On 2013 Jun 17, Mike Fay commented:

This article gives a nice Bayesian argument for using three-sided tests for comparing two treatments. So after running a three-sided test for testing between treatments A and B, we conclude either (1) A is better than B, (2) B is better than A, or (3) the data are not sufficient to say which is better. This makes sense to me, since we usually want to know which is better when we reject the null that they are the same.

For standard use, this essentially translates into using two one-sided tests at the 0.025 level.

Another advantage of shifting to three-sided tests (or two one-sided 0.025 level tests), is that it avoids absurd things such as rejecting a two-sided hypothesis test, but then failing to reject after adding more data in either direction. See Vos and Hudson (2008) http://onlinelibrary.wiley.com/doi/10.1111/j.1467-842X.2007.00501.x/abstract for examples.

On 2013 Jun 17, Mike Fay commented:

This article gives a nice Bayesian argument for using three-sided tests for comparing two treatments. So after running a three-sided test for testing between treatments A and B, we conclude either (1) A is better than B, (2) B is better than A, or (3) the data are not sufficient to say which is better. This makes sense to me, since we usually want to know which is better when we reject the null that they are the same.

For standard use, this essentially translates into using two one-sided tests at the 0.025 level.

Another advantage of shifting to three-sided tests (or two one-sided 0.025 level tests), is that it avoids absurd things such as rejecting a two-sided hypothesis test, but then failing to reject after adding more data in either direction. See Vos and Hudson (2008) http://onlinelibrary.wiley.com/doi/10.1111/j.1467-842X.2007.00501.x/abstract for examples.