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Research Article

volume 35 issue 4 (december 2020) : 245-248,   Doi: 10.18805/BKAP254

Designs involving sequences of treatments with residuals proportional to direct effects

C
Cini Varghese
S
Seema Jaggi
E
Eldho Varghese
M
Mohd Harun
D
Devendra Kumar
1ICAR-Indian Agricultural Statistics Research Institute, Pusa, New Delhi-110012, India.

  • Submitted22-12-2020|

  • Accepted19-01-2021|

  • First Online 28-05-2021|

  • doi 10.18805/BKAP254

Cite article:- Varghese Cini, Jaggi Seema, Varghese Eldho, Harun Mohd, Kumar Devendra (2021). Designs involving sequences of treatments with residuals proportional to direct effects. Bhartiya Krishi Anusandhan Patrika. 35(4): 245-248. doi: 10.18805/BKAP254.

ABSTRACT

Designs involving sequences of treatments are advantageously used when observations are taken repeatedly from same experimental unit period after period as a new treatment is applied in each period. Hence, inclusion of residual effects into the model becomes the most important feature of such designs. Six popular classes of designs involving sequences of treatments are studied under a model with carryover effects proportional to the direct effects where the unknown proportionality parameter assumed values from -1 to +1. The objective of this empirical study was to determine the value of proportionality parameter for which maximum information can be drawn from the design.

REFERENCES

  1. Balaam, L.N. (1968). A two-period design with t2 experimental units. Biometrics, 24(1), 61-73. 
  2. Bailey, R.A. and Kunert, J. (2006). On optimal crossover designs when carryover effects are proportional to direct effects. Biometrika, 93(3), 613-625. 
  3. Bose, M. and Dey, A. (2009). Optimal Crossover Designs. World Scientific Publishing Co. Pte. Ltd., Singapore.
  4. Bose, M. and Stufken, J. (2007). Optimal crossover designs when carryover effects are proportional to direct effects. J. Statist. Plan. Infer., 137, 3291-3302.
  5. Varghese, E., Jaggi, S., Varghese, C. and Bindal, V. (2013). Efficient neighbour balanced block design with proportional neighbour effects. Proceedings of 11th Biennial Conference of the International Biometric Society on Computational Statistics and Bio-Sciences held at Pondicherry University from 8 to 9 March 2012. 23-25.
  6. Kempton, R.A., Ferris, S.J. and David, O. (2001). Optimal change-over designs when carry over effects are proportional to direct effects of treatments. Biometrika, 88, 391-399.
  7. Sharma, V.K. (1981). A class of experimental designs balanced for first residuals. Austral. J. Statist., 23(3), 365-370.
  8. Williams, E.J. (1949). Experimental designs balanced for the estimation of residual effects of treatments. Austral. J. Sci. Res., A2, 149-168.
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    Research Article

    volume 35 issue 4 (december 2020) : 245-248,   Doi: 10.18805/BKAP254

    Designs involving sequences of treatments with residuals proportional to direct effects

    C
    Cini Varghese
    S
    Seema Jaggi
    E
    Eldho Varghese
    M
    Mohd Harun
    D
    Devendra Kumar
    1ICAR-Indian Agricultural Statistics Research Institute, Pusa, New Delhi-110012, India.

    • Submitted22-12-2020|

    • Accepted19-01-2021|

    • First Online 28-05-2021|

    • doi 10.18805/BKAP254

    Cite article:- Varghese Cini, Jaggi Seema, Varghese Eldho, Harun Mohd, Kumar Devendra (2021). Designs involving sequences of treatments with residuals proportional to direct effects. Bhartiya Krishi Anusandhan Patrika. 35(4): 245-248. doi: 10.18805/BKAP254.

    ABSTRACT

    Designs involving sequences of treatments are advantageously used when observations are taken repeatedly from same experimental unit period after period as a new treatment is applied in each period. Hence, inclusion of residual effects into the model becomes the most important feature of such designs. Six popular classes of designs involving sequences of treatments are studied under a model with carryover effects proportional to the direct effects where the unknown proportionality parameter assumed values from -1 to +1. The objective of this empirical study was to determine the value of proportionality parameter for which maximum information can be drawn from the design.

    REFERENCES

    1. Balaam, L.N. (1968). A two-period design with t2 experimental units. Biometrics, 24(1), 61-73. 
    2. Bailey, R.A. and Kunert, J. (2006). On optimal crossover designs when carryover effects are proportional to direct effects. Biometrika, 93(3), 613-625. 
    3. Bose, M. and Dey, A. (2009). Optimal Crossover Designs. World Scientific Publishing Co. Pte. Ltd., Singapore.
    4. Bose, M. and Stufken, J. (2007). Optimal crossover designs when carryover effects are proportional to direct effects. J. Statist. Plan. Infer., 137, 3291-3302.
    5. Varghese, E., Jaggi, S., Varghese, C. and Bindal, V. (2013). Efficient neighbour balanced block design with proportional neighbour effects. Proceedings of 11th Biennial Conference of the International Biometric Society on Computational Statistics and Bio-Sciences held at Pondicherry University from 8 to 9 March 2012. 23-25.
    6. Kempton, R.A., Ferris, S.J. and David, O. (2001). Optimal change-over designs when carry over effects are proportional to direct effects of treatments. Biometrika, 88, 391-399.
    7. Sharma, V.K. (1981). A class of experimental designs balanced for first residuals. Austral. J. Statist., 23(3), 365-370.
    8. Williams, E.J. (1949). Experimental designs balanced for the estimation of residual effects of treatments. Austral. J. Sci. Res., A2, 149-168.
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