Sample sizes have nothing to do with it. If you want to study the determinants of presidency in the US it's a 1:1 sample.
I keep repeating this on news.ycombinator: statistical analysis is predicated on the prior hypothesis that the stuff you're measuring is orthogonal to the stuff that you can't measure.
So: what are we measuring? What are we _not_ measuring? Is our theory that people exerting power have more testosterone and hence have more sons? That can be tested in wider populations, and including presidents might just be a huge confounding factors. Is it that presidents become powerful because they have the Mystery Factor, and that, too, is behind the excess sons?
If, by construction, only presidents have the Mystery Factor, we have to start from there. But then we need theories about the Mystery Factor to test. And controls, men who haven't become president by a matter of chance, and so on.
On the other hand: you can have huge datasets generated from website design tests and still end up doing "A/A testing" and such cargo cult statistics, complete with sacrifices to the gods of large sample sizes.
I keep repeating this on news.ycombinator: statistical analysis is predicated on the prior hypothesis that the stuff you're measuring is orthogonal to the stuff that you can't measure.
So: what are we measuring? What are we _not_ measuring? Is our theory that people exerting power have more testosterone and hence have more sons? That can be tested in wider populations, and including presidents might just be a huge confounding factors. Is it that presidents become powerful because they have the Mystery Factor, and that, too, is behind the excess sons?
If, by construction, only presidents have the Mystery Factor, we have to start from there. But then we need theories about the Mystery Factor to test. And controls, men who haven't become president by a matter of chance, and so on.
On the other hand: you can have huge datasets generated from website design tests and still end up doing "A/A testing" and such cargo cult statistics, complete with sacrifices to the gods of large sample sizes.