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If you already have the p-value, what is the value of then calculating the test statistic, W?
I’m not exactly sure were you are assuming the p-value is calculated from.
For the 2 sample Whitney-Mann-Wilcoxon (WMW) statistic is directly related to the possible combinations for the sample.
Example: if you have a sample of 5, 2 are treatment, 3 are control, you have \frac{1}{2}n(n-1) or 10 possible combinations to get a WMW score with a range of 3 - 9 for treatment and 6-12 for control. Any possible combination will map to a WMW sum in this range for this sample size, but there many combinations that assign treatment vs control to ranks that map to a particular WMW sum.
Because ranks are used, the smallest possible \alpha (2 sided) is 0.2.
The number of possible combinations is directly related to the size of the sample.
The WMW statistic can be used to calculate a nonparameric effect size estimate.