Decision Theory

Abstract

Fisher’s response to the observation that the classical techniques of testing statistical hypotheses are most appropriate where a hypothesis must be tested over and over again, and acted upon each time, was to denigrate this approach to statistical inference as ‘statistics for shopkeepers’, to claim that it had nearly nothing to do with the interesting problems of testing scientific hypotheses, and to develop a quite different approach to these interesting statistical problems. (To be sure his approach started as early as the Neyman-Pearson approach, and on chronological grounds would have as much right to the honorific ‘classical’ as that one.) Another response, and one which is more in line with the development of the classical theory, is to agree that this is indeed the statistics of shopkeepers, but to argue that that is just what statistics ought to be. If we were psychologists or metaphysicians, the argument might go, then we might want to be interested in what does go on or what ought to go on in the heads of scientists who are doing purely theoretical research; but in point of fact what concerns us is the practical difference it will make to accept one hypothesis or another, and, as Peirce or Dewey or James might have argued, a practical difference can only reveal itself in action.