To add to this, the problem with t-tests in not the threshold. It is that the hypothesis you are rejecting (effect is exactly 0.0000000...) is infinitesimaly small. You've rejected basically nothing of your hypothesis space.
Your null should have a width. You should always be rejecting "effect is greater than some margin" which you should have to argue is greater than any bias you might expect in your experiment. There are always at least tiny biases.
Your null should have a width. You should always be rejecting "effect is greater than some margin" which you should have to argue is greater than any bias you might expect in your experiment. There are always at least tiny biases.