Abstract
Interpreted as indices of the support for an hypothesis, Fisherian significance tests are assimilable into the corpus of Bayesian methods. The observed sample coverage is an approximation to the average likelihood, and one that is often more convenient to use (or which can be used as a surrogate when the likelihood function cannot be computed). Moreover, the OSC has a clear and definite meaning as a measure of the improbability of a theory’s accuracy. Any two theories or hypotheses can be compared in this respect, whether they are exclusive or not, and whether they are drawn from the same or disparate fields of science. In what follows, I will refer to this interpretation of significance tests as ‘the Bayesian evidential interpretation’.
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Bibliography
Anscombe, F. J.: 1963, ‘Tests of Goodness of Fit’, J. Roy. Stat. Soc., B, 25, 81–94.
Bakan, D.: 1967, ‘The Test of Significance in Psychological Research’, On Method, Jossey-Bass, San Francisco, 1–29 (reprinted in Morrison and Henkel).
Barnard, G. A.: 1947, ‘The Meaning of a Significance Level’, Biometrika 34, 179–182.
Birnbaum, A.: 1962, ‘On the Foundations of Statistical Inference’, J. Am. Stat. Assoc. 57, 269–306.
Birnbaum, A.: 1969, ‘Concepts of Statistical Evidence’, Philosophy, Science and Method (S. Morgenbesser, P. Suppes, and M. White, eds.), St. Martin’s Press, New York.
Cox, D. R.: 1958, ‘Some Problems Connected With Statistical Inference’, Ann. Math. Stat. 29, 357–372.
Cramer, H.: 1946, Mathematical Methods of Statistics, Princeton University Press, Princeton, New Jersey.
Edwards, A. W. F.: 1972, Likelihood, Cambridge University Press, Cambridge.
Feller, W.: 1957, Introduction to Probability Theory and its Applications, Wiley, New York.
Fisher, R. A.: 1955, ‘Statistical Methods and Scientific Induction’, J. Roy. Stat. Soc., B, 17, 69–78 (reprinted in Fisher, 1974).
Fisher, R. A.: 1956a, ‘On a Test of Significance in Pearson’s Biometrika Tables (No. 10)’, J. Roy. Stat. Soc., B, 56–60 (reprinted in Fisher, 1974).
Fisher, R. A.: 1956b, Statistical Methods and Scientific Inference, Oliver and Boyd, Edinburgh.
Fisher, R. A.: 1974, The Collected Papers of R. A. Fisher, Vol. 5 (ed. by J. H. Bennett), University of Adelaide Press, Adelaide.
Giere, R. N.: 1976, ‘Empirical Probability, Objective Statistical Methods, and Scientific Inquiry’, Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (W. A. Harper and C. K. Hooker, eds.), Vol. 2, pp. 63–101.
Good, I. J.: 1976, ‘The Bayesian Influence, or How to Sweep Subjectivism Under the Carpet’, Foundations of Probability Theory, Statistical Inference and Statistical Theories of Science (W. A. Harper and C. K. Hooker, eds.), Vol. 2, D. Reidel, Dordrecht-Holland.
Hacking, I.: 1965, Logic of Statistical Inference, Cambridge University Press, Cambridge.
Hodges, J. L. and Lehmann, E. L.: 1954, ‘Testing the Approximate Validity of a Null Hypothesis’, J. Roy. Stat. Soc., B, 16,261–268.
Jaynes, E. T.: 1968, ‘Prior Probabilities’, IEEE Trans, on Systems Science and Cybernetics, SSC-4, 227–241.
Jaynes, E. T.: 1976, ‘Confidence Intervals vs Bayesian Intervals’, Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science (W. A. Harper and C. K. Hooker, eds.), Vol. 2, D. Reidel, Dordrecht-Holland.
Kalbfleisch, J. D. and Sprott, D. A.: 1970, ‘Applications of Likelihood Methods to Models Involving Large Numbers of Parameters’, J. Roy. Stat. Soc., B, 32, 175–208.
