  We analyze the conditions under which a statistical error analysis can be
carried out in the case of $\pi\pi$ scattering, namely the normality of
residuals in the conventional $\chi^2$-fit method. Here we check that the
current and benchmarking analyses only present very small violations of the
normality requirements. In particular, we show how it is possible to amend
slightly the selection of the experimental data, and improve the normality of
residuals.
  As an example, we discuss the $0^{++}$ channel and the implications for the
$f_0(500)$ and $f_0(980)$ resonances, obtaining that the new selection of data
provides very similar and compatible results. In addition, the effect on the
$f_0(500)$ and $f_0(980)$ resonance pole parameters is almost negligible, which
reinforces the central results and the uncertainty analysis performed in these
benchmarking determinations.
