We are preparing statistical analysis of cross-sectional study; and have the following question:
We want to check whether difference btw two age medians grouped by categorical variable (died vs alive) is statistically significant. We used Mann-Whitney U test. Did we choose the right test?
No, the Mann-Whitney is not a test for differences in median. It's possible for two samples to have exactly the same median and for the Mann-Whitney test to be significant.
It's quite common, however, to report medians together with a Mann-Whitney test if you have to report a test. That's basically ok as long as you don't claim it's a test for difference in medians.
There is a test for medians, sometimes called "Mood's test", but it's not used very much. More usefully, you could get a bootstrap confidence interval for the difference or ratio of the medians
