Decisions as statistical evidence and Birnbaum's ‘confidence concept’

Conclusion

To whatever extent the use of a behavioral, not an evidential, interpretation of decisions in the Lindley-Savage argument for Bayesian theory undermines its cogency as a criticism of typical standard practice, it also undermines the Neyman-Pearson theory as a support for typical standard practice. This leaves standard practice with far less theoretical support than Bayesian methods. It does nothing to resolve the anomalies and paradoxes of standard methods. (Similar statements apply to the common protestation that the models are not real anyway.) The appropriate interpretation of tests as evidence, if possible at all, is difficult and counterintuitive. Any attempt to support tests as more than rules of thumb is doomed to failure.