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7 - New Perspectives on (Some Old) Problems of Frequentist Statistics

Published online by Cambridge University Press:  29 January 2010

By
Deborah G. Mayo ,
David Cox  and
Aris Spanos
Edited by
Deborah G. Mayo  and
Aris Spanos
Deborah G. Mayo
Affiliation:
Virginia Polytechnic Institute and State University
Aris Spanos
Affiliation:
Virginia Polytechnic Institute and State University
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Summary

Statistics and Inductive Philosophy

What Is the Philosophy of Statistics?

The philosophical foundations of statistics may be regarded as the study of the epistemological, conceptual, and logical problems revolving around the use and interpretation of statistical methods, broadly conceived. As with other domains of philosophy of science, work in statistical science progresses largely without worrying about “philosophical foundations.” Nevertheless, even in statistical practice, debates about the different approaches to statistical analysis may influence and be influenced by general issues of the nature of inductive-statistical inference, and thus are concerned with foundational or philosophical matters. Even those who are largely concerned with applications are often interested in identifying general principles that underlie and justify the procedures they have come to value on relatively pragmatic grounds. At one level of analysis at least, statisticians and philosophers of science ask many of the same questions.

  • What should be observed and what may justifiably be inferred from the resulting data?

  • How well do data confirm or fit a model?

  • What is a good test?

  • Does failure to reject a hypothesis H constitute evidence confirming H?

  • How can it be determined whether an apparent anomaly is genuine? How can blame for an anomaly be assigned correctly?

  • Is it relevant to the relation between data and a hypothesis if looking at the data influences the hypothesis to be examined?

  • How can spurious relationships be distinguished from genuine regularities?

  • How can a causal explanation and hypothesis be justified and tested?

  • […]

Type
Chapter
Information
Error and Inference
Recent Exchanges on Experimental Reasoning, Reliability, and the Objectivity and Rationality of Science
 , pp. 247 - 330
Publisher: Cambridge University Press
Print publication year: 2009

