Advantages of using independent samples T-test over one-way ANOVA for comparing two groups I'm still confused as to why it is often recommended to use an independent samples T-Test when comparing two means rather than a One-way Anova. 
If t^2 = F, and the p values are the same, why use a T-Test? What is the difference? 
I've read that its because a T-Test 'is more flexible', but why is this the case? Is it just because the T distribution is two-tailed, whereas the F distribution is one-tailed? 
 A: With questions like this there is always a bit of ambiguity, since there are lots of different tests that use the T-distribution as the null distribution, and hence, are referred to as "T-tests".  Comparing to the ANOVA test requires consideration of which particular T-test you are talking about.
Gossett's T-test (the two-sample t-test with assumed equal variances) is formally equivalent to a one-way two-group ANOVA test from Gaussian linear regression.  For these tests it can be shown that $T^2 = F$ and so the p-values of both tests are the same.  Since these are the same test, it makes no difference which you use.  Where the T-test becomes "more flexible" is when you remove the assumption of equal variances for the groups and use Welch's T-test or some similar variant.  With this variation you now have a T-test that is not equivalent to the one-way two-group ANOVA test from Gaussian linear regression. 
The greater "flexibility" occurs because the test accomodates cases where the variances of the two groups are substantially different.
