The theoretical prediction that trigonometric parallaxes suffer from a statistical effect, has become topical again now that the results of the Hipparcos satellite have become available. This statistical effect, the so-called Lutz-Kelker bias, causes measured parallaxes to be too large. This has the implication that inferred distances, and hence inferred luminosities are too small. Published analytic calculations of the Lutz-Kelker bias indicate that the inferred luminosity of an object is, on average, 30% too small when the error in the parallax is only 17.5%. Yet, this bias has never been determined empirically. In this paper we investigate whether there is such a bias by comparing the best Hipparcos parallaxes which ground-based measurements. We find that there is indeed a large bias affecting parallaxes, with an average and scatter comparable to predictions. We propose a simple method to correct for the LK bias, and apply it successfully to a sub-sample of our stars. We then analyze the sample of 26 `best Cepheids used by Feast & Catchpole (1997) to derive the zero-point of the fundamental mode pulsators and leads to a distance modulus to the Large Magellanic Cloud - based on Cepheid parallaxes- of 18.56 +/- 0.08, consistent with previous estimates.
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