  We use the exact finite sample likelihood and statistical decision theory to
answer questions of ``why?'' and ``what should you have done?'' using data from
randomized experiments and a utility function that prioritizes safety over
efficacy. We propose a finite sample Bayesian decision rule and a finite sample
maximum likelihood decision rule. We show that in finite samples from 2 to 50,
it is possible for these rules to achieve better performance according to
established maximin and maximum regret criteria than a rule based on the
Boole-Frechet-Hoeffding bounds. We also propose a finite sample maximum
likelihood criterion. We apply our rules and criterion to an actual clinical
trial that yielded a promising estimate of efficacy, and our results point to
safety as a reason for why results were mixed in subsequent trials.
