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 example of jumping to conclusions. 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:
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 lies on the overestimation of an argument based on insufficiently-large samples under an implied margin or error.
A faulty generalization often follows the following format:
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.
"Over-extension" redirects here. For the error common in language-learning, see Errors in early word use.
Hasty generalization is an informal fallacy 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 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").
Hasty generalization usually follows the pattern:
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; 3 is a prime number, 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.
The fallacy is also known as:
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—is said to be involved.