Field experimentation on rough land: the method of Papadakis reconsidered

Abstract

Much of the error in field experiments comes from environmental differences, which traditional methods (e.g. blocks or rows and columns) sometimes fail to control, especially if the fertility pattern is complex or unexpected. In 1937 Papadakis proposed an alternative approach in which the performance of each plot was judged by that of its neighbours. If a plot was situated in an area of generally high cropping, its own high crop was partly discounted but if surrounding plots were yielding poorly, it was given special weight. Adjustment was by the analysis of covariance. The method has not been much used, partly because it still lacks a mathematical basis and partly because it is suspected of bias in the estimation of contrasts between treatments.It has been studied here by simulation, i.e. bodies of data have been generated on the computer with known characteristics and then analysed by Papadakis's method to see if a correct answer was returned. Also, an improvement in the covariate is suggested and an iterative procedure developed to ensure more consistent results.It emerges that the suspicion of bias was unjustified. Also, the method can be extremely effective in reducing experimental error. In all its variant forms it has difficulty with outside plots, and for that reason is more effective on compact areas than on strips. Also, interference between plots is especially serious, because the neighbours affected are those needed to form the adjusting covariate. Discontinuities arising from past use of the land can cause problems but a method is suggested for minimizing their effect.