Some Logic and History of Hypothesis Testing

The foundations of statistics are controversial, as foundations usually are. The main controversy is between so-called Bayesian methods, or rather neo-Bayesian, on the one hand and the non-Bayesian, or ‘orthodox’, or sampling-theory methods on the other.1 The most essential distinction between these two methods is that the use of Bayesian methods is based on the assumption that you should try to make your subjective or personal probabilities more objective, whereas anti-Bayesians act as if they wished to sweep their subjective probabilities under the carpet. (See, for example, Good (1976).) Most anti-Bayesians will agree, if asked, that they use judgment when they apply statistical methods, and that these judgments must make use of intensities of conviction,2 but that they would prefer not to introduce numerical intensities of conviction into their formal and documented reports. They regard it as politically desirable to give their reports an air of objectivity and they therefore usually suppress some of the background judgments in each of their applications of statistical methods, where these judgments would be regarded as of potential importance by the Bayesian. Nevertheless, the anti-Bayesian will often be saved by his own common sense, if he has any. To clarify what I have just asserted, I shall give some examples in the present article.