A Permutation Test for Comparing Multiple Measures of Center in Three-Dimensional Rotation Data


Abstract


Data in the form of three-dimensional rotations arise in various fields, yet statistical techniques for modeling such data receive far less focus in the area of directional statistics than circular and spherical data. In this paper, the focus is on comparison of mean or central matrices for multiple groups of three-dimensional rotations. A permutation test is developed by using the fundamental ideas behind a traditional Analysis of Variance and a simulation study is used to investigate the power of the permutation test under various conditions. The test is then used on a biomechanics data set to compare movement around the calcaneocuboid joint for a human, chimpanzee, and baboon.

DOI Code: 10.1285/i20705948v16n3p711

Keywords: Directional data; Three-Dimensional Rotations; Permutation Test; ANOVA; Misorientation Angle; Biomechanics

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