Experimental Designs Involving Treatments Exhibiting Interference Effects
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Date
2013
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IARI, INDIAN AGRICULTURAL STATISTICS RESEARCH INSTITUTE INDIAN AGRICULTURAL RESEARCH INSTITUTE PUSA, NEW DELHI
Abstract
In agricultural field experiments, interference effects may arise from treatments applied in neighbouring units. These interference effects may also arise from the neighbouring units at distance 2, 3 and so on. Block model with interference effects from the neighbouring units up to distance 2 (or second order) has been studied. The information matrices for estimating direct as well as interference effects have been derived. Some classes of balanced and strongly balanced block designs with interference effect up to distance 2 have been obtained and their characterization properties have been studied. The designs so obtained are totally balanced for estimating direct and interference effects of treatments. Further, considering one-sided interference effects from left neighbouring units up to distance 2, universally optimal balanced and strongly balanced block designs for the estimation of direct effects and interference effects have also been identified. Besides interference effects, there may arise situations where trend effects may also affect the plots within block. Block models with interference effects from both adjacent neighbouring units and from neighbouring units up to distance 2 incorporating trend component have been studied. The information matrices for estimating direct as well as interference effects incorporating trend component along with the conditions for a block design with interference effects to be trend free have been derived. Series of totally balanced trend free designs have been obtained. Further, there may be situations where effects are no longer additive instead direct effects may interact with interference effects. Experimental setup for block designs with interference effects from neighbouring units on both sides under non-additive interference model has been discussed. Strongly balanced block designs with interference effects from immediate neighbouring units have been identified to be universally optimal for separate estimation of direct effects and interference effects (left and right) of treatments under the non-additive model. Considering one-sided interference effects, under block design setup left interference × direct effects non-additivity and direct effects × block effects non-additivity have also been explored. Under these situations optimality aspects have also been studied.
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Keywords
research methods, land resources, additives, animal products, application methods, biological phenomena, diseases, field experimentation, wells, sets