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Equation 1 · AI for Science and Medicine: A First-Principles Introduction

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RR

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RR

Symbol R

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John Ioannidis’s widely cited 2005 analysis formalized why this happens using positive predictive value: the probability that a statistically significant finding reflects a real effect rather than chance. Writing R for the pre-study odds that a tested relationship is genuinely true (the ratio of true to false relationships among everything a field is currently testing), β\beta for the false-negative rate, and α\alpha for the false-positive threshold, the positive predictive value of a significant finding is

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