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The best (most widely) received theory for tests of significance is that due largely to Fisher. Embellished with Neyman's mathematics, Fisher's theory is very well received. But Fisher's logic is not consistent with Bayes' theorem. And Bayes' theorem is beyond reproach. Thus, Fisher's logic is deficient. However, in practice, there is often some redress. Indeed, sometimes Fisher's level of significance P coincides mathematically with the posterior probability of the null hypothesis, i.e. P=p(hOIE), where E is the sample event (evidence). More generally, a good Fisherian tends intuitively (although certainly not inevitably) toward the inference he would make if he employed Bayes' theorem with explicit subjective priors. In effect, he is almost Bayesian. 1 In theory |
