Skip to main content
Log in

Did Pearson reject the Neyman-Pearson philosophy of statistics?

  • Published:
Synthese Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

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.

    Google Scholar 

  • Barnard, G. A.: 1985, A Coherent View of Statistical Inference, Technical Report Series, University of Waterloo, Waterloo Ont.

    Google Scholar 

  • Birnbaum, A.: 1962, ‘On the Foundations of Statistical Inference’, Journal of the American Statistical Association 57, 269–326.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Edwards, A. W. F.: 1972, Likelihood, Cambridge University Press, Cambridge.

    Google Scholar 

  • Fetzer, J. H.: 1981, Scientific Knowledge, D. Reidel, Dordrecht.

    Google Scholar 

  • Fisher, R. A.: 1955, ‘Statistical Methods and Scientific Induction’, Journal of the Royal Statistical Society B17, 69–78.

    Google Scholar 

  • Giere, R. N.: 1969, ‘Bayesian Statistics and Biased Procedures’, Synthese 20, 371–87.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Hacking, I.: 1965, Logic of Statistical Inference, Cambridge University Press, Cambridge.

    Google Scholar 

  • Hacking, I.: 1972, ‘Likelihood’, British Journal for the Philosophy of Science 23, 132–37.

    Google Scholar 

  • 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.

    Google Scholar 

  • Howson, C. and Urbach, P.: 1989, Scientific Reasoning: The Bayesian Approach, Open Court, La Salle.

    Google Scholar 

  • Kempthorne, O. and Folks, L.: 1971, Probability, Statistics, and Data Analysis, Iowa State University Press, Ames.

    Google Scholar 

  • 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.

    Google Scholar 

  • Kyburg, H. E. Jr.: 1974, The Logical Foundations of Statistical Inference, D. Reidel, Dordrecht.

    Google Scholar 

  • LeCam, L.: 1977, ‘A Note on Metastatistics or ‘An Essay Toward Stating a Problem in the Doctrine of Chances’’, Synthese 36, 133–60.

    Google Scholar 

  • Levi, I.: 1980, The Enterprise of Knowledge, MIT Press, Cambridge MA.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Mayo, D.: 1981, ‘Testing Statistical Testing’, in J. C. Pitt (ed.), Philosophy in Economics, D. Reidel, Dordrecht, pp. 175–203.

    Google Scholar 

  • 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.

    Google Scholar 

  • Mayo, D.: 1983, ‘An Objective Theory of Statistical Testing’, Synthese 57, 297–340.

    Google Scholar 

  • Mayo, D.: 1985, ‘Behavioristic, Evidentialist, and Learning Models of Statistical Testing’, Philosophy of Science 52, 493–516.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • Neyman, J.: 1952, Lectures and Conferences on Mathematical Statistics and Probability, 2d edn., Graduate School of U.S. Department of Agriculture, Washington DC.

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Google Scholar 

  • Pearson, E. S.: 1955, ‘Statistical Concepts in Their Relation to Reality’, Journal of the Royal Statistical Society B17, 204–07.

    Google Scholar 

  • 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).

    Google Scholar 

  • 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).

    Google Scholar 

  • Popper, L.: 1972, Objective Knowledge, Oxford University Press, Oxford.

    Google Scholar 

  • Pratt, J. W.: 1977, “Decisions' as Statistical Evidence and Birnbaum's ‘Confidence Concept”, Synthese 36, 59–69.

    Google Scholar 

  • Rosenkrantz, R. D.: 1977, Inference, Method and Decision, D. Reidel, Dordrecht.

    Google Scholar 

  • Seidenfeld, T.: 1979, Philosophical Problems of Statistical Inference, D. Reidel, Dordrecht.

    Google Scholar 

  • Spielman, S.: 1972, ‘A Reflection on the Neyman-Pearson Theory of Testing’, British Journal for the Philosophy of Science 24, 201–22.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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

Reprints 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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00485352

Keywords

Navigation