# Deciphering a reviewer's comment: displaying effect size estimates

I submitted a manuscript and have received the following comment I am not sure how to adequately answer. The context is that I have a table comparing a set of "scores" between men and women to see if there are any gender biases. I performed a Mann–Whitney U test to determine if there is a statistical difference between the male and female datasets. The reviewer said: "I would like to see effect size estimates with confidence intervals so readers can more easily interpret the gender disparities".

How can I compute an effect size estimate given the type of data I am dealing with? The data does not follow a normal distribution. For reference, I am using Python for my data analysis.

Edit: I see that one way to get the effect size from the Mann-Whitney U test is to take the U value and divided by the product of the two sample sizes. I can easily do this, although I do not entirely know how to interpret the results if this is indeed accurate.

I think you may be looking for the Hodges-Lehmann two sample estimator outlined very briefly in this Wikipedia article which is the median of all the pari-wise differences between elements of each sample or possibly Somers' $D$ outlined in this Wikipedia article. I imagine either of these would be available in your preferred statistical software. There is also some discussion in this Q&A Mann-Whitney U-test: confidence interval for effect size
• Many thanks! I've seen the discussion in the last link you posted. That should be easy enough, although I need to calculate $z$ first, and neither Python or MATLAB (which I'm using) provide that for me easily. I'll definitely check out the other links. Thank you. Dec 7, 2016 at 15:22