CI2 for creating and comparing confidence-intervals for time-series bivariate plots

Area of Science:

• Biomechanics
• Data Analysis
• Kinesiology

Background:

• Calculating and comparing confidence intervals (CI) for bivariate time-series plots is currently not feasible.
• Existing methods lack the ability to quantify variability and identify differences in complex time-series data.

Purpose of the Study:

• To develop a novel method, termed CI2, for calculating and comparing confidence intervals on bivariate time-series plots.
• To assess the overlap of confidence intervals between two bivariate time-series to identify differences.
• To analyze running gait data from different treadmill types using the developed CI2 method.

Main Methods:

• The CI2 method calculates 95% confidence-ellipses at each time-point for bivariate data.
• Confidence intervals are determined by points on ellipses perpendicular to the direction vector between adjacent time-point means.
• Consecutive CIs form convex quadrilaterals; overlap analysis with cross-correlation time-lag identifies significant differences.

Main Results:

• CI2 detected no significant group differences between left and right legs on either treadmill.
• Analysis revealed differences in knee extension for the same legs between the standard and curved treadmills, specifically less extension before heel-strike on the curved treadmill.
• The study recommends standardizing CI2 by removing outliers, using 95% confidence-ellipses, and scaling by the Chi-square value.

Conclusions:

• CI2 offers an effective method for quantifying confidence intervals in bivariate plots.
• The method successfully explores differences between two bivariate time-series, as demonstrated in the running gait analysis.
• Provided Matlab code facilitates practical application, standardization, and future development of CI2.