Abstract
Truth claims in the medical literature rely heavily on statistical significance testing. Unfortunately, most physicians misunderstand the underlying probabilistic logic of significance tests and consequently often misinterpret their results. This near-universal misunderstanding is highlighted by means of a simple quiz which we administered to 246 physicians at two major academic hospitals, on which the proportion of incorrect responses exceeded 90%. A solid understanding of the fundamental concepts of probability theory is becoming essential to the rational interpretation of medical information. This essay provides a technically sound review of these concepts that is accessible to a medical audience. We also briefly review the debate in the cognitive sciences regarding physicians' aptitude for probabilistic inference.
Highlights
Medicine is a science of uncertainty and an art of probability. - Sir William Osler [1]While probabilistic considerations have always been fundamental to medical reasoning, formal probabilistic arguments have only become ubiquitous in the medical literature in recent decades [2,3]
End of Part I Uncertainty suffuses every aspect of the practice of medicine, any adequate model of medical reasoning, normative or descriptive, must extend beyond deductive logic
In the Part II, we investigate ways in which probability theory is commonly misunderstood and abused in medical reasoning, especially in interpreting the results of medical research
Summary
Medicine is a science of uncertainty and an art of probability. - Sir William Osler [1]. To avoid any possible confusion, we emphasize that this definition requires that the null hypothesis, H0, be fully specified This means, for example, that the number of data samples n, constituting the data D, the chosen data summary statistic T (D), and more generally a mathematical formula for the probability distribution of values for the data summary statistic under the null hypothesis, Pr(T (D)|H0), be explicitly stated. Perhaps the least committed alternative hypothesis H1 is that for biased coins any heads probability different from 1/2 is likely In this case the false negative rate turns out to be FNR = Pr(D0|H1) = 72.73% Angle 3: P-values from ROC curves To take a third angle, we consider an alternative definition for the P-value [84]. Instinctual Bayesianism? How can the view that in many situations people perform Bayesian inference be reconciled with findings from the Heuristics and Biases movement (and our quiz results), showing that most people understand the elementary concepts of probability and statistics poorly at best? In large part, the answer is that fluency with statistics and probability theory at a formal level need not Abbreviations AMI: acute myocardial infarction; NHST: null hypothesis significance test; NHSTP: null hypothesis significance testing procedure
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