Distributions of the median p-values for an HVS observed sample that crossed a spherical DM halo. Panel a: distributions of the median p-values, p_med (in logarithmic scale), obtained from the KS test comparison of the HVS observed sample generated in a spherical halo against each of the n_s = 8 ensembles of mock HVS samples generated in a DM halo with different shapes. Each distribution is the result of the KS test comparison of the ’s of the n = n_t observed samples against the n_t = 5000 mock samples generated in a DM halo with different shapes, as listed in the panel. Panel b: enlargement of the rightmost portion of panel a, with the p_med axis in linear scale. The yellow and pink distributions are the only distributions with non-null overlap with the gray distribution. The different shape of the distributions in panels a and b is due to the different size of the histogram bins in the logarithmic and linear scales.