Which statistical test is appropriate if we can not measure normality Say I have two devices that purifies milk, device A and device B. I assume Device B is better and it produces milk that is 5% better than A. If I want to test this assumption, I take 8 sample from the milk produced by Device A and 8 samples from Device B, analyse the purity of the samples taken at the lab, and compare the results of 8 sample from A and the 8 samples from B. 
The question is: What is the best statistical test to use? Do I need to run power analysis? How to check normally when we have only 8 samples?
This question and this are similar but I could not make use of the answer there. 
 A: Well, if I understand your problem correctly, you want to test if the purity of samples produced by device B is smaller than the ones from device A.
I would use Mann–Whitney U test .
Null hypothesis (H0): the values of A and B come from the same distribution.
The test show you if one of the samples tend to have values larger than the other.
EDIT (thanks to whuber for point out the 5% test):
Formally, you could try to test if you can disprove that device B is 5% better than device A (you would do that by taking H0: B better than A 5%). Now, this strategy has two problems. One is that, if normality doesn't hold, it is really hard to test it. By the way, you can check normality with Shapiro–Wilk test. The second problem is that, if you can't reject the null (meaning that there is no support for a difference different than 5% you still have not proven that is 5%).
My humble solution would involve bootstrap and confidence intervals. You can use bootstrap to compute a distribution of the ratio of the means (or medians). You can do this in R very easily. Them you have a proper confidence interval for how better B is from A.
