If the null-hypothesis is true, every observation made should be consistent with it. This will result in P(X|H) trending to 1 (since there will be experimental variance). No other experimental design makes sense.<p>&gt;The meaning [of p-value when H is false] is clear: &quot;the probability of getting a value for the statistic as high as the observed one if the null hypothesis was true&quot;<p>This is a logical fallacy. It is counterfactual to consider a world where the null hypothesis is true, when it is not.<p>In fact, this is precisely the feature of the universe that p-value based experimentation exploits and is essentially the only way for us to gain any information about &#x27;reality&#x27;.<p>&gt;By definition, if the null hypothesis is true the p-value is uniformly distributed between 0 and 1.<p>I don&#x27;t think so. If that were true, p-value would be entirely useless.