Reasoning: Generalization Errors
By David Roberts
(printable version here)
Many writers cite statistical data or other research when attempting to support their assertions. While this tactic is good, many of these writers fall into traps in the course of using research to substantiate their claims. Below are two common problems when attempting to infer generalizations:
Sometimes writers attempt to infer characteristics about an entire population /based upon a sample of it. At one level, this inference is necessary: it is difficult to imagine opinion polls for the President to poll nearly 300 million people every time a poll is commissioned. There are still dangers associated with such inferences, however. If the sample poorly resembles the population at large, its results are likely to be skewed.
One prominent example of skewed results can be found in an election poll in 1936 which predicted that Franklin Roosevelt would lose to Alf Landon. Roosevelt, of course, went on to win in a landslide. The poll had an unrepresentative sample: it used names from telephone directories and auto registrations, but during this time many people did not have the resources for such technology. These people, moreover, voted overwhelmingly for Roosevelt. Because the poll drew on an unrepresentative sample, its results were wildly wrong.
In order to avoid this error in papers, writers ought to be familiar with how certain numbers and statistics are derived. While it may not be feasible to remember every detail, writers will do well to be familiar with the process that produced the statistic. The key question writers must ask is, "Does this sample possess any traits likely to make it unrepresentative of the population as a whole?" Asking this question will allow writers to critique others' claims as well as their own.
Ecological Fallacy
Sometimes, people mistakenly attempt to infer characteristics about a single individual based upon characteristics of the individual’s population. This inference is known as the ecological fallacy. It shows poor reasoning because the individual may not be representative of the population.
For an example of the ecological fallacy, imagine a person saying:
“Harvard is a better school than Washington and Lee; since John goes to Harvard, he is a better student than Mary, who goes to Washington and Lee.”
This conclusion does not follow from the premises. Even if Harvard is better than Washington and Lee, John could be a complete slacker while Mary could be quite intelligent and hardworking!
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