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Research Article

volume 35 issue 1-2 (march-june 2020) : 102-105,   Doi: 10.18805/BKAP211

Three-associate class partially balanced incomplete block designs through kronecker product

C
Cini Varghese
S
Seema Jaggi
M
Mohd Harun
D
Devendra Kumar
1<div style="text-align: justify;">ICAR-Indian Agricultural Statistics Research Institute, PUSA, New Delhi&ndash;12, India</div>

  • Submitted02-07-2020|

  • Accepted18-07-2020|

  • First Online 10-09-2020|

  • doi 10.18805/BKAP211

Cite article:- Varghese Cini, Jaggi Seema, Harun Mohd, Kumar Devendra (2020). Three-associate class partially balanced incomplete block designs through kronecker product. Bhartiya Krishi Anusandhan Patrika. 35(1): 102-105. doi: 10.18805/BKAP211.

ABSTRACT

Kronecker product of matrices can be advantageously used to obtain three-associate class partially balanced incomplete block (PBIB) designs from two-associate class PBIB designs, for a larger number of treatments. This method has been described here and two such series of PBIB designs are obtained. If the experimenter is constrained of resources, theses designs can be used as an alternative to balanced incomplete block designs or 2-associate class partially balanced incomplete block designs. 

REFERENCES

  1. Bose, R.C. and Nair, K.R. (1939). Partially balanced incomplete block designs. Sankhya, 4,337-372.
  2. Clatworthy, W.H. (1973). Tables of two-associate partially balanced designs. National Bureau of Standards, Applied Maths. Series No. 63, Washington D.C.
  3. Raghavarao, D. (1960). A generalization of group divisible designs. Annal of Mathematical Statistics, 31, 756-771.
  4. Roy, P.M. (1953). Hierarchical group divisible incomplete block designs with m-associate classes, Science and Culture, 19, 210-211.
  5. Searle, S.R. (1982). Matrix Algebra useful for Statistics. Wiley, New York.
  6. Varghese, C. and Sharma, V.K. (2004). A series of resolvable PBIB (3) designs with two replicates. Metrika, 60, 251–254.
  7. Vartak, M.N. (1960). Relations among the blocks of the kronecker product of designs. Annal of Mathematical Statistics, 31 (3), 772-778.
  8. Zelen, M. (1954).A note on partially balanced designs. Annal of Mathematical Statistics,25, 599-602.
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    Research Article

    volume 35 issue 1-2 (march-june 2020) : 102-105,   Doi: 10.18805/BKAP211

    Three-associate class partially balanced incomplete block designs through kronecker product

    C
    Cini Varghese
    S
    Seema Jaggi
    M
    Mohd Harun
    D
    Devendra Kumar
    1<div style="text-align: justify;">ICAR-Indian Agricultural Statistics Research Institute, PUSA, New Delhi&ndash;12, India</div>

    • Submitted02-07-2020|

    • Accepted18-07-2020|

    • First Online 10-09-2020|

    • doi 10.18805/BKAP211

    Cite article:- Varghese Cini, Jaggi Seema, Harun Mohd, Kumar Devendra (2020). Three-associate class partially balanced incomplete block designs through kronecker product. Bhartiya Krishi Anusandhan Patrika. 35(1): 102-105. doi: 10.18805/BKAP211.

    ABSTRACT

    Kronecker product of matrices can be advantageously used to obtain three-associate class partially balanced incomplete block (PBIB) designs from two-associate class PBIB designs, for a larger number of treatments. This method has been described here and two such series of PBIB designs are obtained. If the experimenter is constrained of resources, theses designs can be used as an alternative to balanced incomplete block designs or 2-associate class partially balanced incomplete block designs. 

    REFERENCES

    1. Bose, R.C. and Nair, K.R. (1939). Partially balanced incomplete block designs. Sankhya, 4,337-372.
    2. Clatworthy, W.H. (1973). Tables of two-associate partially balanced designs. National Bureau of Standards, Applied Maths. Series No. 63, Washington D.C.
    3. Raghavarao, D. (1960). A generalization of group divisible designs. Annal of Mathematical Statistics, 31, 756-771.
    4. Roy, P.M. (1953). Hierarchical group divisible incomplete block designs with m-associate classes, Science and Culture, 19, 210-211.
    5. Searle, S.R. (1982). Matrix Algebra useful for Statistics. Wiley, New York.
    6. Varghese, C. and Sharma, V.K. (2004). A series of resolvable PBIB (3) designs with two replicates. Metrika, 60, 251–254.
    7. Vartak, M.N. (1960). Relations among the blocks of the kronecker product of designs. Annal of Mathematical Statistics, 31 (3), 772-778.
    8. Zelen, M. (1954).A note on partially balanced designs. Annal of Mathematical Statistics,25, 599-602.
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