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References

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
Carnap, R. (1962), Logical Foundations of Probability, University of Chicago Press, Chicago.Google Scholar
Cochran, W.G. (1965), “The Planning of Observational Studies in Human Populations,” (with discussion). Journal of the Royal Statististical Society A, 128: 234–65.CrossRefGoogle Scholar
Cox, D.R. (1958), “Some Problems Connected with Statistical Inference,” Annals of Mathematical Statistics, 29: 357–72.CrossRefGoogle Scholar
Cox, D.R. (1977), “The Role of Significance Tests (with Discussion),” Scandinavian Journal of Statistics, 4: 49–70.Google Scholar
Cox, D.R., and Hinkley, , , D.V. (1974), Theoretical Statistics, Chapman and Hall, London.CrossRefGoogle Scholar
Cox, D.R., and Snell, , , E.J. (1974), “The Choice of Variables in Observational Studies,” Journal of the Royal Statististical Society C, 23: 51–9.Google Scholar
Finetti, B. (1974), Theory of Probability, 2 Vols. English translation from Italian, Wiley, New York.Google Scholar
Fisher, R.A. (1935a), Design of Experiments, Oliver and Boyd, Edinburgh.Google Scholar
Fisher, R.A. (1935b), “The Logic of Inductive Inference,” Journal of the Royal Statistical Society, 98: 39–54.CrossRefGoogle Scholar
Gibbons, J.D., and Pratt, , , J.W. (1975), “P-Values: Interpretation and Methodology,” American Statistician, 29: 20–5.Google Scholar
Jeffreys, H. (1961), Theory of Probability, 3rd ed., Oxford University Press, Clarendon, Oxford.Google Scholar
Kempthorne, O. (1976), “Statistics and the Philosophers,” pp. 273–314 in Harper, W.L. and Hooker, C.A. (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, vol. II: Foundations and Philosophy of Statistical Inference, D. Reidel, Dordrecht, Holland.CrossRefGoogle Scholar
Keynes, J.M. (1921), A Treatise on Probability (reprinted 1952), St. Martin's Press, New York.Google Scholar
Lehmann, E.L. (1993), “The Fisher and Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?” Journal of the American Statistical Association, 88: 1242–9.CrossRefGoogle Scholar
Lehmann, E.L. (1995), “Neyman's Statistical Philosophy,” Probability and Mathematical Statistics, 15: 29–36.Google Scholar
Mayo, D.G. (1996), Error and the Growth of Experimental Knowledge, University of Chicago Press, Chicago.CrossRefGoogle Scholar
Mayo, D.G., and Kruse, M. (2001), “Principles of Inference and Their Consequences,” pp. 381–403 in Cornfield, D. and Williamson, J. (eds.), Foundations of Bayesianism, Kluwer Academic, Dordrecht, The Netherlands.CrossRefGoogle Scholar
Mayo, D.G., and Spanos, A. (2006), “Severe Testing as a Basic Concept in a Neyman-Pearson Philosophy of Induction,” British Journal of Philosophy of Science, 57: 323–357.CrossRefGoogle Scholar
Mill, J.S. (1888), A System of Logic, 8th ed., Harper and Bros., New York.Google Scholar
Morrison, D., and Henkel, R. (eds.) (1970), The Significance Test Controversy, Aldine, Chicago.
Neyman, J. (1955), “The Problem of Inductive Inference,” Communications in Pure and Applied Mathematics, 8: 13–46.Google Scholar
Neyman, J. (1957), “Inductive Behavior as a Basic Concept of Philosophy of Science,” International Statistical Review, 25: 7–22.CrossRefGoogle Scholar
Pearson, E.S. (1955), “Statistical Concepts in Their Relation to Reality,” Journal of the Royal Statistical Society B, 17: 204–7.Google Scholar
Pierce, C.S. (1931–1935). Collected Papers, vols. 1–6, Hartshorne, and Weiss, P. (eds.), Harvard University Press, Cambridge.Google Scholar
Popper, K. (1959), The Logic of Scientific Discovery, Basic Books, New York.Google Scholar
