Tests for how similar two data sets are, by measuring the largest distance between the two functions. The IDL function, kstwo, works by inputting two data sets and outputting the K-S statistic "D" and the corresponding "prob". If prob is small, the tests are likely not from the same origin. I ran this test on my data and a couple sets of random data, and taking the mean and standard deviation of numerous trials for comparison. I got the kinds of results I was expecting between the random sets, but got two differing results on the GOODS stars when I included my whole star catalog versus limiting it to the 27th magnitude.
GOODS-N to 27th mag vs. Random 1 (Normalized*, 1 set vs 9 sets)
*The first time I ran it, I hadn't yet normalized them, so the sets had varying total populations, and resulted in even higher values of d and lower probabilities.
GOODS-N to 28th mag vs. Random 1 (Normalized, 1 set vs 9 sets)
GOODS-S to 27th mag vs. Random 1 (Normalized, 1 set vs 9 sets)
GOODS-S to 28th mag vs. Random 1 (Normalized, 1 set vs 9 sets)
Random 2 vs. Random 3 (1 set vs 9 sets)
Random 2 vs. Random 3 (9 sets vs 9 sets)
Random 4 vs. Random 5 (100 sets vs 100 sets)
I'm more comfortable going with the statistics done on the GOODS data to the 27th magnitude, since in my work before eliminating the dimmest data points gave me a more stellar sample. This means their likenesses to randomness are lowered. The South field I think is still well within range to call "close to random" at about 84%, given the averages and standard deviations where the sets are known to be random. The North field I can't say quite as confidently, at almost 70%, but it lies at the edge of what I'd call random.