  In this work we study white dwarfs where $30\,000\,\text{K} {>}
\mathrm{T}_{\rm{eff}} {>} 5\,000\,\text{K}$ to compare the differences in the
cooling of DAs and non-DAs and their formation channels. Our final sample is
composed by nearly $13\,000$ DAs and more than $3\,000$ non-DAs that are
simultaneously in the SDSS DR12 spectroscopic database and in the \textit{Gaia}
survey DR2. We present the mass distribution for DAs, DBs and DCs, where it is
found that the DCs are ${\sim}0.15\,\mathrm{M}_\odot$ more massive than DAs and
DBs on average. Also we present the photometric effective temperature
distribution for each spectral type and the distance distribution for DAs and
non-DAs. In addition, we study the ratio of non-DAs to DAs as a function of
effective temperature. We find that this ratio is around ${\sim}0.075$ for
effective temperature above ${\sim}22\,000\,\text{K}$ and increases by a factor
of five for effective temperature cooler than $15\,000\,\text{K}$. If we assume
that the increase of non-DA stars between ${\sim}22\,000\,\text{K}$ to
${\sim}15\,000\,\text{K}$ is due to convective dilution, $14{\pm}3$ per cent of
the DAs should turn into non-DAs to explain the observed ratio. Our
determination of the mass distribution of DCs also agrees with the theory that
convective dilution and mixing are more likely to occur in massive white
dwarfs, which supports evolutionary models and observations suggesting that
higher mass white dwarfs have thinner hydrogen layers.
