Multi-Aspect Procedures for Paired Data with Application to Biometric Morphing

As is common in case-control studies, treatments have an influence not only on mean values, but also on variance or distributional aspects. That is why several statistics, each one suitable for a specific aspect, are usually assessed (Salmaso and Solari, 2005). According to Farkas (1947, p. 185), different tests of significance are appropriate to test different features of the same null hypothesis (Lehmann, 1993), thus leading to the Multi-Aspect (MA) testing issue (Pesarin and Salmaso, 2010). When dealing with paired data, usually inferences concern differences between the means. However, there are some circumstances in which it is of interest to test for differences between the variances (McCulloch, 1987). Here, we present a nonparametric permutation solution to this problem. Our goal is to develop MA techniques for paired data, thus finding powerful tests, such that both differences in mean and in variance are separately identified. The inferential procedures proposed in the paper and assessed throughout a simulation study are then applied to a real case study in rhinoseptoplasty surgery.