Comparison of experimental design in a field trial on fertilization of black beans ( Phaseolus vulgaris )

Abstract

A field experiment with black beans (Phaseolus vulgaris L.) was carried out on an alluvial soil in Rio de Janeiro State, with five levels of nitrogen and phosphorus. The results were analysed as a complete factorial 5², and compared with analyses as central composite, central composite plus extremes, small 3 x 3 factorial, and large 3 x 3 factorial. All analyses showed significant linear and quadratic responses to phosphorus except the small 3 x 3 factorial. There was no response to nitrogen fertilizer but rather a tendency of yields to decrease. Phosphorus levels were calculated based on the equations obtained from both elements and also in function of phosphorus only. Economic levels in phosphorus were calculated from to 5 experimental designs, based on fertilizer and bean prices. It was concluded that the traditional complete factorial 5² design can be substituted either by the large 3 x 3 factorial, the central composite plus extremes or the central composite, without loss of precision in conclusions. Using these designs the number of treatments can be reduced to 13 or even 9.