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

We present a detailed description 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 for them. We quantify the accuracy of our corrections using an ensemble of 50 mock galaxy surveys generated with the GalICS semi-analytic model of galaxy formation which incorporate the selection biases and tiling strategy of the real data. We demonstrate that we are able to recover the real-space two-point correlation function xi(s) and the projected correlation function w(p)(r(p)) to an accuracy better than 10% on scales larger than 1 h(-1) Mpc with the sampling strategy used for the first epoch VVDS data. The large number of simulated surveys allows us to provide a reliable estimate of the cosmic variance on the measurements of the correlation length r(0) at z similar to 1, of about 15 - 20% for the first epoch VVDS observation while any residual systematic effect in the measurements of r(0) is always below 5%. The error estimation and measurement techniques outlined in this paper are being used in several parallel studies which investigate in detail the clustering properties of galaxies in the VVDS.