Misapprehensions About Significance Tests and Bayesianism

Abstract

The opposition to Bayesian approach to inverse inference, after the abundant use made of it by Laplace, the first to introduce it into scientific method, formed and developed, as we know, in the positivistic climate of the late nineteenth century. Boole, Venn, and later R.A. Fisher, to mention only three well-known names, saw in the application of Bayes theorem to cases of inverse inference the danger of introducing arbitrary elements connected with the a priori probabilities, in their opinion unjustifiable in the scientific research, which should always and only pursue objectivity. Such opposition seemed to Fisher all the more justified by the fact that for him there was no need to fall back on a priori probabilities, given the availability of alternative non-Bayesian methods, which he had himself helped to work out, including significance tests. These can be easily and pleasantly introduced by Fisher’s well-known example of ‘the tea lady’, i.e. the woman declaring that she can tell, on tasting a cup of tea, whether the milk was put in as first or the tea.