A New Approach to Rank Several Multivariate Normal Populations with Application to Life Cycle Assessment

The need to establish the relative superiority of each treatment when compared to 10 all the others, i.e., ordering the underlying populations according to some pre-specified 11 criteria, often occurs in many applied research studies and technical/business problems. 12 When populations are multivariate in nature, the problem may become quite difficult 13 to deal with especially in case of small sample sizes or unreplicated designs. The 14 purpose of this work is to propose a new approach for the problem of ranking several 15 multivariate normal populations. It will be theoretically argued and numerically proved 16 that our method controls the risk of false ranking classification under the hypothesis of 17 population homogeneity while under the nonhomogeneity alternatives we expect that 18 the true rank can be estimated with satisfactory accuracy, especially for the “best” 19 populations. Our simulation study proved also that the method is robust in the case of 20 moderate deviations from multivariate normality. Finally, an application to a real case 21 study in the field of life cycle assessment is proposed to highlight the practical relevance 22 of the proposed methodology.