probability Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, ...

and

statistics Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, indust ...

, the base rate (also known as prior probabilities) is the class of probabilities unconditional on "featural evidence" (

likelihood The likelihood function (often simply called the likelihood) represents the probability of random variable realizations conditional on particular values of the statistical parameters. Thus, when evaluated on a given sample, the likelihood functi ...

s). For example, if 1% of the population were medical professionals, and remaining 99% were ''not'' medical professionals, then the base rate of medical professionals will be 1%. The method for integrating base rates and featural evidence is given by

Bayes' rule In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For exa ...

. In the

sciences Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence ...

, including

medicine Medicine is the science and practice of caring for a patient, managing the diagnosis, prognosis, prevention, treatment, palliation of their injury or disease, and promoting their health. Medicine encompasses a variety of health care pr ...

, the base rate is critical for comparison. In medicine a treatment's effectiveness is clear when the base rate is available. For example if the

control group In the design of experiments, hypotheses are applied to experimental units in a treatment group. In comparative experiments, members of a control group receive a standard treatment, a placebo, or no treatment at all. There may be more than one t ...

, using no treatment at all, had their own base rate of 1/20 recoveries within 1 day (meaning 1 out of every 20 people recover in 1 day) and a treatment had a 1/100 base rate of recovery within 1 day, we see that the treatment actively decreases the recovery in the first day for the winter cold.

Base rate fallacy

A number of psychological studies have examined a phenomenon called '' base-rate neglect'' or ''

base rate fallacy The base rate fallacy, also called base rate neglect or base rate bias, is a type of fallacy in which people tend to ignore the base rate (i.e., general prevalence) in favor of the individuating information (i.e., information pertaining only to a ...

'', in which category base rates are not integrated with presented evidence in a normative manner, although not all evidence is consistent regarding how common this fallacy actually is. Mathematician

Keith Devlin Keith J. Devlin (born 16 March 1947) is a British mathematician and popular science writer. Since 1987 he has lived in the United States. He has dual British-American citizenship.

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 Cancer is a group of diseases involving abnormal cell growth with the potential to invade or spread to other parts of the body. These contrast with benign tumors, which do not spread. Possible signs and symptoms include a lump, abnormal b ...

. 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 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 The stethoscope is a medical device for auscultation, or listening to internal sounds of an animal or human body. It typically has a small disc-shaped resonator that is placed against the skin, and one or two tubes connected to two earpieces. ...

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%.

References

{{Reflist Epidemiology Psychometrics Bayesian statistics Machine learning

Base rate fallacy

See also

References