The VIMOS VLT Deep Survey: Computing the two point correlation statistics and associated uncertainties

We are presenting in this paper a detailed account of the methods used to compute the three-dimensional two-point galaxy correlation function in the VIMOS-VLT deep survey (VVDS). We investigate how instrumental selection effects and observational biases affect the measurements and identify the methods to correct them. We quantify the accuracy of our correction method using an ensemble of fifty mock galaxy surveys generated with the GalICS semi-analytic model of galaxy formation which incorporate the same selection biases and tiling strategy as the real data does. We demonstrate that we are able to recover the real-space two-point correlation function xi(s) to an accuracy better than 10% on scales larger than 1 h^{-1} Mpc, and of about 30% on scales below 1 h^{-1} Mpc, with the sampling strategy used for the first epoch VVDS data. The projected correlation function w_p(r_p) is recovered with an accuracy better than 10% on all scales 0.1 <= r <= 10 h^{-1} Mpc. There is a tendency for a small but systematic under-estimate of the correlation length derived from w_p(r_p) of 6% on average, remaining after our correction process. The large number of simulated surveys allows us to provide a reliable estimate of the cosmic error on the measurements of the correlation length r_0, of about 15-20% for the first epoch VVDS observation (Le Fevre et al.2004, astro-ph/0409133). The error estimation and measurement techniques outlined in this paper are being used in several studies which investigate in detail the clustering properties of galaxies in the VVDS data.