Wilcoxon Rank Sum Interpretations

Occasional Contributor
Posts: 6

Wilcoxon Rank Sum Interpretations

I am using WRS test for a project I am doing. I have tried to find the answer to my question elsewhere online and in textbooks I have but cannot seem to find it anywhere.


I have recorded the Z score and p values from the normal approximation but am also still unsure of how to interpret that for this test? Can I say that the two groups show a statisitically significant difference for my variable or can it not be simply interpreted like this?


Also, how are the "Mean Scores" interpreted and should I include them in my findings? I know that this stat is not the actual mean, so what is it?


I know this is not the best place to post the question since it doesnt have to do with programming anything but I know someone will know the answer! 




Super User
Posts: 11,114

Re: Wilcoxon Rank Sum Interpretations

Generally with any of the hypothesis tests you should decide your rejection region before the test is performed. Then you only have to find either the appropriate test statistic boundary value (z-score, T or F statistic) or associated p-value. If the test statistic is "large" or "small" enough then you  reject the hypothesis. Common is to use p-value less than 0.05 but that is not magic.


Yes reporting the z-score and other information is a good idea in context.


Something like: With a z-score of x.xx we reject (or fail to reject) the null hypothes of equal mean scores and conclude that there is (or is not) a statistically significant diffence between the mean scores of A.aa and B.bb for (what ever you measured).


Was your sample small enough that you should consider the EXACT options instead of using the large sample approximation (z-score)?


If you look in the SAS documentation for the NPAR1WAY procedure you may find an example tilted Exact Wilcoxon Two-Sample Test that shows an example where the large sample approximation differs notably from the Exact test.

Respected Advisor
Posts: 4,811

Re: Wilcoxon Rank Sum Interpretations

Typically you would present your test results with something like:


Group A median weight (50.5 kg) was greater than Group B median weight (45.2 kg), and the difference was statistically significant (Wilcoxon rank-sum test, p < 0.0...)




Group A median weight (50.5 kg) was greater than Group B median weight (49.2 kg), but the difference was not statistically significant (Wilcoxon rank-sum test, p > 0.05)

Posts: 54

Re: Wilcoxon Rank Sum Interpretations

Wilconxon rank sum is a non-parametric test for 2 independent groups and it test whether a randomly chosen measurement from first group tends to be systematically bigger/smaller than one from the 2nd group.

The null hypothesis mathmatically would be: P(X>=Y)=P(Y>=X)=0.5

The alternative hypothesis would be (depending on whether you are doing a one-side test or two-sided test): P(X>=Y)>0.5 or P(X>=Y)<0.5 or P(X>=Y) !=0.5

If your data distribution is approximately symmetrical then this is testing means and medians.

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