1. I would argue that this is a paper that intentionally goes into detail with regard to the history of statics. After all the main problem here is not how to c

1. I would argue that this is a paper that intentionally goes into detail with regard to the history of statics. After all the main problem here is not how to compute p-values, nor the choice of the threshold (well, that may very well be a problem, but it's a different one) but rather the interpretation, and history is often important for interpretation, even in physics. If one wants a really compact way to convince people that the way they are thinking about p-values is wrong I'd go with the point raised by Steven Goodman in "A Dirty Dozen: Twelve P-Value Misconceptions": since the p-value is computed under the assumption that the null hypothesis is true it cannot be the probability that the null hypothesis is true, by definition. 2. As far as what the difference is, I have to admit I have not found a memorable phrase to explain it. Both Goodman in "Toward Evidence-Based Medical Statistics" and this paper give a similar wording of the difference, which i would rephrase as follows. The p-value works by inference, taking the data and assigning a probability to that data, not to an hypothesis. It is to be used to corroborate our disbelief in the null, i.e. informally. To use inference to test hypothesis one must use Bayes' Theorem, i.e. Bayes factors, and introduce prior probabilities. Hypothesis testing à la Neyman and Pearson is deductive process, in which one does assign probabilities to the hypotheses, paying the price of only being able to minimize the errors commited, not to draw inferences. One should also confront "In Fisher’s approach the researcher sets up a null hypothesis that a sample comes from a hypothetical infinite population with a known sampling distribution." with "Neyman–Pearson results are predicated on the assumption of repeated random sampling from a defined population." Given the natural predisposition by students to works in an inferential manner, it may be wise to bite the bullet and teach Bayes factor instead of the p-value cargo cult (this being a pedagogical choice, not an assessment of frequentism vs. bayesianism or a critique of p-values as conceived by Fischer).