Ok, so the pretty result is mostly arbitrary.  Fair enough.  Re: false negatives... you seem to be living in a world of bell curves, or at least a mostly continuous world.  I can easily make (very contrived) experiments where false negatives just don&#x27;t happen.  For instance: I have two coins.  One is a perfectly fair coin.  The other is a two-headed coin.  You see me flip one of them.  The null hypothesis is that I flipped the fair coin.  A false negative means deciding the coin is fair but it&#x27;s really not.  This will never happen, because you will only decide that if it lands tails, and then it must be fair.  (If I only flip it once, the false positive rate is something like 1&#x2F;3, not 0.)  But this is probably much too contrived for your taste, and maybe even for mine.  But it&#x27;s almost 5am, and I must go to sleep now, or else it will get bright soon, and I never will.  I now appreciate the value of the 20min procrastination setting.