Base rate

In probability and statistics, base rate (also known as prior probabilities) is the class probabilities unconditioned on "featural evidence" (likelihoods). For example, if it were the case that 1% of the public were "medical professionals", and 99% of the public were not "medical professionals", then the base rate of medical professionals is simply 1%. The normative method for integrating base rates and featural evidence is given by Bayes' rule.

This article is about the statistical term. For interest rates, see Central bank.

In the sciences, including medicine, the base rate is critical for comparison. It may be perceived as impressive that 1,000 people recovered from their winter cold while using 'Treatment X', until the entirety of the 'Treatment X' population is evaluated to find that the base rate of success is only 1/100 (i.e. 100,000 people tried the treatment, but the other 99,000 people never recovered from their winter cold). The treatment's effectiveness is clearer when such base rate information (i.e. "1,000 people... out of how many?") is available. Note that controls may likewise offer further information for comparison; if the control groups, who were using no treatment at all, hypothetically had their own base rate success of 5/100. Controls thus indicate that 'Treatment X' makes things worse, despite the initial claim bringing attention to the 1,000 people.

The base rate fallacy
Main article: Base rate fallacy

A large number of psychological studies have examined a phenomenon called base-rate neglect or base rate fallacy, in which category base rates are not integrated with featural evidence in the normative manner. Mathematician Keith Devlin provides an illustration of the risks of this: He encourages imagining that there is a type of cancer that afflicts 1% of all people. A doctor then says there is a test for that cancer which is approximately 80% reliable. He also says that the test provides a positive result for 100% of people who have the cancer, but it also results in a 'false positive' for 20% of people - who do not have the cancer. Testing positive may therefore lead people to believe that it is 80% likely that they have cancer. Devlin explains that the odds are instead less than 5%. What is missing from these statistics is the most relevant base rate information. The doctor should be asked, "Out of the number of people who test positive (base rate group), how many have the cancer?"[1] In assessing the probability that a given individual is a member of a particular class, information other than the base rate needs to be accounted for. In particular, featural evidence should be accounted for. For example, when a person wearing a white doctor's coat and stethoscope is seen prescribing medication, there is evidence that allows for the conclusion that the probability of this particular individual being a "medical professional" is considerably greater than the category base rate of 1%.

See also

References
  1. "Edge.org". Edge.org. Retrieved 2021-03-22.
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