What Properties Might Statistical Inferences Reasonably be Expected to Have?—Crisis and Resolution in Statistical Inference

Abstract

There is a crisis in the foundations of statistical inference. I believe that this crisis will eventually be resolved by regarding the subjective Bayesian paradigm as ideal in principle but often using standard procedures which are not subjective Bayesian for well-defined standard circumstances. As a step toward this resolution, this article looks at the question of what properties statistical inferences might reasonably be expected to have and argues that the use of p-values should be restricted to pure significance testing. The value judgments presented are supported by a range of examples.