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Published online by Cambridge University Press: 28 February 2022
Orthodox statistical theory, which is the theory used by most practicing statisticians, physicists, biologists, and social scientists, assumes there are objective probabilities which are properties of physical systems. Statistical hypothesis testing is a branch of statistical theory concerned with a theory for accepting or rejecting statements which ascribe these objective probabilities to particular physical systems. Since use of the theory of statistical hypothesis testing leads to the acceptance or rejection of a kind of empirical statement, I shall assume that this theory is a part of inductive logic. Recent philosophical inquiries have largely ignored orthodox statistical theory, and personalistic (or Bayesian) statisticians have attacked it. Since the theory is so widely used, it is important to reexamine its foundations and its place in the canon of inductive logic.
1 Neyman, J., ‘The Problem of Inductive Inference’, Communications on Pure and Applied Mathematics 8 (1955) 19CrossRefGoogle Scholar.
2 Reichenbach, H., The Theory of Probability, University of California Press, Berkeley, 1949, p. 364.Google Scholar
3 Ibid., p. 454.
4 Hacking, I., Logic of Statistical Inference, Cambridge University Press, Cambridge, 1965CrossRefGoogle Scholar. My exposition of the Neyman-Pearson theory follows closely that given there by Hacking and also that of Kendall, M. G. and Stuart, A., The Advanced Theory of Statistics, Vol. 2, Hafner, New York, 1967Google Scholar.
5 The most commonly invoked criteria lead to unbiased and invariant tests. See Hacking, op. cit., pp. 97-99, and Kendall and Stuart, op. cit., pp. 200-6, 256-57. A more complete discussion of statistical hypothesis testing is given in Lehmann's, E. L. Testing Statistical Hypotheses, John Wiley and Sons, New York, 1959Google Scholar.