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  • $\begingroup$ A brilliant and very clear explanation, thank you very much. The differences are mostly positive (higher values for group 2), with 51 pairs having a positive difference and 9 pairs having a negative difference. If I exclude the pair with the extreme negative difference (group 1: ph=7.410 and group 2: ph=7.317; difference= -0.093), the estimate is logically slightly higher (0.008541) and the p-value even lower (2.04e-07). Therefore, should we deduce that the WSRt is not sensitive to outliers? $\endgroup$ Commented Aug 19 at 7:28
  • $\begingroup$ On the other hand, the paired t-test you suggest gives an even lower p-value by keeping this outlier difference (p=6.67e-09), but much lower by excluding it (p=0.0018). Would the best approach therefore be to use a paired t-test after excluding outliers? Finally, since pH is physiologically regulated within fairly narrow ranges (normal values 7.35 to 7.45, critical if decompensated at <7.25 or >7.55), it is impossible to extend the selection of values more broadly. $\endgroup$ Commented Aug 19 at 7:28
  • $\begingroup$ +1 very good answer. Also @denis: I'm not so sure about this: "So you picked an inappropriate test (WSRt does not test the median)" - it is true that WSRt doesn't test the median, however I wonder whether it's really the median that is most important here, or whether what is of real interest is that there is an overall tendency of negativity (or generally non-equality in distributions with systematic differences in one direction) here, for which WSRt is just fine. $\endgroup$ Commented Aug 19 at 10:36
  • $\begingroup$ @denis Note that trying out several tests until one gives you what you want to see will invalidate results. Technically, you've got to pick your test in advance, and not only because another one on the same data gave you a result different from what you expect. Of course there is an argument to use another test if the first one was grossly wrong from a statistical perspective, but I'm not sure whether this is the case here, see earlier comment. $\endgroup$ Commented Aug 19 at 10:39
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    $\begingroup$ @denis Deletion of outliers is rarely a good idea, unless you have a strong indication (from other sources than the observed data values alone) that they're indeed erroneous. (Same issue as with tests picked dependently on the data really. Standard theory of tests assumes you don't manipulate the data based on what you observe, so becomes invalid if you do so.) $\endgroup$ Commented Aug 19 at 10:40