Comparison of Circular and Ellipse-Based Methods for Assessing Coordination Variability

Vector coding is a widely adopted technique for analyzing coordination variability, but traditional circular statistics methods with finite difference are sensitive to outliers and artifacts, potentially affecting the accuracy of assessments. To address the limitation, Ellipse-based methods using finite difference or angular velocity have been proposed, but formal statistical comparisons have not been performed. Therefore, this study aimed to (1) assess coordination variability using 3 distinct vector coding methods: circular statistics with finite difference, ellipse-based coding with finite difference, and ellipse-based coding with angular velocity; and (2) examine how each method responds to changes in coordination variability resulting from variations in gait speed. Comparing coordination variability across these methods, the circular statistics method differed from the ellipse methods (ELMs) throughout the gait cycle, while the 2 ELMs showed similar patterns but responded differently to gait speed changes due to input variable differences. Notably, only the ELM with angular velocity consistently detected gait speed-related increases in coordination variability, suggesting caution when comparing findings across studies due to their methodological incompatibility. Furthermore, our findings indicate that the ELM incorporating angular velocity may be the most sensitive for detecting changes in gait speed.