Performing ANOVA Through Linear Programming Models: An Application in Intercroppping Experiment

Abstract

Classical Analysis of variance (acronym, ANOVA) models are popularly used by agricultural and allied scientists to determine the significant difference among treatments or group of treatments. However, linear programming (LP) model through Data Envelopment Analysis (DEA ) theory utilizes economy return to scale to optimize and allocation its input resources in an efficient manner. The DEA approach agrees with the former (standard ANOVA) for univariate responses and simplifies the statistical analysis in the case of multivariate response. The approach is particularly useful for the analysis of intercropping (crop mixture) experiments. This paper describes the Data Envelopment Analysis (DEA )model and computes the efficiency coefficients, which were used to carry out standard analysis of variance and it was found out that the approach resulted into the same decision as in the classical ANOVA ,with even a smaller mean square error. The approach was illustrated using commonly designed experiments (Randomized Complete Block Design (RCBD) ) with an example in intercropping experiment.