Applying circular statistics can cause artefacts in the calculation of vector coding variability: A bivariate solution.

Background: Coordination variability is thought to provide meaningful insights into motor learning, skill level and injury prevention. Current analytical techniques, based on vector coding (VC) methods, use calculations from circular statistics. However a statistical artefact associated with the application of circular statistics may artificially increase the estimated coordination variability, especially when VC vectors are short.

Research Question: Are two popular methods for calculating vector coding coordination variability susceptible to contamination by statistical artefacts and if so, how can coordination variability be calculated without statistical artefact?

Methods: A combination of simulated and experimental data was used to prove the existence of the statistical artefact and to understand the extent to which it may affect experimental running gait data, respectively. An alternative approach that uses ellipse area as a bivariate measure of variability was proposed, applied to the same dataset, and compared to two popular methods of coordination variability analysis.

Results: The simulated data showed the existence of a statistical artefact, which was greater for shorter VC vector lengths in coordination variability measures that used circular statistics. The statistical artefact typically manifests itself as inflated peaks in the coordination variability trace. The experimental data also indicated that short vector lengths are prevalent in running gait. The Ellipse Area Method of coordination variability was not affected by the VC vector length.

Significance: Researchers using current VC variability measures should be particularly aware of the possible effect of the statistical artefact on their data, which is most likely to occur when vector lengths are short. The novel approach we have suggested for calculating VC coordination variability may provide the foundation for future research into vector coding coordination variability.