Optimal Design of Field Experiments for Determination of Production Functions
1988
Hendrickx, J. M. H. | Wierenga, P. J. | Urquhart, N. S.
A technique was needed to assess the optimal number and size of experimental plots for detection of the shape of a production function with confidence intervals of specified length. Therefore, an equation was developed to evaluate the optimal number of replications and the optimal plot size for field experiments with structured quantitative treatments. Use of the equation is illustrated with experimental designs for determination of water production functions of trickle irrigated chile peppers (Capsicum annuum L., var. New Mexico no. 6-4). Input variables for the equation are the variance, error degrees of freedom, plot size of a previous experiment, dependency between adjacent experimental plots of a previous experiment expressed in a coefficient b, size of the difference to be detected, assurance with which it is desired to detect the difference, and level of significance to be used in a future experiment. Application of the equation showed that, for detection of small differences, optimization of the plot size becomes important. In our sample experiment we found that a four-fold increase in experimental plot size decreased the total number of plots from 156 to 42, but increased the total experimental area by only 8%.
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