A Risk Assessment-Risk Management Approach to Selecting Fertilizer Application Rates

Abstract

In many areas of applied or extension-related research there is increasing interest in using statistical significance levels which achieve better balance among the several types of statistical errors than is obtained with traditional choices of significance level. One approach to doing this involves risk assessment, in which the relative seriousness of statistical errors is determined and the risks associated with them are quantified, and risk management, in which the criterion is to select as optimal that significance level which minimizes the weighted average risk. In this paper, the risk assessmentrisk management approach is applied in a somewhat different, but related, context; i.e., in the selection of optimal fertilizer application rates. The procedure is presented and applied to total season hay yields from an experiment involving six rates (0, 100, 200, 300, 400, and 500 lb K/acre) of fall-applied fertilizer on established alfalfa (Medicago sativa L.). Based on a curvilinear regression model, the fertilizer application rate which produced the agronomic maximum yield was estimated to be 412 lb K/acre. For an individual farmer the optimal application rate is generally less, depending on the relative prices of fertilizer and hay and the relative seriousness of statistical errors. An individual farmer's assessment of the latter is influenced by his financial condition, ability to bear risk, attitude towards risk, scale of operations, and other factors. Specific values of optimal application rates obtained in this study are, of course, valid only for those situations in which the particular curvilinear regression model is appropriate, but the risk assessment-risk management approach that is presented is generally applicable to other response models for other situations.