Kalbfleisch, J. D. and Sprott, D. A.: 1974, ‘On the Logic of Tests of Significance with Special Reference to Testing the Significance of Poisson-Distributed Observations’, Information, Inference, and Decision (G. Menges, ed.), D. Reidel, Dordrecht-Holland.
Kalbfleisch, J. D. and Sprott, D. A.: 1976, ‘On Tests of Significance’, Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. 2, D. Reidel, Dordrecht-Holland.
Kendall, M. G. and Stuart, A.: 1967, The Advanced Theory of Statistics, Vol. 2, Griffin, London.
Kyburg, H.: 1974, The Logical Foundations of Statistical Inference, Chapter II, D. Reidel, Dordrecht-Holland.
Kyburg, H. and Smokier, H. (eds.): 1964, Studies in Subjective Probability, Wiley, New York.
Lehmann, E. L.: 1958, ‘Significance Level and Power’ Ann. Math. Stat. 29, 1167–1176.
Lehmann, E. L.: 1959, Testing Statistical Hypotheses, Wiley, New York.
Lieberman, B.: 1971, Contemporary Problems in Statistics, Oxford University Press, Oxford.
Lindley, D. V.: 1957, ‘A Statistical Paradox’, Biometrika 44, 187–192.
Lindley, D. V.: 1971, Bayesian Statistics, a Review, SIAM, Philadelphia.
Marks, M: 1951, ‘Two Kinds of Experiment Distinguished in Terms of Statistical Operations’, Psych. Rev.58, 179–184 (reprinted in Lieberman).
Morrison, D.E. and Henkel, R. E.: 1970, The Significance Test Controversy, Aldine, Chicago.
Morton, N.: 1955, ‘sequential Tests for the Detection of Linkage’, Am. J. Hum. Genetics 7, 277–318.
Neyman, J.: 1950, First Course in Probability and Statistics, Henry Holt, New York.
Neyman, J.: 1957, ‘“Inductive Behavior” as a Basic Concept of Philosophy of Science’, Rev. Inst. Int. de Stat. 25, 7–22.
Neyman, J. and Pearson, E. S.: 1933, ‘The Testing of Statistical Hypotheses in Relation to Probabilities a priori’, Proc. Cambridge Phil. Soc. 29, 492–510.
Neyman, J., Lovasich, J., Scott, E., and Wells, M.: 1971, ‘Further Studies of the Whitetop Cloud-Seeding Experiment’, Proc. Nat. Acad. Sci, 68, 147–151.
Neyman, J., Scott, E., and Shaw, C.D.: 1956, ‘Statistical Images of Galaxies with Particular Reference to Clustering’, Proc. Third Berkeley Symposium on Mathematical Statistics and Probability, Vol. III, University of California Press, Berkeley.
Robbins, H.: 1963, ‘A New Approach to a Classical Statistical Decision Problem’, Induction: Some Current Issues (H. Kyburg and E. Nagel, eds.) Wesleyan University Press, Middletown, Conn.
Rozeboom, W.: 1960, ‘The Fallacy of the Null Hypothesis Significance Test’, Psych. Bull. 57, 416–428 (reprinted in Morrison and Henkel).
Savage, L. J.: 1961, ‘The Foundations of Statistics Reconsidered’, Proc. Fourth Berkeley Symposium on Mathematical Statistics and Probability, University of California Press, Berkeley (reprinted in Kyburg and Smokier).
Savage, L. J., et al.: 1962, The Foundations of Statistical Inference, Methuen, London.
Spielman, S.: 1973, ‘A Refutation of the Neyman-Pearson Theory of Testing’, Brit. J. Phil. Sci. 24, 201–222.
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© 1977 D. Reidel Publishing Company, Dordrecht, Holland
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Rosenkrantz, R.D. (1977). Testing. In: Inference, Method and Decision. Synthese Library, vol 115. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1237-9_10
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DOI: https://doi.org/10.1007/978-94-010-1237-9_10
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