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I understand that Medians should be reported when writing results of Wilcoxon rank-sum test. For example: "For alcohol users depression levels were significantly lower on Wednesday (Mdn = 7.50) than on Sunday (Mdn = 16.0), p = .012, r = −.45."

But suppose that p=.012 but Mdn=7.50 on Wednesday and Mdn=7.50 also on Sunday, but the Mean= 6.45 on Wednesday and Mean = 14.56 on Sunday. How do I report results? How would be the text in the example then? Because depression levels are indeed lower on Wednesday, but results should be reported using Medians..

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    $\begingroup$ Why do you understand that? The Wilcoxon rank-sum test (aka Mann-Whitney test) does not test the difference in medians. $\endgroup$ Jul 8, 2019 at 11:15
  • $\begingroup$ @JeremyMiles That's true, but it is common to report medians along with test results. And OP is confused what to report with equal medians and p<0.05 $\endgroup$ Jul 8, 2019 at 11:43

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It's always worth reporting some measure of disperssion along with measure of central tendency. You probably report standard deviation with mean, when you use it. So maybe just report quartiles or IQR (interquartile range) with median?

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  • $\begingroup$ So it would be ok like this? For alcohol users, the Wilcoxon Signed-Ranks test indicates that the ranks of the depression levels were statistically significantly lower on Wednesday (Mean = 6.45, sd=1.2 Mdn=7.50) than on Sunday (Mean = 14.56, sd= 1.3 Mdn = 7.50), p = .012, r = −.45." $\endgroup$
    – Ana
    Jul 8, 2019 at 11:34
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    $\begingroup$ I would report median and quartiles like "Wednesday (Mdn=7.50, Q1=5, Q3=10)" $\endgroup$ Jul 8, 2019 at 11:42

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