Hello Chandrashekhar,

The M-W test is a test of equality of distributions. Only if you are willing to assume symmetry of distributions can you interpret the test as strictly equality of medians.

Your data set yielded a significant M-W test result, which suggests that the two distributions are not identical; one is displaced relative to the other. The fact that the means differ while you say the medians are comparable suggests differential shapes (e.g., skew; apparently more negative skew in batch B than in batch A).

Minimally, plot the data! I'd suggest starting with box plots for the two batches.

Good luck with your work.

As David Morse says, the MW is not a test of the equality of medians. Try the Mood test, though it has low power (if you want a median test bootstrapping can work better). Here is a good ref on the MW not being a test of the medians.

@article{DivineEA2018,

author = {George W. Divine and H. James Norton and Anna E. Barón and Elizabeth Juarez-Colunga},

title = {The {W}ilcoxon–{M}ann–{W}hitney Procedure Fails as a Test of Medians},

journal = {The American Statistician},

volume = {72},

pages = {278-286},

year = {2018},

doi = {10.1080/00031305.2017.1305291},

}

If the MW test indicates there is no significant difference between the two groups, it is expected that the medians be neighbors, but the equality of medians does not lead to the absence of difference between the groups of interest.

Thank you David and also to Daniel and Babak for the very useful clarification...!