We derive Bayesian distances for all stars in the radial velocity sample of Gaia DR2, and use the statistical method of Schönrich, Binney & Asplund to validate the distances and test the Gaia parallaxes. In contrast to other methods, which rely on special sources, our method directly tests the distances to all stars in our sample. We find clear evidence for a near-linear trend of distance bias f with distance s, proving a parallax offset δp. On average, we find ${\delta _{\rm p}}= -0.054 \, {\rm mas}$ (parallaxes in Gaia DR2 need to be increased) when accounting for the parallax uncertainty underestimate in the Gaia set (compared to ${\delta _{\rm p}}= -0.048 \, {\rm mas}$ on the raw parallax errors), with negligible formal error and a systematic uncertainty of about $0.006 \, {\rm mas}$. The value is in concordance with results from asteroseismic measurements, but differs from the much lower bias found on quasar samples. We further use our method to compile a comprehensive set of quality cuts in colour, apparent magnitude, and astrometric parameters. Lastly, we find that for this sample δp appears to strongly depend on σp (when including the additional $0.043 \, {\rm mas}$) with a statistical confidence far in excess of 10σ and a proportionality factor close to 1, though the dependence varies somewhat with σp. Correcting for the σp dependence also resolves otherwise unexplained correlations of the offset with the number of observation periods ${n_{\rm vis}}$ and ecliptic latitude. Every study using Gaia DR2 parallaxes/distances should investigate the sensitivity of its results on the parallax biases described here and – for fainter samples – in the DR2 astrometry paper.