Simulations containing randomly distributed green and magenta points are used to identify the sources of error typically found in cross-correlations tabulated from images acquired using super-resolution localization microscopy. Here, labeled molecules are distributed randomly as shown in (a). When the localization precision (30 nm) is on the order of the pixel size (25 nm), then it acts to blur the image of molecular centers (b). The smooth blurred image represents a fully sampled PSF. In real localization microscopy images, single labeled molecules are typically localized multiple times, but not often enough to fully sample the super-resolved PSF. Instead the distribution represented by the blurred image is under-sampled. The smooth shape of the PSF is still evident when each PSF is sampled many times (c), but images appear more pixelated as this sampling is reduced (d). All of these factors impact the statistics of measured correlation functions. For all conditions indicated, the top panel shows a representative simulation snapshot for the condition indicated (scale-bar = 500 nm) and the two dimensional cross-correlation, C(r, θ), tabulated from this representative image. The next lower panel shows C(r, <θ>) obtained by averaging C(r, θ) over angles (red squares), as well as <C(r)>, the correlation function obtained by averaging over 100 simulation replicates (black circles). Error bars on these curves are either determined from the angular average as described in the main text (red squares, dC(r, <θ>)), or by taking the SEM over 100 simulation replicates to obtain d<C(r)> (black circles). The bottom panels show how the square root of the variance (dC(r)) depends on radius for the conditions indicated. Black circular points show (d<C(r)>). Red squares show the dC(r, <θ>) error averaged over the 100 replicates <dC(r, <θ>)>. The dC1(r) and dC2(r) points are corrections to dC(r, <θ>) and are calculated as described in Methods. (a) dC(r, <θ>) is a good estimate of d<C(r)> in simulations where the localization precision is much less than the pixel size and when there is good sampling of the super-resolved PSF. (b) dC(r, <θ>) under-estimates d<C(r)> when labeled objects are detected with 30 nm localization precision but when these super-resolved PSFs are fully sampled. This under-estimate can be corrected using the dC1(r) described in Equation 2 of Methods. (c) dC1(r) is sufficient when labeled objects have 30 nm resolution and their super-resolved PSF is well sampled. (d) An additional correction is needed when the super-resolved PSF is not well sampled, as described by dC2(r) in Equation 3 of Methods.