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Evidence and Experimental Design in Sequential Trials

Published online by Cambridge University Press:  01 January 2022

Abstract

To what extent does the design of statistical experiments, in particular sequential trials, affect their interpretation? Should postexperimental decisions depend on the observed data alone, or should they account for the used stopping rule? Bayesians and frequentists are apparently deadlocked in their controversy over these questions. To resolve the deadlock, I suggest a three-part strategy that combines conceptual, methodological, and decision-theoretic arguments. This approach maintains the pre-experimental relevance of experimental design and stopping rules but vindicates their evidential, postexperimental irrelevance.

Type
Research Article
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

I would like to thank José Bernardo, Bruce Glymour, Valeriano Iranzo, Kevin Korb, Deborah Mayo, Jonah Schupbach, Gerhard Schurz, Aris Spanos, Kent Staley, Roger Stanev, Carl Wagner, the referees of Philosophy of Science, and especially Teddy Seidenfeld for their helpful and stimulating feedback.

References

Armitage, Peter (1975), Sequential Medical Trials. Oxford: Blackwell.Google Scholar
Berger, James O., and Berry, Donald A. (1988), “The Relevance of Stopping Rules in Statistical Inference” (with discussion), Gupta, in S. and Berger, J. O. (eds.), Statistical Decision Theory and Related Topics IV. New York: Springer, 2972.CrossRefGoogle Scholar
Berger, James O., and Wolpert, Robert L. (1984), The Likelihood Principle. Hayward, CA: Institute of Mathematical Statistics.Google Scholar
Berry, Donald A. (1987), “Statistical Inference, Designing Clinical Trials, and Pharmaceutical Company Decisions”, Statistical Inference, Designing Clinical Trials, and Pharmaceutical Company Decisions 36:181189.Google Scholar
Birnbaum, Allan (1962), “On the Foundations of Statistical Inference”, On the Foundations of Statistical Inference 57:269306.Google Scholar
Cox, David R. (1958), “Some Problems Connected with Statistical Inference”, Some Problems Connected with Statistical Inference 29:357372.Google Scholar
Edwards, Ward, Lindman, Harold, and Savage, Leonard J. (1963), “Bayesian Statistical Inference for Psychological Research”, Bayesian Statistical Inference for Psychological Research 70:450499.Google Scholar
Goodman, Steven N. (1999), “Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy”, Toward Evidence-Based Medical Statistics. 1: The P Value Fallacy 130:9951004.Google Scholar
Howson, Colin, and Urbach, Peter (2006), Scientific Reasoning: The Bayesian Approach. 3rd ed. La Salle, IL: Open Court.Google Scholar
Kadane, Joseph B., Schervish, Mark J., and Seidenfeld, Teddy (1996), “When Several Bayesians Agree That There Will Be No Reasoning to a Foregone Conclusion”, in Darden, Lindley (ed.), PSA 1996: Proceedings of the 1996 Biennial Meeting of the Philosophy of Science Association, Vol. 1. East Lansing, MI: Philosophy of Science Association, S281S289.Google Scholar
Lele, Subhash (2004), “Evidence Functions and the Optimality of the Law of Likelihood” (with discussion), in Taper, Mark and Lele, Subhash (eds.), The Nature of Scientific Evidence. Chicago: University of Chicago Press, 191216.CrossRefGoogle Scholar
Mayo, Deborah G. (1996), Error and the Growth of Experimental Knowledge. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Mayo, Deborah G., and Kruse, Michael (2001), “Principles of Inference and Their Consequences”, in Cornfield, D. and Williamson, J. (eds.), Foundations of Bayesianism. Dordrecht: Kluwer, 381403.CrossRefGoogle Scholar
Mayo, Deborah G., and Spanos, Aris (2006), “Severe Testing as a Basic Concept in a Neyman-Person Philosophy of Induction”, Severe Testing as a Basic Concept in a Neyman-Person Philosophy of Induction 57:323357.Google Scholar
Royall, Richard (1997), Statistical Evidence: A Likelihood Paradigm. London: Chapman & Hall.Google Scholar
Savage, Leonard J. (1962), The Foundations of Statistical Inference: A Discussion. London: Methuen.Google Scholar
Schervish, Mark (1995), Theory of Statistics. New York: Springer.CrossRefGoogle Scholar
Schervish, Mark J., Kadane, Joseph B., and Seidenfeld, Teddy (2003), “Measures of Incoherence: How Not to Gamble If You Must”, in Bernardo, J. et al. (eds.), Bayesian Statistics 7: Proceedings of the 7th Valencia Conference on Bayesian Statistics. Oxford: Oxford University Press, 385402.Google Scholar
Schervish, Mark J., Seidenfeld, Teddy, and Kadane, Joseph B. (2002), “A Rate of Incoherence Applied to Fixed-Level Testing”, A Rate of Incoherence Applied to Fixed-Level Testing 69 (Proceedings): S248S264.Google Scholar
Wald, Abraham (1947), Sequential Analysis. New York: Wiley.Google Scholar
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