The theoretical prediction that trigonometric parallaxes suffer from a
statistical effect has become topical again now that the results of t
he Hipparcos satellite have become available. This statistical effect,
the so-called Lutz-Kelker bias, causes observed parallaxes to be too
large. This has the implication that inferred distances, and hence inf
erred luminosities are too small. Published analytic calculations of t
he Lutz-Kelker bias indicate that the inferred luminosity of an object
is, on average, 30 per cent too small when the error in the parallax
is only 17.5 per cent. Yet, this bias has never been determined empiri
cally. In this paper we investigate whether there is such a bias by co
mparing ground-based measurements with the best Hipparcos parallaxes.
We find that there is indeed a large bias with an average and scatter
comparable to predictions. We propose a simple method to correct for t
he LK bias, and apply it successfully to a subsample of our stars. We
then analyse the sample of the 26 'best' Cepheids used by Feast & Catc
hpole to derive the zero-point of the period-luminosity relation. The
final result is based on the 20 fundamental mode pulsators and leads t
o a distance modulus to the Large Magellanic Cloud - based on Cepheid
parallaxes - of 18.56 +/- 0.08, consistent with previous estimates.