Ok. So. I have a data set of 60 thousand values, distributed thus:
They are associated with 30 different aircraft types. I wanted to use ANOM to quickly see if any aircraft groups were significantly different than the overall mean. Since the overall population distribution of these values is skewed, I decided to apply ANOM with Transformed Ranks. The original data were all negative values, so without much thought I decided to flip them to positive values before conducting the ANOM:
10 aircraft emerge from the LDL-UDL range.
Then I tried ANOM with TR with the original negative-valued data:
I would have thought that the results would have been the same. Is there a simple explanation for why I wouldn't see the same results either way?