Abstract
I document some of the main evidence showing that E. S. Pearson rejected the key features of the behavioral-decision philosophy that became associated with the Neyman-Pearson Theory of statistics (NPT). I argue that NPT principles arose not out of behavioral aims, where the concern is solely with behaving correctly sufficiently often in some long run, but out of the epistemological aim of learning about causes of experimental results (e.g., distinguishing genuine from spurious effects). The view Pearson did hold gives a deeper understanding of NPT tests than their typical formulation as ‘accept-reject routines’, against which criticisms of NPT are really directed. The ‘Pearsonian’ view that emerges suggests how NPT tests may avoid these criticisms while still retaining what is central to these methods: the control of error probabilities.
Similar content being viewed by others
References
Armitage, P.: 1961, ‘Consistency in Statistical Inference and Decision’, Journal of the Royal Statistical Society B23, 1–37.
Barnard, G. A.: 1985, A Coherent View of Statistical Inference, Technical Report Series, University of Waterloo, Waterloo Ont.
Birnbaum, A.: 1962, ‘On the Foundations of Statistical Inference’, Journal of the American Statistical Association 57, 269–326.
Birnbaum, A.: 1969, ‘Concepts of Statistical Evidence’, in S. Morgenbesser, P. Suppes, and M. White (eds.), Philosophy, Science, and Method: Essays in Honor of Ernest Nagel, St. Martin's Press, New York, pp. 112–143.
Birnbaum, A.: 1977, ‘The Neyman-Pearson Theory as Decision Theory, and as Inference Theory; with a Criticism of the Lindley-Savage Argument for Bayesian Theory’, Synthese 36, 19–49.
Edwards, A. W. F.: 1972, Likelihood, Cambridge University Press, Cambridge.
Fetzer, J. H.: 1981, Scientific Knowledge, D. Reidel, Dordrecht.
Fisher, R. A.: 1955, ‘Statistical Methods and Scientific Induction’, Journal of the Royal Statistical Society B17, 69–78.
Giere, R. N.: 1969, ‘Bayesian Statistics and Biased Procedures’, Synthese 20, 371–87.
Giere, R. N.: 1976, ‘Empirical Probability, Objective Statistical Methods, and Scientific Inquiry’, in W. L. Harper and C. A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. II, D. Reidel, Dordrecht, pp. 63–101.
Good, I. J.: 1981, ‘Some Logic and History of Hypothesis Testing’, in J. C. Pitt (ed.), Philosophy in Economics, D. Reidel, Dordrecht, pp. 149–74.
Hacking, I.: 1965, Logic of Statistical Inference, Cambridge University Press, Cambridge.
Hacking, I.: 1972, ‘Likelihood’, British Journal for the Philosophy of Science 23, 132–37.
Hacking, I.: 1980, ‘The Theory of Probable Inference: Neyman, Peirce and Braithwaite’, in D. H. Mellor (ed.), Science, Belief and Behavior: Essays in Honor of R. B. Braithwaite, Cambridge University Press, Cambridge, pp. 141–60.
Howson, C. and Urbach, P.: 1989, Scientific Reasoning: The Bayesian Approach, Open Court, La Salle.
Kempthorne, O. and Folks, L.: 1971, Probability, Statistics, and Data Analysis, Iowa State University Press, Ames.
Kyburg, H. E. Jr.: 1971, ‘Probability and Informative Inference’, in V. P. Godambe and D. A. Sprott (eds.), Foundations of Statistical Inference, Holt, Rinehart and Winston of Canada, Toronto, pp. 82–103.
Kyburg, H. E. Jr.: 1974, The Logical Foundations of Statistical Inference, D. Reidel, Dordrecht.
LeCam, L.: 1977, ‘A Note on Metastatistics or ‘An Essay Toward Stating a Problem in the Doctrine of Chances’’, Synthese 36, 133–60.
Levi, I.: 1980, The Enterprise of Knowledge, MIT Press, Cambridge MA.
Lindley, D. V.: 1971, ‘The Estimation of Many Parameters’, in V. P. Godambe and D. A. Sprott (eds.), Foundations of Statistical Inference, Holt, Rinehart and Winston of Canada, Toronto, pp. 435–47.
Lindley, D. V.: 1976, ‘Bayesian Statistics’, in W. L. Harper and C. A. Hooker (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. II, D. Reidel, Dordrecht, pp. 353–62.
Mayo, D.: 1981, ‘Testing Statistical Testing’, in J. C. Pitt (ed.), Philosophy in Economics, D. Reidel, Dordrecht, pp. 175–203.
