Hasty generalization

Hasty generalizations, also known as the fallacy of insufficient statistics, the fallacy of insufficient sample, leaping to conclusions and hasty induction, is the practice of drawing a conclusion about a population based on a sample size that is too small.

Syllogism

 * 1) Sample S, too small, is taken from population P.
 * 2) Conclusion C is drawn about population P based on S.

The fallacy is a misuse of the following reasoning, known as generalization, inductive generalization and statistical generalization.


 * 1) X% of all observed A's are B's.
 * 2) Therefore X% of all A's are B's.

This is not fallacious when enough A's are observed to warrant the conclusion.

Examples

 * Jane has met atheist X. X had based his/her lack of belief in any god(s) on invalid reasoning. X is converted to Christianity. Jane concludes that all atheists disbelieve in any god(s) for the same reasons as X.

This statement is fallacious because 1 person is not an adequate sample size of any category.


 * Thomas knows 10 Asian people. Many of them are better educated and/or score higher academically. Thomas concludes that all Asian people are smart.

This statement is fallacious because 10 people are not sufficient to judge a racial category. There are likely other factors at work, including but not limited to the possibility that Thomas doesn't work hard at school, that Thomas does not enjoy learning at school, that Thomas's Asian friends work extremely hard and/or Thomas is/was disadvantaged socioeconomically compared to his Asian friends.


 * Patrick has recently seen a movie where the antagonist was extremely greedy and also happened to be Jewish. Patrick does not know any Jewish people. Based on the movie and another movie he's recently seen, Patrick concludes that all Jewish people are greedy bankers.

This statement is fallacious because he is judging a group (a small group, but substantial nonetheless) based on a stereotype. Patrick is also judging a group without any personal knowledge of anyone within the group, giving him a sample size of zero.

Non-examples
NOTE: Any statistics that follow are completely fictitious.


 * Approximately 70% of the adult population of Scotland is polled to find their views on homosexuality. They have found that Scotland supports the legalization of gay marriage 77% Yes, 17% No, and 6% Unsure.

This is not a fallacious statement because with such a large sample size and with an overwhelming majority (over 4:1), it is unlikely that the 30% who were not polled will tip the balance significantly, especially if the pollsters were careful to not limit themselves to urbanized areas.


 * Jessica has asked everyone within her small town in grade 8 what they thought about the cafeteria lunch food, excluding those who have never tried it. She found that the overwhelming majority disliked the food, 85% Dislike, 12% Don't Care and 3% Like.

This is not a fallacious statement because the only people excluded were those who had never eaten it (those unable to draw a conclusion) and she was only drawing a conclusion about the 8th graders within her town.