Confirming Power of Observations Metricized for Decisions among Hypotheses

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Abstract
Experimental observations are often taken in order to assist in making a choice between relevant hypotheses ~H and H. The power of observations in this decision is here metrically defined by information-theoretic concepts and Bayes' theorem. The exact (or maximum power) of a new observation to increase or decrease Pr(H) the prior probability that H is true; the power of that observation to modify the total amount of uncertainty involved in the choice between ~H and H: the power of a new observation to reduce uncertainty toward the ideal amount, zero; all these powers are systematically shown to be exact metrical functions of where the numerator is the likelihood of the new observation given H, and the denominator is the “expectedness” of the observation.

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