^{2} Nested^{ }Balanced Incomplete Block Designs of Resolvable Type, International Journal of Statistics and Applications, Vol. 8 No. 5, 2018, pp. 267-273. doi: 10.5923/j.statistics.20180805.05.
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Figure 1. Proof of Theorem 4 for k=m |
Figure 2. Proof of Theorem 4 for k = m+1 |
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