This commentary reviews the arguments for and against the use of p-values put forward in the Journal and other forums, and shows that they are all missing both a measure and concept of "evidence." The mathematics and logic of evidential theory are presented, with the log-likelihood ratio used as the measure of evidence. The profoundly different philosophy behind evidential methods (as compared to traditional ones) is presented, as well as a comparative example showing the difference between the two approaches. The reasons why we mistakenly ascribe evidential meaning to p-values and related measures are discussed. Unfamiliarity with the technology and philosophy of evidence is seen as the main reason why certain arguments about p-values persist, and why they are frequently contradictory and confusing.
Goodman et al. (1988) studied this question.