We illustrate how we estimate the completeness limit with the help of the Kolmogorov-Smirnov test. Left column: empirical (shown in blue) and analytical (shown in orange) CDFs. Right column: p value from the Kolmogorov-Smirnov test as a function of probed distance limit. The dashed line indicates the p = 0.05 threshold. Values below the threshold indicate that the empirical and analytical CDFs are significantly different, which means that the spatial distribution of objects in the subsample is not uniform anymore. Thus, the subsample cannot be regarded as statistically complete beyond the completeness radius. Two magnitude ranges are shown here as an example. The dashed line in the lower left panel denotes the re-normalised CDF using the derived completeness limit for this magnitude bin.