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A faulty generalization is an
informal fallacy Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fallac ...
wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an example of
jumping to conclusions Jumping to conclusions (officially the jumping conclusion bias, often abbreviated as JTC, and also referred to as the inference-observation confusion) is a psychological term referring to a communication obstacle where one "judge or decide something ...
. For example, one may generalize about all people or all members of a group, based on what one knows about just one or a few people: * If one meets a rude person from a given country X, one may suspect that most people in country X are rude. * If one sees only white swans, one may suspect that all swans are white. Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization is produced. The essence of this
inductive fallacy A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an exampl ...
lies on the overestimation of an argument based on insufficiently-large samples under an implied margin or error.


Logic

A faulty generalization often follows the following format: : The proportion Q of the sample has attribute A. : Therefore, the proportion Q of the population has attribute A. Such a generalization proceeds from a premise about a sample (often unrepresentative or biased), to a conclusion about the population itself. Faulty generalization is also a mode of thinking that takes the experiences of one person or one group, and incorrectly extends it to another.


Inductive fallacies

* Hasty generalization is the fallacy of examining just one or very few examples or studying a single case and generalizing that to be representative of the whole class of objects or phenomena. * The opposite, slothful induction, is the fallacy of denying the logical conclusion of an inductive argument, dismissing an effect as "just a coincidence" when it is very likely not. * The
overwhelming exception An overwhelming exception is an informal fallacy of generalization. It is a generalization that is accurate, but comes with one or more qualifications which eliminate so many cases that what remains is much less impressive than the initial statemen ...
is related to the hasty generalization but works from the other end. It is a generalization that is accurate, but tags on a qualification that eliminates enough cases (as exceptions); that what remains is much less impressive than what the original statement might have led one to assume. * Fallacy of unrepresentative samples is a fallacy where a conclusion is drawn using samples that are unrepresentative or biased. *
Misleading vividness Anecdotal evidence is evidence based only on personal observation, collected in a casual or non-systematic manner. The term is sometimes used in a legal context to describe certain kinds of testimony which are uncorroborated by objective, independ ...
is a kind of hasty generalization that appeals to the senses. * Statistical special pleading occurs when the interpretation of the relevant statistic is "massaged" by looking for ways to reclassify or requantify data from one portion of results, but not applying the same scrutiny to other categories. * This can be considered a special case of the
fallacy of composition The fallacy of composition is an informal fallacy that arises when one infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber, therefore the ve ...
, where the item under discussion is a group, and the fallacy is what can be derived from knowledge of part of the item.


Hasty generalization

Hasty generalization is an
informal fallacy Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the ''form'' of the argument, as is the case for formal fallacies, but can also be due to their ''content'' and ''context''. Fallac ...
of faulty generalization, which involves reaching an inductive generalization based on insufficient evidence—essentially making a rushed conclusion without considering all of the variables or enough evidence. In statistics, it may involve basing broad conclusions regarding a
statistical survey Survey methodology is "the study of survey methods". As a field of applied statistics concentrating on human-research surveys, survey methodology studies the sampling of individual units from a population and associated techniques of survey da ...
from a small sample group that fails to sufficiently represent an entire population. Its opposite fallacy is called slothful induction, which consists of denying a reasonable conclusion of an inductive argument (e.g. "it was just a coincidence").


Examples

Hasty generalization usually follows the pattern: #X is true for A. #X is true for B. #Therefore, X is true for C, D, E, etc. For example, if a person travels through a town for the first time and sees 10 people, all of them children, they may erroneously conclude that there are no adult residents in the town. Alternatively, a person might look at a number line, and notice that the number 1 is a
square number In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usu ...
; 3 is a
prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
, 5 is a prime number, and 7 is a prime number; 9 is a square number; 11 is a prime number, and 13 is a prime number. From these observations, the person might claim that all odd numbers are either prime or square, while in reality, 15 is an example that disproves the claim.


Alternative names

The fallacy is also known as: *Black Swan fallacy *Illicit generalization *Fallacy of insufficient sample *Generalization from the particular *Leaping to a conclusion *Blanket statement *Hasty induction *Law of small numbers *Unrepresentative sample *''
Secundum quid ''Secundum quid'' (also called ''secundum quid et simpliciter'', meaning " hat is truein a certain respect and hat is trueabsolutely") is a type of informal fallacy that occurs when the arguer fails to recognize the difference between rules of t ...
'' When referring to a generalization made from a single example, the terms "fallacy of the lonely fact", or the "fallacy of proof by example", might be used. When evidence is intentionally excluded to bias the result, the fallacy of exclusion—a form of
selection bias Selection bias is the bias introduced by the selection of individuals, groups, or data for analysis in such a way that proper randomization is not achieved, thereby failing to ensure that the sample obtained is representative of the population in ...
—is said to be involved.


See also


References

{{Authority control Inductive fallacies