When I had found (this Sunday) the notion of p-value together with Plausibility  I could hardly contain my joy, because the last current definition: ____In statistical hypothesis testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true____(Wiki) ,can be cautiously read: *at least as extreme as the one that was actually observed* means really that it?s not impossible to find a larger p-value even that null is true. Plausible states (for me) the exact situation: under null hypotheses true it is more and more unexpected that one get a larger p-value and if it happens by chance we reject H0 as unlike. Of course we has the probability alpha to be wrong (type I error): bad luck to test an *abnormal* data, for example, sample from z~N(0,1) where z >2.
Luis A. Afonso
 Ryan Martin, Chuanhai Liu, (Nov. 12, 2012) On a *plausible* interpretation of p-values. arxiv.org/pdf/1211.1547 - -