I'm not a statistician, so pardon me for being naive on this subject.
I'm trying to understand if there's any statistically significant difference in the medians of 2 groups. Here are some of the salient features of my groups:
- Each of the groups has Millions of observations
- Each of the groups is not normally distributed
- The observations are continuous
- One of the groups has almost 15x the observations in the other group
- The groups are mostly independent of each other
If the groups were normally distributed, I could have used the T-test to figure this out.
So this leads me to believe that a Mann-Whitney test would be more useful in this case. But because I have Millions of observations in both the groups, I'm not sure if the Mann-Whitney test results will hold true. In one of the Stack Overflow posts, I read that Mann-Whitney test does not work well with so many observations.
Should I just take much smaller random samples from my 2 groups and perform the Mann-Whitney test many times and then look at the results?
Or is there a better approach to doing this? Any help would be much appreciated.