How do I determine statistical differences between two independent 2 samples groups? I have two varieties of Barley; Copeland and Synergy.
I have data on the protein levels of this barley. I have 28 data points for protein of Copeland and 24 data points for protein of Synergy. 
What would be the best statistical test to determine whether the barley protein levels are statistically different?
Thanks
 A: The Mann-Whitney U test is probably the best test to use without having enough data to determine if the protein is normally distributed or not. This has several features: 1) It is a test that ranks outcomes so that the underlying shape of the distributions becomes irrelevant, that is, it is a so-called non-parametric test. 2) It is a test for independent random variables and as such can have a different number of results for each variable. 3) It is not as powerful as a paired-sample test that can look at differences of ranking only between the same subjects (e.g., Wilcoxon signed-rank test).
A: The main alternative to the Mann-Whitney U test proposed by Carl would be Student`s t-test. There is some normal distribution assumption in there, but at n= 2*28 it is pretty robust against violations of that assumption. The main advantage is not power (if one of these happens to be significant and the other not significant, then it is a borderline case and one should be cautious to trust any of them). The main advantage is, that it investigates the mean of the protein content, which is a concept easier to grasp for non-statistical audiences. Your audience will be happy to hear, that the mean of one sort is significantly larger by roughly 3.5 units. Also, the t-test is favourable if you are interested in any sort of power analysis. 
So depending on your audience and what else except for a p-value you want to present, the usual choices are Mann-Whitney U aka Wilcoxon rank sum or t-test for independend samples.
