  Statistical modeling is often used to measure the strength of evidence for or
against hypotheses on given data. We have previously proposed an
information-dynamic framework in support of a properly calibrated measurement
scale for statistical evidence, borrowing some mathematics from thermodynamics,
and showing how an evidential analogue of the ideal gas equation of state could
be used to measure evidence for a one-sided binomial hypothesis comparison
(coin is fair versus coin is biased towards heads). Here we take three
important steps forward in generalizing the framework beyond this simple
example. We (1) extend the scope of application to other forms of hypothesis
comparison in the binomial setting; (2) show that doing so requires only the
original ideal gas equation plus one simple extension, which has the form of
the Van der Waals equation; (3) begin to develop the principles required to
resolve a key constant, which enables us to calibrate the measurement scale
across applications, and which we find to be related to the familiar
statistical concept of degrees of freedom. This paper thus moves our
information-dynamic theory substantially closer to the goal of producing a
practical, properly calibrated measure of statistical evidence for use in
general applications.
