Faulty generalization

(Redirected from Fallacy of insufficient sample)

A faulty generalization is a conclusion about all or many instances of a phenomenon that has been reached on the basis of just one or just a few instances of that phenomenon.[1] It is an example of jumping to conclusions. For example, we may generalize about all people, or all members of a group, based on what we know about just one or just a few people. If we meet an angry person from a given country X, we may suspect that most people in country X are often angry. If we see only white swans, we may suspect that all swans are white. Faulty generalizations may lead to further incorrect conclusions. We may, for example, conclude that citizens of country X are genetically inferior, or that poverty is generally the fault of the poor.

Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions yet only weakly buttress the conclusions. A faulty generalization is thus produced. This inductive fallacy is any of several errors of inductive inference.[citation needed]

Logic

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 to a conclusion about the population.

Faulty generalization is a mode of thinking that takes knowledge from one group's or person's experiences 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 is related to the hasty generalization, but working from the other end. It is a generalization which is accurate, but tags on a qualification which eliminates enough cases (as exceptions); that what remains is much less impressive than what the original statement might have led one to assume.
• Biased sample – When the above happen because of (personal) bias of the sampling entity.
• Misleading vividness 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.[2]

Hasty generalization

Hasty generalization is an informal fallacy of faulty generalization by reaching an inductive generalization based on insufficient evidence—essentially making a rushed conclusion without considering all of the variables. In statistics, it may involve basing broad conclusions regarding the statistics of a survey from a small sample group that fails to sufficiently represent an entire population.[3] Its opposite fallacy is called slothful induction, or denying a reasonable conclusion of an inductive argument (e.g. "it was just a coincidence").

Examples

Hasty generalization usually shows the pattern

1. X is true for A.
2. X is true for B.
3. 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.

Or: A person is looking at a number line. 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. Therefore, the person says, all odd numbers are either prime or square. In reality, 15 is a counterexample.

Alternative names

The fallacy is also known as:

• 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

When referring to a generalization made from a single example it has been called the fallacy of the lonely fact[4] or the proof by example fallacy.[5]

When evidence is intentionally excluded to bias the result, it is sometimes termed the fallacy of exclusion and is a form of selection bias.[6]