Welch test

t-test and a welch test

f you're interested in the differences in means between two populations, then you ought to use the Satterthwaite's (unpaired, unequal variances) T-Test always. The data themselves need not be normal in distribution due to the central limit theorem. Hence, there is no reason aside from a sensitivity analysis using a graphical means (such as side-by-side histograms or boxplots) to assess whether the data aren't in egregious violation of certain structures.

The t-test is a test of the weak null hypothesis, that is all moments of the distribution are disregarded in favor of the mean, so, specifically, the t-test doesn't assess whether the populations are different, just whether their means are different. Contrary to how that might sound, this is completely okay because the "means" and "averages" of distribution often drive the majority of our intuitive understanding of trends.

http://www.reddit.com/r/statistics/comments/vqsz0/a_little_help_with_biostatistics/c56z0gu