Savage, L.J. (1964), “The Foundations of Statistics Reconsidered,” pp. 173–188 in Kyburg, H.E. and Smokler, H.E. (eds.), Studies in Subjective Probability, Wiley, New York.Google Scholar
Shaffer, J.P. (2006), “Recent Developments Towards Optimality in Multiple Hypothesis Testing,” pp. 16–32 in Rojo, J. (ed.), Optimality: The Second Erich L. Lehmann Symposium, Lecture Notes-Monograph Series, vol. 49, Institute of Mathematical Statistics, Beachwood, OH.CrossRefGoogle Scholar
Spanos, A. (2000), “Revisiting Data Mining: ‘Hunting’ with or without a License,” Journal of Economic Methodology, 7: 231–64.CrossRefGoogle Scholar
Whewell, W. (1847), The Philosophy of the Inductive Sciences. Founded Upon Their History. 2nd ed., vols. 1 and 2 (reprinted 1967). Johnson Reprint, London.Google Scholar
Will, C. (1993), Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Yates, F. (1951), “The Influence of Statistical Methods for Research Workers on the Development of the Science of Statistics,” Journal of the American Statistical Association, 46: 19–34.Google Scholar
Berger, J. (2004), “The Case for Objective Bayesian Analysis,” Bayesian Analysis, 1: 1–17.Google Scholar
Bernardo, J.M. (2005), “Reference Analysis,” Handbook of Statistics, vol. 35, Elsevier, Amsterdam.Google Scholar
Birnbaum, A. (1962), “On the Foundations of Statistical Inference,” Journal of the American Statistical Association, 57: 269–306.CrossRefGoogle Scholar
Cox, D.R. (1958), “Some Problems Connected with Statistical Inference,” Annals of Mathematical Statistics, 29: 357–72.CrossRefGoogle Scholar
Cox, D.R. (1990), “Role of Models in Statistical Analysis,” Statistical Science, 5: 169–74.Google Scholar
Cox, D.R. (2006), Principles of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Cox, D.R., and Brandwood, L. (1959), “On a Discriminatory Problem Connected with the Works of Plato,” Journal of the Royal Statistical Society B, 21: 195–200.Google Scholar
Cox, D.R. and Hinkley, D.V. (1974), Theoretical Statistics, Chapman and Hall, London.CrossRefGoogle Scholar
Dawid, A.P., Stone, M. and Zidek, J.V. (1973), “Marginalization Paradoxes in Bayesian and Structural Inference,” (with discussion), Journal of the Royal Statistical Society B, 35: 189–233.Google Scholar
Fisher, R.A. (1935), Design of Experiments, Oliver and Boyd, Edinburgh.Google Scholar
Hacking, I. (1965), Logic of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Lehmann, E.L. (1986), Testing Statistical Hypotheses, 2nd ed., Wiley, New York.CrossRefGoogle Scholar
Mayo, D.G. and Cox, D.R. (2006), “Frequentist Statistics as a Theory of Inductive Inference,” in Rojo, J. (ed.), Optimality: The Second Erich L. Lehmann Symposiun, Lecture Notes-Monograph Series, Institute of Mathematical Statistics (IMS), 49: 77–97.CrossRefGoogle Scholar
Berger, J.O., and Wolpert, R.L. (1988), The Likelihood Principle, California Institute of Mathematical Statistics, Hayward, CA.Google Scholar
Birnbaum, A. (1962), “On the Foundations of Statistical Inference” (with discussion), Journal of the American Statistical Association, 57: 269–326.CrossRefGoogle Scholar
Birnbaum, A. (1970), “More on Concepts of Statistical Evidence,” Journal of the American Statistical Association, 67: 858–61.CrossRefGoogle Scholar
Casella, G., and Berger, R.L. (2002), Statistical Inference, 2nd ed., Duxbury, Pacific Grove, CA.Google Scholar
Cox, D.R. (1977), “The Role of Significance Tests” (with discussion), Scandinavian Journal of Statistics, 4: 49–70.Google Scholar
Cox, D.R. and Hinkley, D.V. (1974), Theoretical Statistics, Chapman and Hall, London.CrossRefGoogle Scholar
Durbin, J. (1970), “On Birnbaum's Theorem and the Relation between Sufficiency, Conditionality and Likelihood,” Journal of the American Statistical Association, 65: 395–8.CrossRefGoogle Scholar
