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I'm using the Mann Whitney test to verify if two population samples are equal. If the p-value is less than alpha (in this case, 0.05) I reject the null hypothesis and use the median of each population sample to verify which one tends to have bigger value.

However, if the two medians are equal, what should I do? I tried ploting histograms, but they are not always clear.

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    $\begingroup$ Please, do read some top Q/A of the site about M-W and Kruskal-Wallis tests. These tests are not tests specifically of medians. Your two distributions must be different in shape and so the medians can be equal while the p-value is significant. $\endgroup$
    – ttnphns
    Commented Mar 23, 2015 at 21:51
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    $\begingroup$ The dominant sample is the one with greater mean rank (the test is based on ranks, as you probably know). $\endgroup$
    – ttnphns
    Commented Mar 23, 2015 at 21:54
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    $\begingroup$ I know that they don't test medians, but stochastic dominance. However, they are often reported along with the sample's median. That's why I'm using it. My doubt is: how to report which one of the samples domines the other or probably have bigger values than the other? $\endgroup$ Commented Mar 23, 2015 at 21:56
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    $\begingroup$ An alternative option also is to report two-sample Hodges-Lehmann pseudomedian (see Wikipedia) which is "closer" to data than mean rank. $\endgroup$
    – ttnphns
    Commented Mar 23, 2015 at 22:00
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    $\begingroup$ @ttnphns it may be worth collecting your comments into an answer; I think there's an aspect to this question that's really not duplicated in related answers (since it's about what to report), and you've answered that well (if briefly). $\endgroup$
    – Glen_b
    Commented Mar 23, 2015 at 23:39

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