  Despite its common practice, statistical hypothesis testing presents
challenges in interpretation. For instance, in the standard frequentist
framework there is no control of the type II error. As a result, the
non-rejection of the null hypothesis cannot reasonably be interpreted as its
acceptance. We propose that this dilemma can be overcome by using agnostic
hypothesis tests, since they can control the type I and II errors
simultaneously. In order to make this idea operational, we show how to obtain
agnostic hypothesis in typical models. For instance, we show how to build
(unbiased) uniformly most powerful agnostic tests and how to obtain agnostic
tests from standard p-values. Also, we present conditions such that the above
tests can be made logically coherent. Finally, we present examples of
consistent agnostic hypothesis tests.
