Measurement of Statistical Evidence: Picking Up Where Hacking (et al.) Left Off

Hacking’s (1965) Law of Likelihood says – paraphrasing– that data support hypothesis H1 over hypothesis H2 whenever the likelihood ratio (LR) for H1 over H2 exceeds 1. But Hacking (1972) noted a seemingly fatal flaw in the LR itself: it cannot be interpreted as the degree of “evidential significance” across applications. I agree with Hacking about the problem, but I don’t believe the condition is incurable. I argue here that the LR can be properly calibrated with respect to the underlying evidence, and I sketch the rudiments of a methodology for so doing