1. Mann-Whitney U test

While I was analysing my data (regards to number of chemotherapy received by 2 groups of patients) I note the median values of both groups are same but applying the Mann-Whitney U test, it showed that there was significant difference in the number of chemptherapy received. Is it possible?
Thank you
Chandramsk

2. i think yes.

The test statistic only depends on the ordering of data, not its actual value. You can contruct a sample where the test statistic is significant but the subsample medians are arbitrarily close to each other. The example below assumes that data is continuous).

Suppose you had some data $X$ where the subsample medians were very different and the U statistic was significant. You could take a transformation of the data $X' = aX +b, ~~~ a \in (0, \epsilon]$ which would make both subsample medians arbitrarily close to b (and hence, arbitrarily close to each other). The U statistic would be unaffected since the above transformation doesn't change the ordering of any data.

3. Re: Mann-Whitney U test

Suppose I have a non-normal distribution with a big skew, apply a treatment to it and then want to compare the distributions (same population) pre/post treatment. I think the Mann-Whitney U test should work right? Is there a better option?