Hasty Generalization

Description:

The argument draws a conclusion from a sample that is too small, i.e. that is made up of too few cases.

Examples:

"In both of the murder mysteries I have read, the District Attorney was the culprit. All mystery writers like to make lawyers out to be villains."

"We have now had five dates together. It is clear we are well matched. Let's get married." (With apologies to Max Schulman)

Discussion:

The size of the sample needed to draw a valid conclusion
depends, in part, upon the size of the class from which the sample is drawn. The
larger the size of the population, the larger the size of the necessary sample.
However, the needed sample size does not increase at the same rate as the
population size, so the *proportion* of a very large class that must be
sampled is much smaller than the proportion of a very small class. For example,
political opinion polls can be very accurate (over a population of over 300
million citizens of the United States) with a sample size of less than a
thousand respondants. That is a tiny proportion of the population: less than
.00001%. But at the other end--very small populations--it takes a huge
proportion of the population to make up a statistically significant sample. A
small population of 10 would require a sample of 7 to be statistically
significant! That's 70% of the population.

What that means, is that there is *no* (reasonably
diverse) population so small that a sample of one or two could be considered
sufficient. Hence, any inductive argument using a sample of one (or two)
instances commits the fallacy of Hasty Generalization, regardless of the size of
the population to which the generalization is made.

Source: I first became
aware of this fallacy from W. Ward Fearnside and William B. Holther, *
Fallacy: the Counterfeit of Argument* (1959). This is surely not the
earliest source for this fallacy.

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