An adequate design for regression analysis of yield trials

Abstract

Based on theoretical demonstrations and illustrated with a numerical example from triticale yield trials in Portugal, the Completely Randomized Design is proposed as the one suited for Regression Analysis. When trials are designed in Complete Randomized Blocks the regression of plot production on block mean instead of the regression of cultivar mean on the overall mean of the trial is proposed as the correct procedure for regression analysis. These proposed procedures, in addition to providing a better agreement with the assumptions for regression and the philosophy of the method, induce narrower confidence intervals and attenuation of the hyperbolic effect. The increase in precision is brought about by both a decrease in the t Student values by an increased number of degrees of freedom, and by a decrease in standard error by a non proportional increase of residual variance and non proportional increase of the sum of squares of the assumed independent variable. The new procedures seem to be promising for a better understanding of the mechanism of specific instability.