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

Abstract

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.

Keywords:

• Combination-based permutation test
• Finite-sample consistency
• Multi-aspect procedure
• Shape analysis

Mathematics Subject Classification:

• 62G09
• 62H15

Acknowledgments

The authors wish to thank the University of Padova (CPDA088513/08) for providing the financial support for this research. The authors also wish to thank the anonymous referees for valuable comments and suggestions which led to an improved version of this article.