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05/11/2011

faulty generalization

Filed under: Logic — anlactunay @ 10:02 PM

faulty generalization
A fallacy produced by some error in the process of generalizing. See Hasty Generalization or Unrepresentative Generalization for examples.
Hasty Generalization
A hasty generalization is a fallacy of jumping to conclusions in which the conclusion is a generalization. See also Biased Statistics.
Example:
I’ve met two people in Nicaragua so far, and they were both nice to me. So, all people I will meet in Nicaragua will be nice to me.
In any hasty generalization the key error is to overestimate the strength of an argument that is based on too small a sample for the implied confidence level or error margin. In this argument about Nicaragua, using the word “all” in the conclusion implies zero error margin. With zero error margin you’d need to sample every single person in Nicaragua, not just two people.
Unrepresentative Generalization
If the plants on my plate are not representative of all plants, then the following generalization should not be trusted.
Example:
Each plant on my plate is edible.
So, all plants are edible.
The set of plants on my plate is called “the sample” in the technical vocabulary of statistics, and the set of all plants is called “the target population.” If you are going to generalize on a sample, then you want your sample to be representative of the target population, that is, to be like it in the relevant respects. This fallacy is the same as the Fallacy of Unrepresentative Sample.
Unrepresentative Sample
If the means of collecting the sample from the population are likely to produce a sample that is unrepresentative of the population, then a generalization upon the sample data is an inference committing the fallacy of unrepresentative sample. A kind of hasty generalization. When some of the statistical evidence is expected to be relevant to the results but is hidden or overlooked, the fallacy is called suppressed evidence. There are many ways to bias a sample. Knowingly selecting atypical members of the population produces a biased sample.
Example:
The two men in the matching green suits that I met at the Star Trek Convention in Las Vegas had a terrible fear of cats. I remember their saying they were from France. I’ve never met anyone else from France, so I suppose everyone there has a terrible fear of cats.
Most people’s background information is sufficient to tell them that people at this sort of convention are unlikely to be representative, that is, are likely to be atypical members of the rest of society. Having a small sample does not by itself cause the sample to be biased. Small samples are OK if there is a corresponding large margin of error or low confidence level.
Large samples can be unrepresentative, too.
Example:
We’ve polled over 400,000 Southern Baptists and asked them whether the best religion in the world is Southern Baptist. We have over 99% agreement, which proves our point about which religion is best.
Getting a larger sample size does not overcome sampling bias.
http://www.iep.utm.edu/fallacy/

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