Evans, M., Fraser, D.A.S., and Monette, G. (1986), “Likelihood,” Canadian Journal of Statistics, 14: 180–90.Google Scholar
Lee, P.M. (2004), Bayesian Statistics: an Introduction, 3rd ed., Hodder Arnold, New York.Google Scholar
Lehmann, E.L. (1981), “An Interpretation of Completeness in Basu's Theorem,” Journal of the American Statistical Association, 76: 335–40.CrossRefGoogle Scholar
Mayo, D.G. and Cox, D.R. (2006), “Frequentist Statistics as a Theory of Inductive Inference,” in Rojo, J. (ed.), Optimality: The Second Erich L. Lehmann Symposium, Lecture Notes-Monograph Series, Institute of Mathematical Statistics (IMS), Vol. 49: 77–97.CrossRefGoogle Scholar
Robins, J., and Wasserman, , , L. (2000), “Conditioning, Likelihood, and Coherence: A Review of Some Foundational Concepts,” Journal of the American Statistical Association, 95: 1340–6.CrossRefGoogle Scholar
Royall, R.M. (1997), Statistical Evidence: A Likelihood Paradigm, Chapman & Hall, London.Google Scholar
Savage, L., ed. (1962a), The Foundations of Statistical Inference: A Discussion. Methuen, London.
Savage, L. (1962b), “‘Discussion on Birnbaum (1962),” Journal of the American Statistical Association, 57: 307–8.CrossRefGoogle Scholar
Berger, J. (2003), “Could Fisher, Jeffreys and Neyman Have Agreed on Testing?” Statistical Science, 18: 1–12.CrossRefGoogle Scholar
Berger, J. (2004), “The Case for Objective Bayesian Analysis,” Bayesian Analysis, 1: 1–17.Google Scholar
Berger, J., and Wolpert, R. (1988), The Likelihood Principle, 2nd ed., Institute of Mathematical Statistics, Hayward, CA.Google Scholar
Birnbaum, A. (1962), “On the Foundations of Statistical Inference” (with discussion), Journal of the American Statistical Association, 57: 269–306.CrossRefGoogle Scholar
Cox, D.R. (1958), “Some Problems Connected with Statistical Inference,” Annals of Mathematical Statistics, 29: 357–72.CrossRefGoogle Scholar
Cox, D.R. (1990), “Role of Models in Statistical Analysis,” Statistical Science, 5: 169–74.CrossRefGoogle Scholar
Cox, D.R. (2006), Principles of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Cox, D.R., and Hinkley, D.V. (1974), Theoretical Statistics, Chapman & Hall, London.CrossRefGoogle Scholar
Fisher, R.A. (1922), “The Mathematical Foundations of Theoretical Statistics,” Philosophical Transactions of the Royal Society A, 222: 309–68.CrossRefGoogle Scholar
Fisher, R.A. (1925), “Theory of Statistical Estimation,” Proceedings of the Cambridge Philosophical Society, 22: 700–25.CrossRefGoogle Scholar
Fisher, R.A. (1934), “Two New Properties of Maximum Likelihood,” Proceedings of the Royal Statistical Society A, 144: 285–307.CrossRefGoogle Scholar
Fisher, R.A. (1935), The Design of Experiments, Oliver and Boyd, Edinburgh.Google Scholar
Fisher, R.A. (1955) “Statistical Methods and Scientific Induction,” Journal of the Royal Statistical Society B, 17: 69–78.Google Scholar
Ghosh, J.K., Delampady, M., and Samanta, T. (2006), An Introduction to Bayesian Analysis: Theory and Methods, Springer, New York.Google Scholar
Giere, R.N. (1969), “Bayesian Statistics and Biased Procedures,” Synthese, 20: 371–87.CrossRefGoogle Scholar
Gigerenzer, G. (1993), “The Superego, the Ego, and the Id in Statistical Reasoning,” pp. 311–39 in Keren, G. and Lewis, C. (eds.), A Handbook of Data Analysis in the Behavioral Sciences: Methodological Issues, Lawrence Erlbaum Associates, Hillsdale, NJ.Google Scholar
Godambe, V.P., and Sprott, D.A. (eds.) (1971), Foundations of Statistical Inference: a Symposium, Holt, Rinehart and Winston, Toronto.
Hacking, I. (1965), Logic of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Hand, D.J., and Herzberg, A.M. (2005), Selected Statistical Papers of Sir David Cox, vols. 1–2, Cambridge University Press, Cambridge.Google Scholar
