in the areas ranged from 13% to 14%, while the SNLS data showed the greater discrepancies, reaching up to $\sim$53%.

Conclusion {#sec:conclusions}
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In this work we considered the SDSS first year compilation and compared two different approaches (traditional $\chi^2$ and likelihood) to determine constraints from SN Ia processed by two of the most used light curve fitters in the literature, the MLCS2k2 and the SALT2. The MLCS2k2 gives a cosmology-independent estimation of the distance modulus for each SN Ia, with its corresponding variance, which can be directly compared with the model prediction for this quantity. The SALT2 is not a distance estimator, consequently, we can only have an estimate of the distance modulus depending on parameters to be obtained simultaneously with the cosmological ones. Furthermore, in the SNe Ia analysis, it is common to introduce a residual, unknown, contribution $\sigma_\text{int}$ to the variance which, in the traditional approach, is determined by imposing that the reduced $\chi^2$ be unity, when considering the full sample, in the SALT2 case, or only nearby SNe Ia, in the MLCS2k2 case.

By comparing the results obtained from the traditional $\chi^2$ approach with the likelihood ones, we showed that, for current data and chosen cosmological 