ABSTRACT
In this chapter we distinguish between the specific question whose answer we seek and other important statistical questions that are closely related to it. We find the answer to our question in the simplest possible case, where the proper interpretation of statistical evidence is transparent. And we begin to test that answer with respect to intuition, or face-validity; consistency with other aspects of reasoning in the face of uncertainty (specifically, with the way new evidence changes probabilities); and operational consequences. We also examine some of the common examples that have been cited as proof that the answer we advocate is wrong. We observe two general and profound implications of accepting the proposed answer. These suggest that a radical reconstruction of statistical methodology is needed. Finally, to define the concept of statistical evidence more precisely, we illustrate the distinction between degrees of uncertainty, measured by probabilities, and strength of evidence, which is measured by likelihood ratios.
