Two-stage Inference in Experimental Design Using Dea: an Application to Intercropping and Evidence from Randomization Theory

In this article we propose the use of Data Envelopment Analysis (DEA) measures of efficiency, under constant returns to scale and input equal to unity, in the analysis of multidimensional nonnegative responses in the design of experiments. The approach agrees with the standard Analysis of Variance (Covariance) for univariate responses and simplifies the statistical analysis in the multivariate case. The best treatments provided by the analysis optimize a combined output defined by shadow prices, which are the solutions of the DEA problem. The approach is particularly useful for the analysis of intercropping (crop mixtures) experiments. In this context we discuss two examples. To properly address the issue of correlation and non-normality of DEA measurements in different experimental plots we validate the results via Randomization Theory.