  Statistical analysis is used throughout biomedical research and elsewhere to
assess strength of evidence. We have previously argued that typical outcome
statistics (including p-values and maximum likelihood ratios) have poor
measure-theoretic properties: they can erroneously indicate decreasing evidence
as data supporting an hypothesis accumulate; and they are not amenable to
calibration, necessary for meaningful comparison of evidence across different
study designs, data types, and levels of analysis. We have also previously
proposed that thermodynamic theory, which allowed for the first time derivation
of an absolute measurement scale for temperature (T), could be used to derive
an absolute scale for evidence (E). Here we present a novel
thermodynamically-based framework in which measurement of E on an absolute
scale, for which "one degree" always means the same thing, becomes possible for
the first time. The new framework invites us to think about statistical
analyses in terms of the flow of (evidential) information, placing this work in
the context of a growing literature on connections among physics, information
theory, and statistics.