Mayo, D.: 1982, ‘On After-Trial Criticisms of Neyman-Pearson Theory of Statistics’, in P. Asquith and T. Nickles (eds.), PSA 1982, Vol. 1, PSA, East Lansing, pp. 145–58.
Mayo, D.: 1983, ‘An Objective Theory of Statistical Testing’, Synthese 57, 297–340.
Mayo, D.: 1985, ‘Behavioristic, Evidentialist, and Learning Models of Statistical Testing’, Philosophy of Science 52, 493–516.
Mayo, D.: 1988, ‘Toward a More Objective Understanding of the Evidence of Carcinogenic Risk’, in A. Fine and J. Leplin (eds.), PSA 1988, Vol. 2, PSA, East Lansing, pp. 489–503.
Mayo, D.: 1991, ‘Novel Evidence and Severe Tests’, Philosophy of Sciences 58 (December).
Neyman, J.: 1950, First Course in Probability and Statistics, Henry Holt, New York.
Neyman, J.: 1952, Lectures and Conferences on Mathematical Statistics and Probability, 2d edn., Graduate School of U.S. Department of Agriculture, Washington DC.
Neyman, J.: 1971, ‘Foundations of Behavioristic Statistics’, in V. P. Godambe and D. A. Sprott (eds.), Foundations of Statistical Inference, Holt, Rinehart and Winston of Canada, Toronto, pp. 1–13 (Comments and Reply, pp. 14–19).
Neyman, J. and Pearson, E. S.: 1928, ‘On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference. Part I’, Biometrika 20A, 175–240 (reprinted in Joint Statistical Papers, University of California Press, Berkeley, 1967, pp. 1–66).
Neyman, J. and Pearson, E. S.: 1933, ‘On the Problem of the Most Efficient Tests of Statistical Hypotheses’, in Philosophical Transactions of the Royal Society A231, 289–337 (reprinted in Joint Statistical Papers, University of California Press, Berkeley, 1967, pp. 203–39).
Pearson, E. S.: 1947, ‘The Choice of Statistical Tests Illustrated on the Interpretation of Data Classed in a 2 × 2 Table’, Biometrika 34, 139–67 (reprinted in The Selected Papers of E. S. Pearson, University of California Press, Berkeley, 1966, pp. 169–97).
Pearson, E. S.: 1950, ‘On Questions Raised by the Combination of Tests Based on Discontinuous Distributions’, Biometrika 37, 383–98 (reprinted in The Selected Papers of E. S. Pearson, University of California Press, Berkeley, 1966, pp. 217–32).
Pearson, E. S.: 1955, ‘Statistical Concepts in Their Relation to Reality’, Journal of the Royal Statistical Society B17, 204–07.
Pearson, E. S.: 1962, ‘Some Thoughts on Statistical Inference’, Annals of Mathematical Statistics 33, 394–403 (reprinted in The Selected Papers of E. S. Pearson, University of California Press, Berkeley, 1966, pp. 276–83).
Pearson, E. S. and Wilks, S.: 1933, ‘Methods of Statistical Analysis Appropriate for k Samples of Two Variables’, Biometrika 25, 353–78 (reprinted in The Selected Papers of E. S. Pearson, University of California Press, Berkeley, 1966, pp. 81–106).
Popper, L.: 1972, Objective Knowledge, Oxford University Press, Oxford.
Pratt, J. W.: 1977, “Decisions' as Statistical Evidence and Birnbaum's ‘Confidence Concept”, Synthese 36, 59–69.
Rosenkrantz, R. D.: 1977, Inference, Method and Decision, D. Reidel, Dordrecht.
Seidenfeld, T.: 1979, Philosophical Problems of Statistical Inference, D. Reidel, Dordrecht.
Spielman, S.: 1972, ‘A Reflection on the Neyman-Pearson Theory of Testing’, British Journal for the Philosophy of Science 24, 201–22.
Author information
Authors and Affiliations
Additional information
A portion of this research was carried out during tenure of a National Endowment for the Humanities Summer Stipend Fellowship; I gratefully acknowledge that support. A version of this paper was presented at the 1987 meeting of the Society for Exact Philosophy. This paper benefited from discussions and communications with George Barnard and Isaac Levi. I thank Harlan Miller for helpful comments on earlier drafts.
Rights and permissions
About this article
Cite this article
Mayo, D.G. Did Pearson reject the Neyman-Pearson philosophy of statistics?. Synthese 90, 233–262 (1992). https://doi.org/10.1007/BF00485352
Issue Date:
DOI: https://doi.org/10.1007/BF00485352