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-bytwo
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.