Interpreting Statistical Insignificance: A Bayesian Perspective

It is often stated that results which are not statistically significant at conventional levels (5% is the common benchmark) represent neither evidence against the null hypothesis nor for it. That is, tests of significance have no logical facility to support the hypothesis tested. This logical standpoint appears in the writings of R. A. Fisher and is endorsed in various textbooks. Notwithstanding the position taken by Fisher (who appears later to have changed his mind), statistical theorists, both orthodox and Bayesian, accept that results which are statistically insignificant may represent strong evidence in favor of the null hypothesis, particularly if the sample size is very large (power is high). This is contrary to the interpretation advocated by a great many researchers in applied disciplines. Among those who use classical (Fisherian) tests of significance, Fisher's initial standpoint remains widely accepted.