In an episode of a medical themed television show, a woman was found to have sickle cell disease. The woman appeared to be Caucasian and it was therefore assumed that she must have hidden "African" ancestry. The presence of sickle cell disease, as determined by tests, was the sole factor that was used to make assumptions about her racial makeup.
The problem with the assumption about the woman's ancestry was this: African descent is not the only possibility when a person has sicke cell disease, since there are variants of the genetic disorder in many ethnic groups and places in the world.
There are two types of information that go into the "Base Rate" (BR) fallacy.
There is Generic, or "Type 1" information, where deductions and inferences can be made, often using mathematical equations and probability statistics. The statistical occurrences of sickle cell in the human population are obviously much higher in people of African descent, making the occurrence of the disorder the base rate. In using the base rate, specific information is left out entirely.
Then, there is Specific, or "Type 2" information, where actual tests and experimentation produces verifiable and specific information. Genetic and other testing can tell if the person has the trait or the full blown disorder, but the testing could be in error, or the person could be definitely Caucasian, Asian or Hispanic, but with the disorder or one of its variants. No one knows whether the disorder came from the origins of mankind or from human migrations, intermixing and movements that occurred at any time throughout history.
In some cases, there is no specific, or type 2 information, so it is necessary, logical and acceptable to rely solely on generic or type 1 information to assess probabilities. In some cases, there are both types of information available.
The base rate fallacy is, when there is type 2, or specific information available, to ignore the available generic, or type 1 information to judge probability. Tests can be wrong. Many people go untested. There are a lot of humans who have vastly ancient African ancestry and who have a variant of Sickle Cell disease. There are hundreds of variants of Sickle Cell disease.
If a person must choose between one or the other, then the specific information is the more logical and reasonable choice. But the best option is to use both types of information, or all the available information to judge or to assess probability.
Conversely, in the case of rare disorders or disorders that have a recessive trait, for example, the tendency of medicine is to reject the idea of specific information at all! This is a case of probabilities that are constructed strictly from generic or general information, then used to prevent getting specific information.
"That would be so rare that we are not going to bother testing for the disorder." is a common justification in medicine. Thus, women and girls are not tested for rare genetic disorders when they have recessive traits that make them much more common in males.
Only the specific information would give the full answers, but getting the specific information is blocked or rejected in favor of using only the base rate to not only judge the probability of having the disorder, but to prevent anyone from incurring the costs of getting the specific information in the first place.
Thus, base rate fallacy is based on the proposition that. while specific information can be superior, general information is valuable too. Given the value of using all available information, both types should be used when possible.
A converse fallacy is to use the base rate, or general information about rarity to excuse or to prevent specific information from being obtained, based on the fallacy that it will not be worth it to obtain any specific facts.