Also called Fallacy of Insufficient Statistics, Fallacy of Insufficient Sample, Leaping to A Conclusion, Hasty Induction.
This fallacy is committed when a person draws a conclusion about a population based on a sample that is not large enough. It has the following form:
The person committing the fallacy is misusing the following type of reasoning, which is known variously as Inductive Generalization, Generalization, and Statistical Generalization:
The fallacy is committed when not enough a's are observed to warrant the conclusion. If enough a's are observed then the reasoning is not fallacious.
Small samples will tend to be unrepresentative. As a blatant case, asking one person what she thinks about gun control would clearly not provide an adequate sized sample for determining what Canadians in general think about the issue. The general idea is that small samples are 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 possible be representative of the whole population of marbles. As the sample size of marbles increases the more likely it becomes that marbles of each color will be selected in proprtion to their numbers in the whole population. The same holds true for things others than marbles, such as people and their political views.
Since Hasty Generalization is committed when the sample (the observed instances) is too small, it is important to have samples that are large enough when making a generalization. The most reliable way to do this is to take as large a sample as is practical. There are no fixed numbers as to what counts as being large enough. If the population in question is not very diverse (a population of cloned mice, for example) then a very small sample would suffice. If the population is very diverse (people, for example) then a fairly large sample would be needed. The size of the sample also depends on the size of the population. Obviously, a very small population will not support a huge sample. 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 far 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 one woman crashed one. People also commonly commit Hasty Generalizations because of laziness or sloppiness. 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.
One final point: a Hasty Generalization, like any fallacy, might have a true conclusion (see Fallacy fallacy). However, as long as the reasoning is fallacious there is no reason to accept the conclusion based on that reasoning.
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 American squirrels are white.
Sam is riding her bike in her home town 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 that she had seen enough of 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."
Fred, the Australian, stole my wallet. Thus, all Australians are thieves.
Of course, we shouldn't judge all Australians on the basis of one example.
I asked six of my friends what they thought of the new spending restraints and they agreed it is a good idea. The new restraints are therefore generally popular.
Identify the size of the sample and the size of the population, then show that the sample size is too small. Note: a formal proof would require a mathematical calculation. This is the subject of probability theory. For now, you must rely on common sense.