This paper studies models in which hypothesis tests have trivial power, that is, power smaller than size. This testing impossibility, or impossibility type A, arises when any alternative is not distinguishable from the null. We also study settings where it is impossible to have almost surely...

As I document using evidence from a journal data repository that I manage, the datasets used in empirical work are getting larger. When we use very large datasets, it can be dangerous to rely on standard methods for statistical inference. In addition, we need to worry about computational issues....