Base rate
Encyclopedia
In probability
and statistics
, base rate generally refers to the (base) class probabilities unconditioned on featural evidence, frequently also known as prior probabilities. In plainer words, 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%.
In science
, particularly medicine
, the base rate is critical for comparison. It may at first seem impressive that 1000 people beat their winter cold while using 'Treatment X' , until we look at the entire 'Treatment X' population and find that the base rate of success is actually only 1/100 (i.e. 100 000 people tried the treatment, but the other 99 000 people never really beat their winter cold). The treatment's effectiveness is clearer when such base rate information (i.e. "1000 people... out of how many?") is available. Note that controls may likewise offer further information for comparison; maybe the control groups, who were using no treatment at all, had their own base rate success of 5/100. Controls thus indicate that 'Treatment X' actually makes things worse, despite that initial proud claim about 1000 people.
provides an illustration of the risks of committing, and the challenges of avoiding, the base rate fallacy
. He asks us to imagine 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 about 80% reliable
. He also says that the test provides a positive result for 100% of people who have the cancer, but it is also results in a 'false positive' for 20% of people - who actually do not have the cancer. Now, if we test positive, we may be tempted to think it is 80% likely that we have the cancer. Devlin explains that, in fact, our odds are less than 5%. What is missing from the jumble of statistics is the most relevant base rate information. We should ask the doctor "Out of the number of people who test positive at all (this is the base rate group that we care about), how many end up actually having the cancer?".
Naturally, in assessing the probability that a given individual is a member of a particular class, we must account for other information besides the base rate. In particular, we must account for featural evidence. For example, when we see a person wearing a white doctor's coat and stethoscope
, and prescribing medication, we have evidence which may allow us to conclude that the probability of this particular individual being a "medical professional" is considerably greater than the category base rate of 1%.
The normative method for integrating base rates (prior probabilities) and featural evidence (likelihood
s) is given by Bayes rule
. A large number of psychological studies have examined a phenomenon called base-rate neglect
in which category base rates are not integrated with featural evidence in the normative manner.
Probability
Probability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
and statistics
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, base rate generally refers to the (base) class probabilities unconditioned on featural evidence, frequently also known as prior probabilities. In plainer words, 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%.
In science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
, particularly medicine
Medicine
Medicine is the science and art of healing. It encompasses a variety of health care practices evolved to maintain and restore health by the prevention and treatment of illness....
, the base rate is critical for comparison. It may at first seem impressive that 1000 people beat their winter cold while using 'Treatment X' , until we look at the entire 'Treatment X' population and find that the base rate of success is actually only 1/100 (i.e. 100 000 people tried the treatment, but the other 99 000 people never really beat their winter cold). The treatment's effectiveness is clearer when such base rate information (i.e. "1000 people... out of how many?") is available. Note that controls may likewise offer further information for comparison; maybe the control groups, who were using no treatment at all, had their own base rate success of 5/100. Controls thus indicate that 'Treatment X' actually makes things worse, despite that initial proud claim about 1000 people.
Overview
Mathematician Keith DevlinKeith Devlin
Keith J. Devlin is a British mathematician and popular science writer. He has lived in the USA since 1987 and has dual American-British citizenship.- Biography :...
provides an illustration of the risks of committing, and the challenges of avoiding, the base rate fallacy
Base rate fallacy
The base rate fallacy, also called base rate neglect or base rate bias, is an error that occurs when the conditional probability of some hypothesis H given some evidence E is assessed without taking into account the "base rate" or "prior probability" of H and the total probability of evidence...
. He asks us to imagine 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 about 80% reliable
Reliability (statistics)
In statistics, reliability is the consistency of a set of measurements or of a measuring instrument, often used to describe a test. Reliability is inversely related to random error.-Types:There are several general classes of reliability estimates:...
. He also says that the test provides a positive result for 100% of people who have the cancer, but it is also results in a 'false positive' for 20% of people - who actually do not have the cancer. Now, if we test positive, we may be tempted to think it is 80% likely that we have the cancer. Devlin explains that, in fact, our odds are less than 5%. What is missing from the jumble of statistics is the most relevant base rate information. We should ask the doctor "Out of the number of people who test positive at all (this is the base rate group that we care about), how many end up actually having the cancer?".
Naturally, in assessing the probability that a given individual is a member of a particular class, we must account for other information besides the base rate. In particular, we must account for featural evidence. For example, when we see a person wearing a white doctor's coat and stethoscope
Stethoscope
The stethoscope is an acoustic medical device for auscultation, or listening to the internal sounds of an animal body. It is often used to listen to lung and heart sounds. It is also used to listen to intestines and blood flow in arteries and veins...
, and prescribing medication, we have evidence which may allow us to conclude that the probability of this particular individual being a "medical professional" is considerably greater than the category base rate of 1%.
The normative method for integrating base rates (prior probabilities) and featural evidence (likelihood
Likelihood
Likelihood is a measure of how likely an event is, and can be expressed in terms of, for example, probability or odds in favor.-Likelihood function:...
s) is given by Bayes rule
Bayes' theorem
In probability theory and applications, Bayes' theorem relates the conditional probabilities P and P. It is commonly used in science and engineering. The theorem is named for Thomas Bayes ....
. A large number of psychological studies have examined a phenomenon called base-rate neglect
Base rate fallacy
The base rate fallacy, also called base rate neglect or base rate bias, is an error that occurs when the conditional probability of some hypothesis H given some evidence E is assessed without taking into account the "base rate" or "prior probability" of H and the total probability of evidence...
in which category base rates are not integrated with featural evidence in the normative manner.