Mathematics and Examples for Avoiding Common Probability Fallacies in Medical Disciplines
This chapter presents and explores many ‘fallacies’ about probability encountered in medical fields. These include the Arithmetic Fallacies, the Inverse Fallacy, the Favorable-Event Fallacy, the Conditional-Marginal Fallacy, Simpson’s Paradox, the Conjunction Fallacy, the Appeal-to-Probability Fallacy, the Base-Rate Neglect, and the Representative-Sampling Fallacy. We allude to simple mathematical and visual representations as well as to demonstrative calculations to understand these fallacies, their detrimental effects, and their possible remedies. We pay a special attention to the computation of the posterior probability of disease given a positive test. Besides exposing fallacies that jeopardize such a computation, we offer an approximate method to achieve this computation under justified typical assumptions, and we present an exact method for it via the normalized two-by-two contingency matrix. Our tutorial exposition herein should hopefully be of significant help to our intended audience in the medical community, including medical students and medical practitioners alike. It might ensure that they acquire the necessary knowledge of elementary probability, but it does not demand that they gain too much knowledge that might distract them from their genuine (vital and critical) subject matter. It also attempts to remedy the notorious and grave ramifications of probabilistic fallacies residing as permanent misconceptions in their “private” knowledge databases. As an offshoot, the pedagogical nature of the chapter could also be of benefit to probability educators who deliberately want to engage their students in the learning process, i.e., to guide them to be active learners. There are many reasons why ‘active learning’ is beneficial. However, we believe that the single most important reason why it is so is the fact that it is the most effective method for unraveling misconceptions and eradicating fallacies.
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