t-test with logistic and Gumbel distributions I know that one of the basic assumptions of a t-test is that the data is drawn from a Gaussian distribution.
Using an Anderson-Darling test, I've found that the datasets I am working with are either drawn from a logistic distribution or a Gumbel distribution (both centered around 0, and both closely resemble a Gaussian).
I was wondering if I can safely use the two-sided t-test (e.g. the scipy.stats.ttest_ind function) with this type of distribution or is there another alternative to the two-sided t-test that is better recommended for the logistic and Gumbel distributions?
 A: The independent t-test is fairly robust to deviations from normality if they are not too severe and if the sample sizes are roughly equal and the variances roughly equal.
But, since there are many nonparametric tests of location, why not use one of them?  
E.g. Mann-Whitney test, which tests whether a value from one sample is equally likely to be smaller or larger than a value from the other sample. (This test is also known as Wilcoxon Mann Whitney)
A: For something more-or-less like the logistic -- somewhat heavier tailed and peakier than normal, I'd suggest the Wilcoxon-Mann-Whitney test. 
Firstly, it's distribution-free so the fact that you don't know the distribution isn't of much concern with regard to significance level.
Secondly, it has excellent power as a test of location shift (which is what I assume you're mainly concerned with) for distributions like the logistic. You'll be hard-pressed to beat it.
Unless you have a more specific comparison in mind (like "Well, actually I want to compare lower quartiles"), I think this one's almost a no-brainer.
That said, a t-test doesn't have bad power in this situation -- just a bit lower (e.g. the relative efficiency at a sample size of 30, when the Wilcoxon power is about 0.5 is in the ballpark of 95%). Its significance level is not much affected either -- it's just a little lower than the nominal level.

However, I must add a comment on your phrasing here (converting and expanding on a comment I made much earlier): 

Using an Anderson-Darling test, I've found that the datasets I am working with are either drawn from a logistic distribution or a Gumbel distribution 

No, you didn't find that. Failure to reject a logistic doesn't mean you actually have a logistic. Failure to reject a Gumbel doesn't mean you actually have a Gumbel. 
The Anderson Darling test cannot tell you that data were drawn from some specific distribution. Indeed those unrejected nulls are almost certain to be false. (Further, because the logistic and Gumbel are very different, if there's any case where you fail to reject both, you haven't pinned down the distribution much at all.)
