[@Vishwakarma2010]). In [@Kim2011] a likelihood approach to simulated data for the distance moduli was used, and the focus was on the determination of the intrinsic dispersion, without reference to a particular light-curve fitter. In our work, by using real-data, the problem is reconsidered in the context of the MLCS2K2 and SALT2 light-curve fitters. In particular, we point out that, in principle, with SALT2 additional difficulties could arise due to the astrophysical parameters. We compare the results of the traditional $\chi^2$ treatment to the likelihood one. We restrict ourselves to SNe Ia datasets only, without taking into account other important sources of information (such as CMB, BAOs or clusters) in order to make our point pristine, by avoiding the masking due to any other such probes.

The structure of the paper is as follows. In Section \[sec:light\_curve\_fitting\], we briefly remind the general procedure to go from the raw data to the final estimated parameters. In Section \[sec:least\_squares\], we describe the two most widely used “fitter pipelines” (MLCS2k2 and SALT2), which use the traditional $\chi^2$ approach. In Section \[sec:likelihood\], we critically review the aforementioned traditional approach and present the likelihood-based one. In Section \[sec:results\], the main numerical results are shown, for both 