This is a place for questions, answers, and discussion about session 10 of the Biostatistics for Biomedical Research airing 2020-01-17 covering nonparametric statistical tests and associated confidence intervals. Session topics are listed here. The video will be in the YouTube BBRcourse Channel and will be directly available here after the broadcast.
I’m struggling to understand for the Wilcoxon-Mann-Whitney test why the p-value is only a function of the sample sizes in each group, and doesn’t take into account the test statistic.
If you already have the p-value, what is the value of then calculating the test statistic, W? I think I must be missing something obvious here…
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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.
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Your response cleared it up, thanks. I had misread that the p-value is 2/(n!/(n1!*n2!)) only if there is no overlap between measurements from each group.
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