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I have two groups of independent, unpaired data. I would like to estimate how much bigger one group is than the other on average - e.g. being able to say that group 1 is no more than 50% higher than group 2 on average, or something like that. Obtaining an upper limit on how much bigger group 1 likely is than group 2 is important for subsequent steps of analysis.

One group has about 40 samples, the other has about 30. Both groups could be normal but a non parametric method is probably preferred due to one being potentially skewed. I'm familiar with t-tests and the Mann-Whitney U Test, and found a p-value of .08 from a Mann-Whitney test for an alternative hypothesis that Group 1 is bigger than Group 2 - so one could argue that it is significant or not depending on what significance level I require. But, while this is helpful it does not help me in trying to estimate what I've described above.

Do any techniques in trying to estimate an upper limit on the difference in size between groups exist? I haven't been able to find any that do, but would appreciate any advice.

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