Also Known As: Fallacy of Insufficient Statistics, Fallacy of Insufficient Sample, Faulty Generalization, Hasty Induction, Leaping to a Conclusion, Over-Generalization.
This fallacy is committed when a conclusion is inferred about a population based on a sample that is not large enough to adequately support that conclusion. It has the following form:
Premise 1: Sample S (which is not large enough) is taken from population P.
Conclusion: Claim C is made about Population P based on S.
It can also be presented as:
Premise 1: Sample S (which is too small) is taken from population P.
Premise 2: In Sample S X% of the observed A’s are B’s.
Conclusion: X% of all A’s are B’s in Population P.
This fallacy also occurs due to an error in making (or a misuse of) an Inductive Generalization. This argument type, which need not be fallacious, has this form:
Premise 1: X% of all observed A’s are B’s.
Conclusion: X% of all A’s are B’s.
The fallacy is committed when the sample is too small to warrant the conclusion. If the sample size is adequate and the sample is not biased (see the Biased Generalization) then the reasoning is not fallacious.
Small samples tend to be unrepresentative. As an extreme case, asking one Canadian what they think about gun control would not be an adequate sample for determining what Canadians in general think about the issue.
Small samples are also less likely to contain numbers proportional to the whole population. For example, if a bucket contains blue, red, green, and orange marbles, then a sample of three marbles cannot be representative. As the sample size of marbles increases the more likely it becomes that marbles of each color will be selected in proportion to their numbers in the whole population. The same holds true for things others than marbles, such as people who like marbles.
Since Hasty Generalization is committed when the sample (the observed instances) is too small, good reasoning requires samples of adequate size. What counts as adequate size will vary with the context, but in general larger samples will be better.
If the population is not very diverse, such as a population of cloned mice, then a small sample could suffice for a generalization. If the population is very diverse then a larger sample would be needed. The size of the sample also depends on the size of the population. For example, a class of thirty-five people could be adequately sampled by a much smaller sample than would be needed to make a strong Inductive Generalization about the entire freshman class of a university.
Finally, the required size will depend on the purpose of the sample. If Bill wants to know what Joe and Jane think about gun control, then a sample consisting of Bill and Jane would (obviously) be large enough. If Bill wants to know what most Australians think about gun control, then a sample consisting of Bill and Jane would be too small.
People often commit Hasty Generalizations because of bias or prejudice. For example, someone who is a sexist might conclude that all women are unfit to fly jet fighters because a woman crashed one. People also commit Hasty Generalizations due to sloppy reasoning or a lack of effort. It is very easy to simply leap to a conclusion and much harder to gather an adequate sample and draw a justified conclusion. Thus, avoiding this fallacy requires minimizing the influence of bias and taking care to select a sample that is large enough. A sample can be large but biased, which is one reason that Hasty Generalization and Biased Generalization are distinct fallacies.
Formal or professional Inductive Generalizations, such as those conducted in research studies or news surveys, will include a margin of error. This number, often presented as plus or minus X%, denotes the range of percentage points within which the conclusion of an Inductive Generalization falls. With a margin of error, an Inductive Generalization looks like this:
Premise 1: X% of all observed A’s are B’s.
Conclusion: X% +/- M% of all A’s are B’s.
While properly discussing statistics goes far beyond the scope of this work, it is useful to know that even properly conducted small samples of relatively large populations will have large margins of error. For example, a sample of 10 Florida voters would have a margin of error of +/- 30. If the sample showed that 60% of voters would vote for the Republican, the actual percentage of the population who would vote for the Republican could range from 30-90%. Increasing the sample size will reduce the margin of error, but this will soon run into diminishing returns. For example, a survey of 100 Florida voters would have a margin of error of +/-10 and increasing the sample to 1,000 would result in a margin of error of +/-3. The way the margin of error works illustrates why overconfident inferences based on small samples yields a Hasty Generalization.
This fallacy is often exploited in “click bait” stories that report on small samples with eye-catching results. For example, a story might report that “Most People Are Cheaters!” because 52% of people surveyed said they cheated on their partner. This story might downplay that the survey had 25 respondents (a margin of error of +/- 22). With such a small sample, the overconfidence expressed in the headline would be an example of a Hasty Generalization.
One final point is that a Hasty Generalization, like any fallacy, might have a true conclusion. However, if the reasoning is fallacious there is no reason to accept the conclusion based on that reasoning.
Defense: While a good understanding of the relevant parts of statistics provides a good defense against this fallacy, a working practical defense is to consider whether an inference is based on a large enough sample before accepting a claim based on it. You should also consider whether the sample is biased or not. It is especially important to be on guard against Hasty Generalizations about populations that your like or dislike. For example, Democrats should be especially wary about generalizations about Republicans (and vice-versa).
Smith, who is from England, decides to attend graduate school at Ohio State University. He has never been to the US before. The day after he arrives, he is walking back from an orientation session and sees two white (albino) squirrels chasing each other around a tree. In his next letter home, he tells his family that all American squirrels are white.
Sam is riding her bike in her hometown in Maine, minding her own business. A station wagon comes up behind her and the driver starts beeping his horn and then tries to force her off the road. As he goes by, the driver yells “get on the sidewalk where you belong!” Sam sees that the car has Ohio plates and concludes that all Ohio drivers are jerks.
Bill: “You know, those feminists all hate men.”
Bill: “Yeah. I was in my philosophy class the other day and that Rachel chick gave a presentation.”
Joe: “Which Rachel?”
Bill: “You know her. She’s the one that runs that feminist group over at the Women’s Center. She said that men are all sexist pigs. I asked her why she believed this, and she said that her last few boyfriends were real sexist pigs.”
Joe: “That doesn’t sound like a good reason to believe that all of us are pigs.”
Bill: “That was what I said.”
Joe: “What did she say?”
Bill: “She said she’s seen enough men to know we are all pigs. She obviously hates all men.”
Joe: “So you think all feminists are like her?”
Bill: “Sure. They all hate men.”