ANOVA vs pairwise t-tests with multiple test correction What is the difference between doing a multiple comparison test (e.g. ANOVA) vs multple pairwise comparisons (e.g. t-tests) with appropiate multiple test corrections?
 A: The difference becomes clear if you understand the null/alternative hypothesis of each test.
ANOVA's null hypothesis is that the group means are the same, while the alternative is that at least one group mean is different from the others.  This analysis does not tell you which group mean is different, or which differences between groups are significant, it only tells you that they are not the same. This sort of approach is favorable, because assuming the data satisfy the assumptions of linear models, we need not utilize any correction method and can interpret the p-value readily.
Compare this to a t-test.  The null hypothesis is usually that the difference between groups is zero. Assuming we utilize an appropriate test correction methodology, we will be able to say something to the effect of "the differences between group i and group j are significant at the $\alpha$ level of significance".  While I think most practitioners would suggest something like a Bonferroni method to account for the inflation of the type 1 error when doing this, I would personally caution making inferences from these sorts of analysis. 
