(also known as: argument from small numbers, statistics of small numbers, insufficient statistics, argument by generalization, faulty generalization, hasty induction, inductive generalization, insufficient sample, lonely fact fallacy, over generality, overgeneralization, unrepresentative sample)
Description: Drawing a conclusion based on a small sample size, rather than looking at statistics that are much more in line with the typical or average situation.
Sample S is taken from population P.
Sample S is a very small part of population P.
Conclusion C is drawn from sample S and applied to population P.
My father smoked four packs of cigarettes a day since age fourteen and lived until age sixty-nine. Therefore, smoking really can’t be that bad for you.
Explanation: It is extremely unreasonable (and dangerous) to draw a universal conclusion about the health risks of smoking by the case study of one man.
Four out of five dentists recommend Happy Glossy Smiley toothpaste brand. Therefore, it must be great.
Explanation: It turns out that only five dentists were actually asked. When a random sampling of 1000 dentists was polled, only 20% actually recommended the brand. The four out of five result was not necessarily a biased sample or a dishonest survey; it just happened to be a statistical anomaly common among small samples.
Exception: When statistics of a larger population are not available, and a decision must be made or opinion formed if the small sample size is all you have to work with, then it is better than nothing. For example, if you are strolling in the desert with a friend, and he goes to pet a cute snake, gets bitten, then dies instantly, it would not be fallacious to assume the snake is poisonous.
What Now: Don’t base decisions on small sample sizes when much more reliable data exists.
Hurley, P. J. (2011). A Concise Introduction to Logic. Cengage Learning.