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$\begingroup$ Rejection regions can only lead to all-or-none outcomes and are not relevant to p-values. It is hard to see how thinking on those terms can help. $\endgroup$
– Michael Lew
Commented Jul 5 at 21:27
$\begingroup$ It is helpful for understanding. However, perhaps there is a statistic that is not equivalent to the p-value, that is reasonable to consider? It is true that "accusing the computer of cheating if I see 6 doubles, but accept that it is fair if I see 9 doubles" does not seem sensible, but perhaps there is something which we did not think about (such as rare cases when it does make sense) $\endgroup$
– Sam
Commented Jul 14 at 11:31

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