Thanks to whoever just downvoted me, as I now have a completely different answer to this question.I have accordingly deleted my original answer as it is incorrect from this perspective.
In the context of this question, which is only dealing with the question "was A or B a better discriminator in my study", we are dealing with a census and not a sample. Thus, the use of inferential statistics such as those used to produce p-values are irrelevant. Inferential statistics are used to infer population estimates from those we obtain from our sample. If we do not wish to generalise to a population, then those methods are unnecessary. (There are some specific issues around missing values in a census, but those are irrelevant in this situation.)
There is no probability of obtaining a result in a population. We obtained the result we got. Therefore, the probability of our results is 100%. There is no need to construct a confidence interval - the point estimate for the sample is exact. We're simply not having to estimate anything at all.
In the specific case of "which variable worked better with the data I have", all one needs to do is look at the results in simple summary form. A table may be sufficient, maybe a graph like a box plot.