THE FREQUENTIST FACADE AND THE FLIGHT FROM EVIDENTIAL INFERENCE

Recent critics of the use of significance tests (e.g. Cohen, 1994) rec ommend the use of confidence intervals. They use Bayes' theorem in fre quentist examples aimed at illustrating the 'odds-against-chance fanta sy' (Carver, 1978). It is argued below that their criticisms are inapp ropriate and confused. In particular, they have confounded competing d efinitions of probability as relative frequency and as a measure of ev idence in the single case. Moreover, they fail to address the very sam e issue (that they have just raised in the context of significance tes ting)in their recommended or preferred context of confidence intervals . This is demonstrated with an analogous Bayesian example of the evide ntiary interpretation of confidence intervals. As these different defi nitions of probability are definitions, the paper concludes with the a dvice that each one of us must decide where we stand on the issue of p robabilistic evidence in a single research application, as we do with other criteria for evaluating the scientific implications of a single piece of research.