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

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.

三维旋转形式的数据广泛存在于诸多研究领域，但在方向统计（directional statistics）领域中，针对这类数据的建模统计方法受关注程度远低于圆形数据与球面数据。本文聚焦于多组三维旋转数据的均值矩阵（或中心矩阵）比较问题，基于传统方差分析（Analysis of Variance）的核心思想构建置换检验（permutation test）方法，并通过模拟实验探究该置换检验在不同条件下的检验效能。随后将该检验方法应用于一组生物力学数据集，用于比较人类、黑猩猩与狒狒的跟骰关节（calcaneocuboid joint）周围运动差异。