Certainty and uncertainty in science: the subjectivistic concept of probability in physiology and medicine.

Most physiological scientists have restricted understanding of probability as relative frequency in a large collection (for example, of atoms). Most appropriate for the relatively circumscribed problems of the physical sciences, this understanding of probability as a physical property has conveyed the widespread impression that the "proper" statistical "method" can eliminate uncertainty by determining the "correct" frequency or frequency distribution. However, many relatively recent developments in the theory of probability and decision making deny such exalted statistical ability. Proponents of Bayes's subjectivist theory, for example, assert that probability is "degree of belief," a more tentative idea than relative frequency or physical probability, even though degree of belief assessment may utilize frequency information. In the subjectivist view, probability and statistics are means of expressing a consistent opinion (a probability) to handle uncertainty but never means to eliminate it. In the physiological sciences the contrast between the two views is critical, because problems dealt with are generally more complex than those of physics, requiring judgments and decisions. We illustrate this in testing the efficacy of penicillin by showing how the physical probability method of "hypothesis testing" may contribute to the erroneous idea that science consists of "verified truths" or "conclusive evidence" and how this impression is avoided in subjectivist probability analysis.