Abstract

It has been claimed that if statistical power and p-values are both used to measure the strength of our evidence for the null-hypothesis when the results of our tests are not significant, then they can also be used to derive inconsistent epistemic judgements as we compare two different experiments. Those problematic derivations are known as power approach paradoxes. The consensus is that we can avoid them if we abandon the idea that statistical power can measure the strength of our evidence. In this paper however, I put forward a different solution. I argue that every power approach paradox rests on an equivocation on "strong evidence". The main idea is that we need to make a careful distinction between the evidence provided by the quality of the test and the evidence provided by the outcome of the test. Both provide different types of evidence and their respective strength are to be evaluated differently.