Harper, W.L., and Hooker, C.A. (eds.) (1976), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, Vol. II: Foundations and Philosophy of Statistical Inference, Reidel, Dordrecht, The Netherlands.
Hendry, D.F. (1995), Dynamic Econometrics, Oxford University Press, Oxford.CrossRefGoogle Scholar
Howson, C., and Urbach, P. (1993), Scientific Reasoning: The Bayesian Approach, 2nd ed., Open Court, Chicago.Google Scholar
Mayo, D.G. (1981), “Testing Statistical Testing,” pp. 175–230 in Pitt, J. (ed.), Philosophy in Economics, D. Reidel, Dordrecht.CrossRefGoogle Scholar
Mayo, D.G. (1996), Error and the Growth of Experimental Knowledge, University of Chicago Press, Chicago.CrossRefGoogle Scholar
Mayo, D.G. (2005), “Philosophy of Statistics,” pp. 802–15 in Sarkar, S. and Pfeifer, J. (eds.), Philosophy of Science: An Encyclopedia, Routledge, London.Google Scholar
Mayo, D.G., and Spanos, , , A. (2004), “Methodology in Practice: Statistical Misspecification Testing,” Philosophy of Science, 71: 1007–25.CrossRefGoogle Scholar
Mayo, D.G. and Spanos, , , A. (2006), “Severe Testing as a Basic Concept in a Neyman-Pearson Philosophy of Induction,” British Journal for the Philosophy of Science, 57: 323–57.CrossRefGoogle Scholar
Neyman, J. (1937), “Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability,” Philosophical Transactions of the Royal Statistical Society of London A, 236: 333–80.CrossRefGoogle Scholar
Neyman, J. (1956), “Note on an Article by Sir Ronald Fisher,” Journal of the Royal Statistical Society B, 18: 288–94.Google Scholar
Neyman, J. (1957), “Inductive Behavior as a Basic Concept of Philosophy of Science,” Revue de L'Institut International de Statistique, 25: 7–22.CrossRefGoogle Scholar
Neyman, J., and Pearson, , , E.S. (1933), “On the Problem of the Most Efficient Tests of Statistical Hypotheses,” Philosophical Transactions of the Royal Society A, 231: 289–337.CrossRefGoogle Scholar
Pearson, E.S. (1955), “Statistical Concepts in Their Relation to Reality,” Journal of the Royal Statistical Society B, 17: 204–7.Google Scholar
Savage, L., ed. (1962a), The Foundations of Statistical Inference: A Discussion. Methuen, London.
Savage, L. (1962b), “Discussion” on Birnbaum (1962), Journal of the American Statistical Association, 57: 307–8.CrossRefGoogle Scholar
Seidenfeld, T. (1979), Philosophical Problems of Statistical Inference: Learning from R.A. Fisher, Reidel, Dordrecht, The Netherlands.Google Scholar
Spanos, A. (1986), Statistical Foundations of Econometric Modelling, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Spanos, A. (1999), Probability Theory and Statistical Inference: Econometric Modeling with Observational Data, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Spanos, A. (2005), “Misspecification, Robustness and the Reliability of Inference: The Simple t-Test in the Presence of Markov Dependence,” Working Paper, Virginia Tech.
Spanos, A. (2007a), “Sufficiency and Ancillarity Revisited: Testing the Validity of a Statistical Model,” Working Paper, Virginia Tech.
Spanos, A. (2007b), “Revisiting the Welch Uniform Model: A Case for Conditional Inference?” Working Paper, Virginia Tech.
Spanos, A. (2008), “Stephen Ziliak and Deirdre McCloskey's The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives,” Erasmus Journal for Philosophy and Economics, 1: 154–64.CrossRefGoogle Scholar
Welch, B.L. (1939), “On Confidence Limits and Sufficiency, and Particular Reference to Parameters of Location,” Annals of Mathematical Statistics, 10: 58–69.CrossRefGoogle Scholar
