Using directional statistics to test hypotheses regarding rigid body attitude: Comparison to univariate and multivariate Cardan angle tests

Rigid body attitude and single-joint kinematics are typically expressed using three Cardan angles which represent rotations in anatomical planes. It was recently shown in the Biomechanics literature that Cardan angles inaccurately estimate true mean attitude due to an important mathematical inadequacy: attitude under-representation; at least four quantities are needed to unambiguously specify attitude. Directional statistics, which is the multivariate generalization of (univariate) circular statistics, solves this problem using four-dimensional unit vectors and the mathematics of hyperspherical geometry. The purpose of this study was to compare the results of directional analysis to the results of uni- and multi-variate Cardan analysis for representative joint kinematic data during gait. We analyzed hip, knee and pelvis data from three open datasets and report exemplary results for knee kinematics in v-cut vs. side shuffle tasks. We also conducted Monte Carlo simulations, using synthetic data with precisely controlled true angular effects, to systematically compare directional and Cardan analyses. Results show that directional analysis yielded considerably smaller p values (p<0.03) than Cardan analysis (p>0.055) for the exemplary dataset. Simulation results confirmed that directional analysis is considerably more powerful (i.e., much more able to detect true angular effects) than both uni- and multi-variate Cardan analysis. These results suggest that directional statistics should be used to analyse attitude, including 3D joint kinematics, to avoid false negatives.

Files

Metadata

Work Title Using directional statistics to test hypotheses regarding rigid body attitude: Comparison to univariate and multivariate Cardan angle tests
Access
Open Access
Creators
  1. Todd C. Pataky
  2. John H. Challis
Keyword
  1. Biomechanics
  2. Kinematics
  3. Joint angles
  4. Three dimensional orientation
  5. Human movement
License In Copyright (Rights Reserved)
Work Type Article
Publisher
  1. Journal of Biomechanics
Publication Date August 25, 2020
Publisher Identifier (DOI)
  1. https://doi.org/10.1016/j.jbiomech.2020.109976
Deposited August 01, 2022

Versions

Analytics

Collections

This resource is currently not in any collection.

Work History

Version 1
published

  • Created
  • Added Challis_DirectionalStatistics_JournalOfBiomechanics.pdf
  • Added Creator Todd C. Pataky
  • Added Creator John H. Challis
  • Published
  • Updated Keyword, Publication Date Show Changes
    Keyword
    • Biomechanics, Kinematics, Joint angles, Three dimensional orientation, Human movement
    Publication Date
    • 2020-10-09
    • 2020-08-25
  • Updated