Clarification on the calculation of the 90% confidence ellipsis
Pierre-Marie GAGEY, Dmitri SKVORTSOV & Maurice OUAKNINE
The actual President of the ISPGR (2010), B Bloem, having decided to mandate a Committee of Standardization for clinical stabilometry (the first Committee having given up in 1983, during the Houston [Tx] Congress), it seems important that we use the same way to calculate the area of a confidence ellipsis containing 90% of the sampled positions of the pressure center.
To prepare this work, Dmitri SKVORTSOV, Maurice OUAKNINE and myself compared our algorithms for calculating the area of a confidence ellipsis containing 90% of the sampled positions of the center of pressure and we perceived that these calculations were identical to determine the axes of the ellipsis, and to determine the standard-deviation of the projection of the cloud of points on each of these axes. BUT, from this point and to determine the radius of each of the axes of the confidence ellpse containing 90% of the sampled positions of the center of pressure, our statistical solutions were completely different.
An experimental program of verification of the number of positions of the center of pressurer that are effectively inside the theoretically determined ellipsis by each of these three algorithms showed that not only these three algorithms didn't give the same value of the area of the 90% confidence elllipse, but also that the number of positions of the center of pressure situated inside the ellipsis varied according to the algorithms.
As none of us are great specialists in statistics, I referred to a professor of mathematics in an unit teaching and searching in statistics; he had the extreme kindness to write for us a text on the solution of this statistical problem:
by Brieuc CONAN-GUEZ
May 21, 2010
The conclusion of this survey is clear:
"The radius of each axis is given by 2.14 times the standard-deviation of the projection on the axis."
Thanks to MM Th Fahmy et J Jaeger, authors of the XLSTAT® statistical program who helped me to read papers on Bivariate Normal Distribution and Error Ellipses