Young, G.A., and Smith, R.L. (2005), Essentials of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Ziliak, S.T., and McCloskey, D.N. (2008), The Cult of Significance: How the Standard Error Costs Us Jobs, Justice and Lives, University of Michigan Press, Ann Arbor, MI.Google Scholar
Bartz-Beielstein, T. (2008), “How Experimental Algorithmics Can Benefit From Mayo's Extensions To Neyman-Pearson Theory Of Testing,” Synthese (Error and Methodology in Practice: Selected Papers from ERROR 2006), vol. 163(3): 385–96.Google Scholar
Casella, G. (2004), “Commentary on Mayo,” pp. 99–101 in Taper, M.L. and Lele, S.R. (eds.), The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations, University of Chicago Press, Chicago.Google Scholar
Mayo, D.G. (2003), “Severe Testing as a Guide for Inductive Learning,” pp. 89–118 in Kyburg, Jr H.. and Thalos, M. (eds.), Probability Is the Very Guide of Life: The Philosophical Uses of Chance, Open Court, Chicago and La Salle, Illinois.Google Scholar
Mayo, D.G. (2004), “An Error-Statistical Philosophy of Evidence,” pp. 79–97 and “Rejoinder” pp. 101–15, in Taper, M.L. and Lele, S.R. (eds.), The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations, University of Chicago Press, Chicago.CrossRefGoogle Scholar
Taper, M.L. and Lele, S.R. (eds.) (2004), The Nature of Scientific Evidence: Statistical, Philosophical, and Empirical Considerations, University of Chicago Press, Chicago.CrossRef
Altman, D.G., Machin, D., Bryant, T.N., and Gardner, M.J. (2000), Statistics with Confidence, (eds.), British Medical Journal Books, Bristol.Google Scholar
Barnett, V. (1982), Comparative Statistical Inference, 2nd ed., John Wiley & Sons, New York.Google Scholar
Cohen, J. (1994), “The Earth is Round (p < .05),” American Psychologist, 49:997–1003.CrossRefGoogle Scholar
Harlow, L.L., Mulaik, S.A., and Steiger, J.H. (1997) What If There Were No Significance Tests? Erlbaum, Mahwah, NJ.Google Scholar
Lieberman, B. (1971), Contemporary Problems in Statistics: a Book of Readings for the Behavioral Sciences, Oxford University Press, Oxford.Google Scholar
Morrison, D.E., and Henkel, R.E. (1970), The Significance Test Controversy: A Reader, Aldine, Chicago.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.CrossRefGoogle Scholar
Carnap, R. (1962), Logical Foundations of Probability, University of Chicago Press, Chicago.Google Scholar
Cochran, W.G. (1965), “The Planning of Observational Studies in Human Populations,” (with discussion). Journal of the Royal Statististical Society A, 128: 234–65.CrossRefGoogle Scholar
Cox, D.R. (1958), “Some Problems Connected with Statistical Inference,” Annals of Mathematical Statistics, 29: 357–72.CrossRefGoogle Scholar
Cox, D.R. (1977), “The Role of Significance Tests (with Discussion),” Scandinavian Journal of Statistics, 4: 49–70.Google Scholar
Cox, D.R., and Hinkley, , , D.V. (1974), Theoretical Statistics, Chapman and Hall, London.CrossRefGoogle Scholar
Cox, D.R., and Snell, , , E.J. (1974), “The Choice of Variables in Observational Studies,” Journal of the Royal Statististical Society C, 23: 51–9.Google Scholar
Finetti, B. (1974), Theory of Probability, 2 Vols. English translation from Italian, Wiley, New York.Google Scholar
Fisher, R.A. (1935a), Design of Experiments, Oliver and Boyd, Edinburgh.Google Scholar
Fisher, R.A. (1935b), “The Logic of Inductive Inference,” Journal of the Royal Statistical Society, 98: 39–54.CrossRefGoogle Scholar
Gibbons, J.D., and Pratt, , , J.W. (1975), “P-Values: Interpretation and Methodology,” American Statistician, 29: 20–5.Google Scholar
Jeffreys, H. (1961), Theory of Probability, 3rd ed., Oxford University Press, Clarendon, Oxford.Google Scholar
