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For many cropping situations, especially in developing countries, quadratic surfaces do not fit the responses of certain crops to fertilizer. Use of the second order designs with standard statistical and economic interpretive techniques may result in costly biases in the estimates of the optimal fertilizer rate. Also, there is a potential pollution problem. A family of linear-plateau models, consisting of intersecting straight lines, is proposed for fitting fertilizer response data which exhibit a plateau effect. The regression coefficients are easily computed using a desk calculator or computer, and the economic interpretations are simple. Techniques for fitting, parameter estimation, and economic interpretation are described. For multi-nutrient experiments, a complete factorial experiment with a number of levels of each nutrient is considered to be the best design for both evaluating the model and then estimating the optimal nutrient levels. Preliminary information may provide a basis for deciding which fertilizer nutrients are apt to produce response. In many soil-crop situations, only NP or N experiments are required, because the other nutrients are already at adequate levels; hence, the amount of experimental material may be redistributed by having fewer factors, but more levels of each factor studied. Two currently used fertilizer response designs, based on preliminary information on optimal nutrient levels, are described; a one-factor-at-a-time design has the disadvantage of providing no estimate of interaction. Several other designs are suggested. We recommend concentrating several treatment levels in the vicinity of the anticipated optimum. Since the sloping phase of the response pattern is more important than the plateau phase, it should receive more attention when distributing treatment levels.
Biometrics is a scientific journal emphasizing the role of statistics and mathematics in the biological sciences. Its object is to promote and extend the use of mathematical and statistical methods in pure and applied biological sciences by describing developments in these methods and their applications in a form readily assimilable by experimental scientists. JSTOR provides a digital archive of the print version of Biometrics. The electronic version of Biometrics is available at http://www.blackwell-synergy.com/servlet/useragent?func=showIssues&code;=biom. Authorized users may be able to access the full text articles at this site.
The International Biometric Society is an international society for the advancement of biological science through the development of quantitative theories and the application, development and dissemination of effective mathematical and statistical techniques. The Society welcomes as members biologists, mathematicians, statisticians, and others interested in applying similar techniques.
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