The standard t-test for detecting an effect is already probabalistic. In science and medicine a 95% confidence value is commonly used, which means a 1/20 of detecting something that isn't there.
Unless things have been radically relaxed in the last decade, the standard in hard sciences and medicine remains a 99% confidence interval. It's the social sciences that allow for a 95% confidence interval. Having worked in all the different schools out there, I think I have some confidence in my assertion.