Base rate

This article is about the statistical term. For the financial term, see Interest rates § Related terms.

In probability and statistics, the base rate (also known as prior probabilities) is the class of probabilities unconditional on "featural evidence" (likelihoods).

For example, if 1% of the public were medical professionals, and 99% of the public were not medical professionals, then the base rate of medical professionals is 1%. The method for integrating base rates and featural evidence is given by Bayes' rule.

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. The treatment's effectiveness is clearer when the base rate is available. Note that controls may likewise offer further information for comparison; for example, this would be the case if the control groups, who were using no treatment at all, had their own base rate success of 1/20. This would indicate that 'Treatment X' actively worsens the winter cold, despite the initial claim bringing attention to the 1,000 recoveries.

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 presented evidence in a normative manner. Mathematician Keith Devlin provides an illustration of the risks as a hypothetical type of cancer that afflicts 1% of all people. Suppose a doctor then says there is a test for said cancer that is approximately 80% reliable, and that the test provides a positive result for 100% of people who have cancer, but it also results in a 'false positive' for 20% of people - who do not have 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?" 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, especially featural evidence. 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 more significant than the category base rate of 1%.

See also

• Bayes' rule
• Prevalence