"I have always considered the arguments for the use of P (p-value) absurd. They amount to saying that a hypothesis that may or may not be true is rejected because a greater departure from the trial was improbable: that is, that it has not rejected something that has not happened'"H. Jeffreys, 1980. Some general points in probability theory. In A Zellner (ed.), Bayesian Analysis in Probability and Statistics. North-Holland, Amsterdam, p. 453.
© 2013, David E. Giles
Great quote. Maybe fair to say that's at the heart of why I've always preferred likelihood ratios to p-values. What I usually want to know is whether p(H1|x) >> p(H0|x) and, if so, is p(x|H1) significant? (If the likelihood ratio is high but p(x|H1) is low then perhaps the observation is the result of some other effect which I hadn't considered.)
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