Ellipse area calculations and their applicability in posturography

- We clarify the difference between univariate confidence and prediction intervals.
- We extend this to the bivariate case of confidence and prediction ellipses.
- We derive formulas to calculate the areas of both ellipses.
- Confidence ellipses are inappropriate for COP scatter evaluation.
- The prediction ellipse area is the more appropriate measure for COP scatter.

The quantification of postural sway is considered to be an essential part of posturography and is important for research and clinical utility. A widely used method to calculate the scatter of center of pressure data is an ellipse that encloses about 100(1 − α)% of the observations. However, underlying definitions and terminologies have been misused in many cases. Hence, outcomes of different studies are proved to be incommensurable. In order to attain inter-study comparability, standardization of calculation methods has to be advanced. This work features a comprehensive and consistent overview of the methods for elliptic area approximation contrasting general principles of confidence and prediction regions. As a result, we recommend the usage of the prediction ellipse, as far as we demonstrate that confidence ellipses emerge to be inappropriate for posturographic scatter evaluation. Furthermore, we point at problems that come along with different sample sizes.