Statistical Evidence Measured on a Properly Calibrated Scale across Nested and Non-nested Hypothesis Comparisons
1
Battelle Center for Mathematical Medicine, The Research Institute at Nationwide Children's Hospital, 575 Children's Crossroad, Columbus, OH 43215, USA
2
Departments of Pediatrics and Statistics, The Ohio State University, Columbus, OH 43215, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Carlos Alberto De Bragança Pereira and Adriano Polpo
Entropy 2015, 17(8), 5333-5352; https://doi.org/10.3390/e17085333
Received: 18 May 2015 / Revised: 14 July 2015 / Accepted: 21 July 2015 / Published: 29 July 2015
(This article belongs to the Special Issue Inductive Statistical Methods)
Abstract
Statistical modeling is often used to measure the strength of evidence for or against hypotheses about 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” vs. “coin is biased towards heads”). Here we take three important steps forward in generalizing the framework beyond this simple example, albeit still in the context of the binomial model. We: (1) extend the scope of application to other forms of hypothesis comparison; (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. View Full-TextKeywords:
statistical evidence; information dynamics; thermodynamics
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MDPI and ACS Style
Vieland, V.J.; Seok, S.-C. Statistical Evidence Measured on a Properly Calibrated Scale across Nested and Non-nested Hypothesis Comparisons. Entropy 2015, 17, 5333-5352.