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.
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