I've read through several posts on the WMN test, but can't seem to find information on this question. What are the consequences if one assumes equal scale in distributions for a location shift model using the Mann-Whitney U test? I would like to test equality of medians between two groups (and calculate a confidence interval for the shift in median), but due to extreme values the variances tend to be quite different. In reality, I could assume the population distributions have equal variances, but I am wondering what the consequences are for my conclusions in the median difference estimate and the confidence interval if the assumption is not true in reality.
Here are some results for what I'm looking at. If I remove extreme values from Group 1, the variances do become more similar, but this requires removing around 10% of the data from Group 1.
count 373.00 mean 19413.72 std 279752.91 min -291124.25 25% 39.80 50% 53.27 75% 69.97 max 4264238.32
count 23.000000 mean 54.952899 std 16.609280 min 9.416667 25% 44.283333 50% 55.900000 75% 66.733333 max 80.850000
Group 1 with extreme values removed:
count 329.000000 mean 50.527102 std 22.833582 min 0.000000 25% 39.666667 50% 52.600000 75% 64.350000 max 113.650000