Kempthorne, O. (1976), “Statistics and the Philosophers,” pp. 273–314 in Harper, W.L. and Hooker, C.A. (eds.), Foundations of Probability Theory, Statistical Inference, and Statistical Theories of Science, vol. II: Foundations and Philosophy of Statistical Inference, D. Reidel, Dordrecht, Holland.CrossRefGoogle Scholar
Keynes, J.M. (1921), A Treatise on Probability (reprinted 1952), St. Martin's Press, New York.Google Scholar
Lehmann, E.L. (1993), “The Fisher and Neyman-Pearson Theories of Testing Hypotheses: One Theory or Two?” Journal of the American Statistical Association, 88: 1242–9.CrossRefGoogle Scholar
Lehmann, E.L. (1995), “Neyman's Statistical Philosophy,” Probability and Mathematical Statistics, 15: 29–36.Google Scholar
Mayo, D.G. (1996), Error and the Growth of Experimental Knowledge, University of Chicago Press, Chicago.CrossRefGoogle Scholar
Mayo, D.G., and Kruse, M. (2001), “Principles of Inference and Their Consequences,” pp. 381–403 in Cornfield, D. and Williamson, J. (eds.), Foundations of Bayesianism, Kluwer Academic, Dordrecht, The Netherlands.CrossRefGoogle Scholar
Mayo, D.G., and Spanos, A. (2006), “Severe Testing as a Basic Concept in a Neyman-Pearson Philosophy of Induction,” British Journal of Philosophy of Science, 57: 323–357.CrossRefGoogle Scholar
Mill, J.S. (1888), A System of Logic, 8th ed., Harper and Bros., New York.Google Scholar
Morrison, D., and Henkel, R. (eds.) (1970), The Significance Test Controversy, Aldine, Chicago.
Neyman, J. (1955), “The Problem of Inductive Inference,” Communications in Pure and Applied Mathematics, 8: 13–46.CrossRefGoogle Scholar
Neyman, J. (1957), “Inductive Behavior as a Basic Concept of Philosophy of Science,” International Statistical Review, 25: 7–22.CrossRefGoogle Scholar
Pearson, E.S. (1955), “Statistical Concepts in Their Relation to Reality,” Journal of the Royal Statistical Society B, 17: 204–7.Google Scholar
Pierce, C.S. (1931–1935). Collected Papers, vols. 1–6, Hartshorne, and Weiss, P. (eds.), Harvard University Press, Cambridge.Google Scholar
Popper, K. (1959), The Logic of Scientific Discovery, Basic Books, New York.Google Scholar
Savage, L.J. (1964), “The Foundations of Statistics Reconsidered,” pp. 173–188 in Kyburg, H.E. and Smokler, H.E. (eds.), Studies in Subjective Probability, Wiley, New York.Google Scholar
Shaffer, J.P. (2006), “Recent Developments Towards Optimality in Multiple Hypothesis Testing,” pp. 16–32 in Rojo, J. (ed.), Optimality: The Second Erich L. Lehmann Symposium, Lecture Notes-Monograph Series, vol. 49, Institute of Mathematical Statistics, Beachwood, OH.CrossRefGoogle Scholar
Spanos, A. (2000), “Revisiting Data Mining: ‘Hunting’ with or without a License,” Journal of Economic Methodology, 7: 231–64.CrossRefGoogle Scholar
Whewell, W. (1847), The Philosophy of the Inductive Sciences. Founded Upon Their History. 2nd ed., vols. 1 and 2 (reprinted 1967). Johnson Reprint, London.Google Scholar
Will, C. (1993), Theory and Experiment in Gravitational Physics, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Yates, F. (1951), “The Influence of Statistical Methods for Research Workers on the Development of the Science of Statistics,” Journal of the American Statistical Association, 46: 19–34.Google Scholar
Berger, J. (2004), “The Case for Objective Bayesian Analysis,” Bayesian Analysis, 1: 1–17.Google Scholar
Bernardo, J.M. (2005), “Reference Analysis,” Handbook of Statistics, vol. 35, Elsevier, Amsterdam.Google Scholar
Birnbaum, A. (1962), “On the Foundations of Statistical Inference,” Journal of the American Statistical Association, 57: 269–306.CrossRefGoogle Scholar
Cox, D.R. (1958), “Some Problems Connected with Statistical Inference,” Annals of Mathematical Statistics, 29: 357–72.CrossRefGoogle Scholar
