We ignore the background probability and get swept up in the particular case.
If a medical test is 90% accurate and comes back positive, how likely is it that you actually have the disease? Most people answer "90%", and the real answer is almost always much lower. Base rate neglect is ignoring how common something is in the general population and focusing only on the specific information of the case in front of us.
In a study on medical diagnosis, physicians were presented with a scenario of a disease that affects 1 in every 1,000 people, with a test that gives 5% false positives. When asked what the real probability is that a patient with a positive result actually has the disease, most physicians answered figures close to 95%. The correct answer, applying the real base rate, is around 2%. Almost no physician in the study calculated it correctly.
The concrete, vivid information right in front of us (the positive test result) weighs more heavily on our judgment than an abstract statistic about the general population, even though that statistic is what actually determines the correct probability.
Source: Gigerenzer, G. & Hoffrage, U. (1995). How to Improve Bayesian Reasoning Without Instruction: Frequency Formats. Psychological Review, 102(4), 684-704.
Presenting risks as natural frequencies ("2 out of 100", not "2%") rather than only as conditional probabilities tends to substantially improve correct interpretation, in both health and credit risk contexts.
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