The growing availability of computer power and statistical software has greatly increased the ease with which practitioners apply statistical methods, but this has not been accompanied by attention to checking the assumptions on which these methods are based. At the same time, disagreements about inferences based on statistical research frequently revolve around whether the assumptions are actually met in the studies available, e.g., in psychology, ecology, biology, risk assessment. Philosophical scrutiny can help disentangle 'practical' problems of model validation, and conversely, (...) a methodology of statistical model validation can shed light on a number of issues of interest to philosophers of science. (shrink)

The article revisits the large n problem as it relates to the Jeffreys-Lindley paradox to compare the frequentist, Bayesian, and likelihoodist approaches to inference and evidence. It is argued that what is fallacious is to interpret a rejection of as providing the same evidence for a particular alternative, irrespective of n; this is an example of the fallacy of rejection. Moreover, the Bayesian and likelihoodist approaches are shown to be susceptible to the fallacy of acceptance. The key difference is that (...) in frequentist testing the severity evaluation circumvents both fallacies but no such principled remedy exists for the other approaches. (shrink)

The interpretation of tests of a point null hypothesis against an unspecified alternative is a classical and yet unresolved issue in statistical methodology. This paper approaches the problem from the perspective of Lindley's Paradox: the divergence of Bayesian and frequentist inference in hypothesis tests with large sample size. I contend that the standard approaches in both frameworks fail to resolve the paradox. As an alternative, I suggest the Bayesian Reference Criterion: it targets the predictive performance of the null hypothesis in (...) future experiments; it provides a proper decision-theoretic model for testing a point null hypothesis and it convincingly accounts for Lindley's Paradox. (shrink)