  By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN
Ia) compilation, we compare two different approaches (traditional \chi^2 and
complete likelihood) to determine parameter constraints when the magnitude
dispersion is to be estimated as well. We consider cosmological constant + Cold
Dark Matter (\Lambda CDM) and spatially flat, constant w Dark Energy + Cold
Dark Matter (FwCDM) cosmological models and show that, for current data, there
is a small difference in the best fit values and $\sim$ 30% difference in
confidence contour areas in case the MLCS2k2 light-curve fitter is adopted. For
the SALT2 light-curve fitter the differences are less significant ($\lesssim$
13% difference in areas). In both cases the likelihood approach gives more
restrictive constraints. We argue for the importance of using the complete
likelihood instead of the \chi^2 approach when dealing with parameters in the
expression for the variance.
