  By collecting distances from the literature, a set of 73 planetary nebulae
with mean distances of high accuracy is derived. This sample is used for
recalibration of the mass-radius relationship, used by many statistical
distance methods. An attempt to correct for a statistical peculiarity, where
errors in the distances influences the mass--radius relationship by increasing
its slope, has been made for the first time. Distances to PNe in the Galactic
Bulge, derived by this new method as well as other statistical methods from the
last decade, are then used for the evaluation of these methods as distance
indicators. In order of achieving a Bulge sample that is free from outliers we
derive new criteria for Bulge membership. These criteria are much more
stringent than those used hitherto, in the sense that they also discriminate
against background objects. By splitting our Bulge sample in two, one with
optically thick (small) PNe and one with optically thin (large) PNe, we find
that our calibration is of higher accuracy than most other calibrations.
Differences between the two subsamples, we believe, are due to the
incompleteness of the Bulge sample, as well as the dominance of optical
diameters in the ``thin'' sample and radio diameters in the ``thick'' sample.
  Our final conclusion is that statistical methods give distances that are at
least as accurate as the ones obtained from many individual methods. Also, the
`long' distance scale of Galactic PNe is confirmed.
