Treatment Designs to Estimate Optimum Plant Density for Maximum Corn Grain Yield1

Abstract

AbstractUse of an exponential regression model relating corn (Zea mays L.) grain yield to plant density allows estimation of the optimum density for producing maximum yield. The experimenter's choice of treatment design (i.e. the particular plant densities included in an experiment) has an important influence on the precision of the estimated optimum density. The best treatment designs provide the greatest precision with a given number of replications, or, alternatively, provide a given level of precision with the smallest number of replications.Expression of yield as a proportion of maximum yield and plant densities as proportions of the optimum density greatly simplifies the evaluation of treatment designs with respect to their ability to provide precise estimates of the optimum density. A total of 375 three, four, and five density treatment designs were evaluated on the dimensionless proportional scale in order to determine those which provide the greatest precision. Maximum allowable relative errors for the best three, four, and five density treatment designs are reported for each of 15 combinations of minimum and maximum densities expressed on a proportional scale. The best treatment designs contain unequally incremented densities and provide considerably more precise estimates of the optimum density than do designs with equally incremented densities.