The Principle of Total Evidence and Classical Statistical Tests

Classical statistical inferences have been criticised for various reasons. To assess the soundness of such criticisms is a very important task because they are widely used in everyday scientific research. This is one of the reasons why the philosophy of statistics is an exciting field of study.\ud In this paper, I focus on two such criticisms. The first one claims that the use of the p-value violates (or can violate) the principle of total evidence (PTE). It is a thesis that has been defended by Elliott Sober and Bengt Autzen. The second one says that the result of classical tests does not only depend on the data but on the sampling plan of the experimenter also. The underlying criticism of course is that the sampling plan is not part of the evidence and that classical tests therefore violate PTE. The intentions of the experimenter should not affect the result of an inference.\ud My aim is to show that both criticisms are unsound. Doing so, I hope to clarify the concept of p-value and the nature of the evidence in classical statistical tests. The point of my paper is to show that the identification of the evidence on which those criticisms rest is inadequate