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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. Neste artigo é proposto o uso de medidas de eficiência DEA, com retornos constantes à escala e input unitário, na análise de respostas multidimensionais não negativas de ensaios experimentais. A abordagem proposta concorda com a Análise de Variância (Covariância) clássica para respostas unidimensionais e simplifica a análise estatística para o caso multidimensional. Os melhores tratamentos indicados pela análise otimizam um output combinado, definido por preços sombra, que são as soluções dos problemas lineares de DEA. A abordagem é particularmente útil na análise de experimentos consorciados (plantio simultâneo de mais de uma cultura agrícola). São aqui discutidos dois exemplos. Os resultados são validados via Teoria de Aleatorização, de modo a estudar apropriadamente as questões de correlação e não-normalidade das medidas DEA nas diferentes parcelas experimentais

Two-stage inference in experimental design using dea: an application to intercropping and evidence from randomization theory