Greg Gandenberger

I present a new proof of the likelihood principle that avoids two responses to a well-known proof due to Birnbaum ([1962]). I also respond to arguments that Birnbaum’s proof is fallacious, which if correct could be adapted to this new proof. On the other hand, I urge caution in interpreting proofs of the likelihood principle as arguments against the use of frequentist statistical methods. 1 Introduction2 The New Proof3 How the New Proof Addresses Proposals to Restrict Birnbaum’s Premises4 A Response to Arguments that the Proofs Are Fallacious5 Conclusion.

Frequentist statistical methods continue to predominate in many areas of science despite prominent calls for "statistical reform." They do so in part because their main rivals, Bayesian methods, appeal to prior probability distributions that arguably lack an objective justification in typical cases. Some methodologists find a third approach called likelihoodism attractive because it avoids important objections to frequentism without appealing to prior probabilities. However, likelihoodist methods do not provide guidance for belief or action, but only assessments of data as evidence. I argue that there is no good way to use those assessments to guide beliefs or actions without appealing to prior probabilities, and that as a result likelihoodism is not a viable alternative to frequentism and Bayesianism for statistical reform efforts in science.

When a technique purports to provide information that is not available to the unaided senses, it is natural to think that the only way to validate that technique is by appealing to a theory of the processes that lead from the object of study to the raw data. In fact, scientists have a variety of strategies for validating their techniques. Those strategies can yield multiple independent arguments that support the validity of the technique. Thus, it is possible to produce a robust body of data with a single technique. I illustrate and support these claims with a historical case study. *Received September 2009; revised October 2009. †To contact the author, please write to: Department of History and Philosophy of Science, 1017 Cathedral of Learning, University of Pittsburgh, Pittsburgh, PA 15260; e‐mail: [email protected].