Designs for animal experiments under two-way blocking structure in the presence of systematic trend
Keywords:Latin square design, Systematic trend, Trend-free designs, Trend resistance, Two-way blocking
Designs under two-way blocking structure are quite useful in animal experiments. Further, in animal experiments, situations are also quite prevalent where there are evidences of systematic trend component influencing the response. These effects are generally neglected but they may have significant impact on the precision of the experiments, if considered. Suitably choosing a design will nullify the effect of such systematic trend. The present article describes the model under two-way blocking structure incorporating systematic trend component. The condition to nullify the effects of trend component when they are present in the experimental material has been obtained and illustrated under a two-way blocking structure. The analytical procedure has been explained through a hypothetical dataset to show the significance of such effects. The results shows that systematic trend component have significant impact on the precision of the experiments and hence will affect the inference.
Bhowmik A. 2013. Experimental designs involving treatments exhibiting interference effects. Unpublished Ph.D. Thesis, IARI, New Delhi.
Bhowmik A, Jaggi S, Varghese C and Varghese E. 2014. Trend free block designs balanced for interference effects from neighbouring experimental units. Journal of Combinatorics, Information and System Sciences 39(1–4): 117–33.
Bhowmik A, Jaggi S, Varghese C and Varghese E. 2015. Trend free second order neighbour balanced block designs. Journal of Indian Statistical Association 53(1 and 2): 63–78.
Bhowmik A, Jaggi S, Varghese E and Yadav S K. 2017. Trend free design under two-way elimination of Heterogeneity. RASHI 2(1): 34–38.
Jacroux M, Majumdar D and Shah K R. 1997. On the determination and construction of optimal block designs in the presence of linear trend. Journal of the American Statistical Association 92: 375–82.
Lal K, Parsad R and Gupta V K. 2007. Trend-free nested balanced incomplete block designs and designs for diallel cross experiments. Calcutta Statistical Association Bulletin 59: 203– 21.
Majumdar D and Martin R J. 2002. Finding optimal designs in the presence of trends. Journal of Statistical Planning and Inference 106: 177–90.
Sarkar K A, Jaggi S, Bhowmik A, Varghese E and Varghese C. 2017. Trend resistant neighbour balanced bipartite block designs. Journal of the Indian Society of Agricultural Statistics 71: 53–59.
The copyright of the articles published in The Indian Journal of Animal Sciences is vested with the Indian Council of Agricultural Research, which reserves the right to enter into any agreement with any organization in India or abroad, for reprography, photocopying, storage and dissemination of information. The Council has no objection to using the material, provided the information is not being utilized for commercial purposes and wherever the information is being used, proper credit is given to ICAR.