Credible intervals do not make worst case guarantees, but average case guarantees (given your prior). There is nothing wrong with confidence intervals as a worst case guarantee technique. To grandparent: I wouldn’t take statistical methodology advice from lesswrong. If you really need such advice, ask a smart frequentist and a smart bayesian.
You could use Bayesian estimation to compute credible differences in mean task completion time between your groups.
Described in excruciating detail in this pdf.
Credible intervals do not make worst case guarantees, but average case guarantees (given your prior). There is nothing wrong with confidence intervals as a worst case guarantee technique. To grandparent: I wouldn’t take statistical methodology advice from lesswrong. If you really need such advice, ask a smart frequentist and a smart bayesian.