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Hasty generalization, also known as "fallacy of insufficient statistics", "fallacy of insufficient sample", "fallacy of the lonely fact", "leaping to a conclusion", "hasty induction" or "secundum quid", is the logical fallacy A logical fallacy is an error in logical argument which is independent of the truth of the premises. It is a flaw in the structure of an argument as opposed to an error in its premises. When there is a fallacy in an argument it is said to be invalid. The presence of a logical fallacy in an argument does not necessarily imply anything about the argument's premises or its conclusion. Both may actually be true, but the argument is still invalid because the conclusion does not follow from the premises using the inference principles of the argument. By extension, an argument can have a logical fallacy even if the argument is not a purely logical one; for instance an argument that incorrectly applies principles of probability or causality can be said to have a logical fallacy.

Examples:

"I loved the hit song, therefore I'll love the album it's on." (Fallacious because the album might have one good song and lots of filler.)
"This Web site looks OK to me on my computer; therefore, it will look OK on your computer, too." (My screen size is smaller than yours, and I'm using a computer in a public library, so I can't adjust it!)
"In my lifetime, there has been a leap year every fourth year; therefore, every fourth year, past, present, and future, is a leap year." (Not true; see the leap year A leap year (or intercalary year) is a year containing an extra day or month in order to keep the calendar year in sync with an astronomical or seasonal year. Seasons and astronomical events do not repeat at an exact number of days, so a calendar which had the same number of days in each year would over time drift with respect to the event it was supposed to track. By occasionally inserting (or intercalating) an additional day or month into the year, the drift can be corrected.
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"My dog is black. Therefore, all dogs must be black."
See also faulty generalization A faulty generalization, also known as an inductive fallacy, can be a common speech term for:

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 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.