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I am conducting a statistical analysis of thromboelastographic data I have collected regarding antepartum and postpartum blood samples in two different patient populations: vaginal and caesarian deliveries.

I have consulted a biostatistician and am using the wilcoxon signed rank test to compare ante and postpartum quantitative data sets for the vaginal and caesarian data sets, respectively. I understand that this is the appropriate test because each pre and post delivery data point comes from the same patient, thus making them "paired."

My question is what is the appropriate test to do when comparing data sets between antepartum caesarian and antepartum vaginal delivery patients? Is it the wilcoxon rank sum test? While I have 21 complete sets of data for pre and post vaginal and caesarian arms of the study, my understanding is that caesarian antepartum and vaginal antepartum sets cannot be compared with the wilcoxon signed rank test because they are no longer paired i.e. they do not come from the same patient. Therefore, I believe it would be appropriate to use the wilcoxon rank sum test.

We assume that the data sets are independent and are not necessarily normally distributed. Null hypothesis is that the data sets are identical.

I believe a comparison of antepartum caesarian section and antepartum vaginal delivery data sets is useful to demonstrate that our data sets in vaginal vs. caesarian are not statistically different before the "treatment" i.e. mode of delivery occurs.

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You are right that for the unpaired antepartum part the rank sum test is appropriate for non-normal data in small(ish) sample sizes. You can do that. However, even if this test is non-significant that does not mean, there is no difference in the antepartum data, as test power is not extremely high with n = 42.

There is nothing wrong with what you are trying to do and I have seen it done in medicine regularly. But I advise you to read Gelman and Sterns famous paper "The Difference Between “Significant” and “Not Significant” is not Itself Statistically Significant" because I think there is a risk for a wrong interpretation of the results if you are not aware, that die difference between significant and non-significant is in itself not significant: http://www.stat.columbia.edu/~gelman/research/published/signif4.pdf

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    $\begingroup$ Thank you so much for the response! I will take a look at this paper and will be wary of making overreaching conclusions due to the sample size. $\endgroup$
    – Luke
    Commented Apr 1, 2021 at 3:07

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