Asymmetric data analyses I have a data set containing bacterial count values before treatment and after treatment. These data look asymmetric. Please advise me for a suitable statistical test to find if the introduction of the new drug significantly reduced the bacterial count. I was thinking of the Wilcoxon signed-rank test. If you think that's the correct one, on what basis should I define hypothetical median value. 
 A: Since your data seems to be paired and is asymmetric (thus, non-normal), I agree that the Wilcoxon test is a good choice.
As for the descriptive statistics, I suggest that you compute the quartiles before treatment and the quartiles after treatment. It may also be interesting to create a new variable $\Delta = a - b$, i.e., the difference between the bacterial count $a$ after the treatment and the bacterial count $b$ before the treatment (negative values of $\Delta$ indicate a decrease in bacterial count). Then, you can take a look at the quartiles of $\Delta$ (in general, they may not be equal to each quartile of $a$ - the same quartile of $b$). 
Edit: The Wilcoxon test will compare the bacterial count before treatment $b$ with the bacterial count after the treatment $a$. Therefore, you will get one $p$ value for each experiment.
Edit2: A $p$ value below the usual cut-off of 0.05 means that you can reject the null hypothesis that the distributions of the bacterial count before the treatment $b$ and after the treatment $a$ are the same, which means that the distributions are significantly different. Remember that you can take a look at the median of each group and/or at the median of $\Delta$ to help you understand in which direction are the differences.
