[EpiMath]

Yes, okay. There are implicit assumptions in scientific studies ( e.g.: there are no invisible elephants, or the study we are doing is actually related to the question we are investigating! ). Power calculations refer to the model and not to whether it is the correct model. To some extent we routinely worry about certain types of "hidden from observation" problems: we have zero-inflated poisson models, or we worry about what happens if there is a limited susceptible subpopulation ( that could deplete over time differentially depending on treatment, etc ). But it is not correct to suggest that if a study of whatever power does not find an effect, then a huge effect and no effect are equally plausible.

I have seen outrageous examples of "accepting the null hypothesis" many times, but many negative result studies have great value and even a single negative study can provide evidence against a very large effect.

[lutorm]

* There are implicit assumptions in scientific studies ... Power calculations refer to the model and not to whether it is the correct model.*

True, but this crucial assumption needs to be kept in mind when using the study to inform yourself of the state of the world. Too often, it's forgotten that there are two questions that need answering for the study to be relevant and, only one of those has a number associated with it.

In that sense, Bayesian statistics, where this is explicit, are less misleading because they actually draw attention to the fact that we don't know that the model is correct.

[EpiMath]

Agreed.

Interesting point about Bayesian methods, whenever there are potential flaws or additional uncertainty, it's better if they are more explicit to prompt thoughtful interpretation.