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Multi-aspect procedures for paired data with application to biometric morphing. (English) Zbl 1284.62272

Summary: 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 [L. Salmaso and A. Solari, Metrika 62, No. 2–3, 331–340 (2005; Zbl 1078.62043)]. According to R. A. Fisher [The design of experiments. 4th ed. New York: Hafner Press (1947), p. 185], different tests of significance are appropriate to test different features of the same null hypothesis [E. L. Lehmann, J. Am. Stat. Assoc. 88, No. 424, 1242–1249 (1993; Zbl 0805.62023)], thus leading to the multi-aspect (MA) testing issue [F. Pesarin and L. Salmaso, Permutation tests for complex data: theory, applications and software. Chichester, New York: Wiley (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 [C. E. McCulloch, Commun. Stat., Theory Methods 16, 1377–1391 (1987; Zbl 0615.62039)].
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.

MSC:

62G09 Nonparametric statistical resampling methods
62H15 Hypothesis testing in multivariate analysis
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