Solved – Mann Whitney test results interpretation

interpretationwilcoxon-mann-whitney-test

I have two samples both bigger than 99999 and I get the following result in Python:

MannwhitneyuResult(statistic=2395063024.0, pvalue=2.3093898533164459e-128)

U critical = 135807.32

If I understand it correctly, I cannot reject the null hypothesis that samples (distributions) are the same because U obtained > U critical.

However, If I make boxplots it seems like one distribution is bigger than the other one.

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Are my results correct and what can I conclude?

Best Answer

Unfortunately, the conclusion is reversed.  Because $p \ll \alpha$, you would reject the null (which assumes the distributions have the same parameter).  Additionally, the sample size all but guarantees that you will reject the null.  In this case, it may be more beneficial to accept that the distributions are different and address the difference between the two samples from a practical significance (an effect size) instead of a statistical significance.

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