Experimental design and response surface analysis of pesticide trials

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Abstract
The search for combinations of pesticides or herbicides which have a synergistic effect is an important area of study and one which presents challenges for the statistician as well as for the experimenter. The aim is to find and to describe the interaction between a number of quantitative factors, and having done so to determine a combination which is economically optimal for a given level of control. The present paper discusses the role of a family of response functions called Inverse Polynomials to describe such phenomena. Examples are given of such functions and it is shown how it is possible to fit these functions to data and to plot the results on a routine basis. The importance of the experimental design for the estimation of such nonlinear regression models is investigated, and examples are given of experimental designs which are ‘optimal’ with respect to particular aims of the experimenter.