You definitely do not know what a p-value is. When you wrote &quot;P(X|H)&quot; I though X was shorthand for T&gt;T(X) where T is the statistic, not that you were referring to the actual data X.<p>P(X|H) doesn&#x27;t have the properties you claim, anyway. P(X|H)=1 corresponds to the case where only one outcome is possible. In non-trivial cases, the more data you add the lower this number will be.<p>Assume H=&quot;you have a fair coin&quot;. You throw it once: heads. P(X|H)=P(h|faircoin)=1&#x2F;2 You throw it again: tails. P(X|H)=P(ht|faircoin)=1&#x2F;4. You throw it again: tails. P(X|H)=P(htt|faircoin)=1&#x2F;8. I guess the experiment is not well-formed...