What is an appropriate statistical test for equivalence of two population means? I'd like the null hypothesis to be that the populations are different. The problem with the t-test is that the null hypothesis says that the populations are the same. It is more appropriate in my application that I assume the populations are different unless I can proove otherwise. Example: treatment A1 is well understood and the distribution is well known. Treatment A2 is a newer and cheaper version, and we only accept that it is as good as treatment A1 if the null hypothesis is rejected. in other words it will be assumed that A2 is not as good as A1 unless there is enough data to show otherwise. Any thoughts on how to do this?