I want to compare the delays of packets belonging to some kind of traffic to the delays of packets belonging to some other (different and larger) traffic, all generated from the same machine.
I would like to see if the distributions of the two groups of delays are the same. Samples for the first group are between size 20 and 2 000 (bust most of the time between 20 and 75), while the comparison group is always of the order of a few thousands (up to 15 000).
When the first group has more than 250 values, I just (randomly) subsample it in smaller groups of size 50, since it I noticed that it really takes nothing for large samples to get rejected with Kolmogorov-Smirnov. If the majority of subsamples gets accepted by the test, the original sample also does.
Now, due to the precision of timestamping, there are lots of duplicate delays (i.e. ties) in my observations. For instance, out of 15000 delays in my second group, I have only 1000 unique values, with a mean of 0.7 milliseconds and a standard deviation of around 7 milliseconds. 200 values appear up to 10 times; 90 values between 11 and 100; 30 between 101 and 300; 4 between 301 and 500.
What should I take into account in order to choose a non-parametric test that best suits my case?
Also, is my subsampling correct?
I've been using a significance level of 0.01, but I'm getting 20% of false positives, of which roughly half greater, half smaller than the second group (after the two-sided test, I always used the two one-sided ones just to check).