Very small sample compared to comparatively very large baseline I would like to know if a small test group (~5 samples) is significantly different from baseline (300-400 samples). I initially considered Student's T-Test, but it seems that I wouldn't be able to reliably determine normality with the small test group (and the baseline group seems not to be normally distributed). Is the Mann-Whitney U Test a suitable choice, or should I consider something else? I know these tests don't require equal sample sizes, but is there a point when a large difference in sample sizes becomes a concern, particularly when the smaller group is less than 5 or 10? 
 A: The t-test does not require equal sample sizes (cf., How should one interpret the comparison of means from different sample sizes?), although violations of the assumptions could have more impact as this becomes more extreme.  In general, it isn't considered a good idea to test for normality and then select a test based on the results (cf., How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples).  You could you the Mann-Whitney U-test, but it's worth noting that it actually tests a slightly different hypothesis (cf., Why would parametric statistics ever be preferred over nonparametric?).  In your case, I would probably bootstrap.  For more information, see this CV thread:  How to perform a bootstrap test to compare the means of two samples?  (Edit: I thought that the bootstrap would be OK because of the large sample size in the baseline group, but this is apparently not true; thus, bootstrapping is not a good choice here.)

I suppose the Mann-Whitney U-test would be your best choice.  
