Statistical analysis of galaxy surveys - IV. An objective way to quantify the impact of superstructures on galaxy clustering statistics

For galaxy clustering to provide robust constraints on cosmological parameters and galaxy formation models, it is essential to make reliable estimates of the errors on clustering measurements. We present a new technique, based on a spatial jackknife (JK) resampling, which provides an objective way to estimate errors on clustering statistics. Our approach allows us to set the appropriate size for the JK subsamples. The method also provides a means to assess the impact of individual regions on the measured clustering, and thereby to establish whether or not a given galaxy catalogue is dominated by one or several large structures, preventing it to be considered as a 'fair sample'. We apply this methodology to the two- and three-point correlation functions measured from a volume-limited sample of M* galaxies drawn from Data Release 7 of the Sloan Digital Sky Survey (SDSS). The frequency of JK subsample outliers in the data is shown to be consistent with that seen in large N-body simulations of clustering in the cosmological constant plus cold dark matter cosmology. We also present a comparison of the three-point correlation function in SDSS and Two-degree-Field Galaxy Redshift Survey using this approach and find consistent measurements between the two samples.