Comments on "Ellipse area calculations and their applicability in posturography" (Schubert and Kirchner, vol.39, pages 518-522, 2014).

Dear Editor: I would like to congratulate the authors for the article regarding the calculation of the so-called ellipse area [1]. As the authors indicated, the algorithms employed to calculate the area of the 95% prediction ellipse using the chi-square or the Rayleigh distribution are in fact only exact when the number of samples of the bivariate variable tends to infinite (when each univariate variable is assumed to have a normal distribution) [2]. As the authors also observed, for a typical data size in posturography, 30 s of data sampled at 100 Hz (3000 samples), this approximation is probably good enough, since the error is only 0.1%. The problem appears when the data size is much less: for 100 samples, the error is 2.5%, and for 10 samples, the error is 26%. These last two cases are unlikely scenarios in posturography, but possible for an unadvised user; and besides, the prediction ellipse area can be employed in any other data analysis. The authors described the calculation (see the supplementary data in [1]) but did not publish any algorithm to compute the exact 95% prediction ellipse area. They only made available the algorithm with the known approximation (i.e., they used the chi-square distribution and not the F distribution for the exact calculation). To fill this lacuna, at the end of this letter it is presented a computer program to calculate the exact 95% prediction ellipse area [2] for a Matlab-like environment software