Cox, D.R. (1990), “Role of Models in Statistical Analysis,” Statistical Science, 5: 169–74.CrossRefGoogle Scholar
Cox, D.R. (2006), Principles of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Cox, D.R., and Brandwood, L. (1959), “On a Discriminatory Problem Connected with the Works of Plato,” Journal of the Royal Statistical Society B, 21: 195–200.Google Scholar
Cox, D.R. and Hinkley, D.V. (1974), Theoretical Statistics, Chapman and Hall, London.CrossRefGoogle Scholar
Dawid, A.P., Stone, M. and Zidek, J.V. (1973), “Marginalization Paradoxes in Bayesian and Structural Inference,” (with discussion), Journal of the Royal Statistical Society B, 35: 189–233.Google Scholar
Fisher, R.A. (1935), Design of Experiments, Oliver and Boyd, Edinburgh.Google Scholar
Hacking, I. (1965), Logic of Statistical Inference, Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Lehmann, E.L. (1986), Testing Statistical Hypotheses, 2nd ed., Wiley, New York.CrossRefGoogle Scholar
Mayo, D.G. and Cox, D.R. (2006), “Frequentist Statistics as a Theory of Inductive Inference,” in Rojo, J. (ed.), Optimality: The Second Erich L. Lehmann Symposiun, Lecture Notes-Monograph Series, Institute of Mathematical Statistics (IMS), 49: 77–97.CrossRefGoogle Scholar
Berger, J.O., and Wolpert, R.L. (1988), The Likelihood Principle, California Institute of Mathematical Statistics, Hayward, CA.Google Scholar
Birnbaum, A. (1962), “On the Foundations of Statistical Inference” (with discussion), Journal of the American Statistical Association, 57: 269–326.CrossRefGoogle Scholar
Birnbaum, A. (1970), “More on Concepts of Statistical Evidence,” Journal of the American Statistical Association, 67: 858–61.CrossRefGoogle Scholar
Casella, G., and Berger, R.L. (2002), Statistical Inference, 2nd ed., Duxbury, Pacific Grove, CA.Google Scholar
Cox, D.R. (1977), “The Role of Significance Tests” (with discussion), Scandinavian Journal of Statistics, 4: 49–70.Google Scholar
Cox, D.R. and Hinkley, D.V. (1974), Theoretical Statistics, Chapman and Hall, London.CrossRefGoogle Scholar
Durbin, J. (1970), “On Birnbaum's Theorem and the Relation between Sufficiency, Conditionality and Likelihood,” Journal of the American Statistical Association, 65: 395–8.CrossRefGoogle Scholar
Evans, M., Fraser, D.A.S., and Monette, G. (1986), “Likelihood,” Canadian Journal of Statistics, 14: 180–90.Google Scholar
Lee, P.M. (2004), Bayesian Statistics: an Introduction, 3rd ed., Hodder Arnold, New York.Google Scholar
Lehmann, E.L. (1981), “An Interpretation of Completeness in Basu's Theorem,” Journal of the American Statistical Association, 76: 335–40.CrossRefGoogle Scholar
Mayo, D.G. and Cox, D.R. (2006), “Frequentist Statistics as a Theory of Inductive Inference,” in Rojo, J. (ed.), Optimality: The Second Erich L. Lehmann Symposium, Lecture Notes-Monograph Series, Institute of Mathematical Statistics (IMS), Vol. 49: 77–97.CrossRefGoogle Scholar
Robins, J., and Wasserman, , , L. (2000), “Conditioning, Likelihood, and Coherence: A Review of Some Foundational Concepts,” Journal of the American Statistical Association, 95: 1340–6.CrossRefGoogle Scholar
Royall, R.M. (1997), Statistical Evidence: A Likelihood Paradigm, Chapman & Hall, London.Google Scholar
Savage, L., ed. (1962a), The Foundations of Statistical Inference: A Discussion. Methuen, London.
Savage, L. (1962b), “‘Discussion on Birnbaum (1962),” Journal of the American Statistical Association, 57: 307–8.CrossRefGoogle Scholar

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Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

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Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

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