Common Fallacies of Probability in Medical Context: A Simple Mathematical Exposition
Rufaidah Ali Rushdi
Department of Pediatrics, Kasr Al-Ainy Faculty of Medicine, Cairo University, Cairo, 11562, Arab Republic of Egypt.
Ali Muhammad Rushdi *
Department of Electrical and Computer Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia.
*Author to whom correspondence should be addressed.
Abstract
This paper presents and explores the most frequent and most significant fallacies about probability in the medical fields. We allude to simple mathematical representations and derivations as well as to demonstrative calculations to expose these fallacies, and to suggest possible remedies for them. We pay a special attention to the evaluation of the posterior probability of disease given a positive test. Besides exposing fallacies that jeopardize such an evaluation, we offer an approximate method to achieve it under justified typical assumptions, and we present an exact method for it via the normalized two-by-two contingency matrix. Our tutorial exposition herein might hopefully be helpful for our intended audience in the medical community to avoid the detrimental effects of probabilistic fallacies. As an offshoot, the pedagogical nature of the paper might allow probability educators to utilize it in helping their students to learn by unraveling their private misconceptions about probability.
Keywords: Fallacy, misconception, paradox, conditional probability, posterior probability, medical context, normalized contingency table