I have to perform a comparability study between pre and post change of a production process. I'm using the final purity to measure comparability and wanted to compare medians between pre (n=40 runs) and post(n=?). Median of purity pre-change is ~99% so distribution is very skewed and so far I'm using a beta distribution which fits the data very nicely. I'm asked, of course, to perform as fewer post-change runs as possible so I'm trying to find a method that allows me to test comparability considering a big difference between dataset sizes. Would Wilcoxon make sense in this scenario. If not, are there any suggestions? Thanks a lot in advance
