Disputes between advocates of Bayesians and more orthodox approaches to statistical inference presuppose that Bayesians must regard must regard stopping rules, which play an important role in orthodox statistical methods, as evidentially irrelevant.In this essay, I show that this is not the case and that the stopping rule is evidentially relevant given some Bayesian confirmation measures that have been seriously proposed. However, I show that accepting a confirmation measure of this sort comes at the cost of rejecting two useful ancillaryBayesian (...) principles. (shrink)

To what extent does the design of statistical experiments, in particular sequential trials, affect their interpretation? Should postexperimental decisions depend on the observed data alone, or should they account for the used stopping rule? Bayesians and frequentists are apparently deadlocked in their controversy over these questions. To resolve the deadlock, I suggest a three‐part strategy that combines conceptual, methodological, and decision‐theoretic arguments. This approach maintains the pre‐experimental relevance of experimental design and stopping rules but vindicates their evidential, postexperimental irrelevance. †To (...) contact the author, please write to: Tilburg Center for Logic and Philosophy of Science, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands; e‐mail: [email protected]. (shrink)

The Bayesian theory is outlined and its status as a logic defended. In this it is contrasted with the development and extension of Neyman-Pearson methodology by Mayo in her recently published book (1996). It is shown by means of a simple counterexample that the rule of inference advocated by Mayo is actually unsound. An explanation of why error-probablities lead us to believe that they supply a sound rule is offered, followed by a discussion of two apparently powerful objections to the (...) Bayesian theory, one concerning old evidence and the other optional stopping. (shrink)

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. In this paper, I focus on two such criticisms. The first one claims that the use of the p-value violates the principle of total evidence. 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. 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. (shrink)