p-values are two way decision procedures. For historical reasons we report the critical value of the type I error, because that was the piece people figured out

p-values are two way decision procedures. For historical reasons we report the critical value of the type I error, because that was the piece people figured out before we got decision theory and the Neyman-Pearson lemma. All the null hypothesis vs other hypothesis stuff is distractions from the basic fact of choosing between two decisions based on data. I wrote an explanation for clinicians a while back that I people have had good luck with: http://madhadron.com/posts/2016-01-25-p_values_for_clinicians.html http://madhadron.com/posts/2016-01-25-p_values_for_clinician... > Likewise, we're supposed to assume that there is something magical about our prior assumptions? No, we construct trials that a reasonable practitioner thinks satisfies the assumptions of the analysis used. And sometimes we learn that we had overlooked something and all those trials we did before we accounted for it were flawed.